Extreme automatic control systems. Extremum search methods. Extreme project management: New in the management of modern projects Theory of chaos is a mathematical area dedicated to the description and study of the behavior of nonlinear dynamics
There are many books that can be called useful. But there are books - breakthroughs, books - revelations, books - bombs. They excite consciousness, awaken the exhausted routine intellect, create hope, you want to go back again and again. One of these books, in my opinion, is the book of Doug Decarlo " Extreme project management».
In 2005, I worked as a PM over a rather complicated project with high risks. In the company where I worked was the traditional culture of project management, based on document templates, calendar plans with Gantt Charts (Gantt Chart), sufficiently rigid budgets, standard reports. This culture is based on the fact that the requirements for the result, the budget and the calendar plan should be approved once and any changes to the crane are undesirable. In this paradigm, the project manager must invent the plan at the very beginning and strictly follow him as if the implementation of the plan is an end in itself. If you managed not to deviate from the plan, then you are an experienced project manager, if not, you need to learn a lot. I understood that something was wrong here, but did not find like-minded people. Most of the literature was on the side of the template management.
And here the dogma caused a powerful blow. It was very unexpected and as nice to meet a like-minded person who risked to write a whole book about the emerging new approach, where common sense and entrepreneurial logic prevailed. I really want this book for many. If the book helps move the old paradigm, much in your life and work will change. The views of the Decarlo arc fully comply with the principles of Lean.
Doug Decarlo indicates that it does not need to be closed from reality formal plans, budgets, approved procedures, which is important not to achieve an initial purpose, but searching and obtaining the desired result. It represents an extreme project as a shooting on a moving target, as a self-based rocket, which is looking for a real-time goal. Relief reality! - says Doug Decarlo. Extremely manage the project does not mean to make the project "on the knees", this is the opposite - the highest pilot. It is like F1 in car racing. Extreme project management requires special skills and abilities, flexibility, decision-making speeds, coverage latitude.
"People would like the world to be a wonderful, neat place, where everything is already definitely predictable. We all know that this is not real, but we behave as if it is, and that is why we get into trouble. In the management of projects, for example, we approximately determine how much time we will spend on solving one or another task, then we include our calculations to the program for planning the course of work and as a result we obtain a compiled plan of work using the method of the critical path to which we are already Treat as something due. This is absolute nonsense, because the program in the consciousness of senior managers creates the illusion that we have a certainty that does not exist, and these false expectations in the future create problems for all of us. "
"We live in the world of quantum projects in which change and uncertainty is the norm. What then is the project management in the light of such circumstances? "
"What I am really convinced is that this book will either cause a huge stir in the world of project management, or will be recognized as heretical. It can also be a source of paradigm shift. In any case, you will not be left as before reading this book. You will no longer be able to find a consolation in your clear work plan using the method of a critical path, such an elegant in its illusion of certainty. "
"Recently, the world of project management has changed radically and irreversible. Today's projects simply do not even have a remote similarity with yesterday's. The world itself, in which project management passed, irrevocably went into the past. "
"That's the main signs of the extreme project:
Requirements are changing overnight.
The project requires the use of new technology and new methods, which is not previously tested.
The execution date of the project (in comparison with the usual project) is reduced by twice.
The quality of life during the work on the project is rather reminiscent of non-existence.
In the midst of work on the project, the customer unexpectedly decides that it requires another end result.
The environment in which there is a project can be described as chaotic, unpredictable, and randomly changing. "
"Traditional project management is dealing with something famous. Extreme projects deal with an unknown. Traditional projects are developing slowly and stable, their planning occurs methodically. Extreme projects are chaotic, indiscriminate and unpredictable nature; The speed and innovation are crucial, and planning is carried out at the last moment. "
"Extreme projects are messy. This is reality. And the reality exists independently of the plans of the plans, and we cannot interfere with it. She has his own plans. "Relief reality!" . And we can only respond to changes. This position is so fundamentally and so important to memorize that if you participate in the work on an extreme project, I strongly recommend that you write on my forehead phrase " Relief reality!", And do it in the mirror image."
"If you give time to careful planning of each step, the project will most likely lose its relevance when you complete it. During this time, the problem itself or the possibility that you studied may change beyond recognition. And since for extreme projects, constant changes are the rule (and stability - exception), yesterday's plans will be no more fresh than the monthly pressure of a fish sandwich».
"Innovations are extremely important for extreme projects. They are the very essence of extreme projects. Here, first of all, it is required to create innovative processes and project management methods, as a result of which advanced products and services appear. You will not be able to shorten the period of work on the project if you become twice as hard as well. This is hopelessly outdated worldview. "
« Extreme project It is the process of searching for the desired result by the method of trial and error. His can be compared with a rocket looking for thermal radiation target. The extreme project is self-correcting phenomenon, and you will not have time to discuss every solution with higher management. But even if you find it, people on top of the hierarchical staircase will not always be available. Project teams need to take urgent and immediate decisions in the light of rapidly changing requirements and circumstances. The purpose of traditional projects, on the contrary, is the achievement of the result with maximum efficiency when minimizing deviations from the initial plan. Optimization and efficiency are target. Project teams go to the result, following predefined processes and rules. Often, rigid control principles are introduced so that the project does not deviate from the established values \u200b\u200bat cost, quality or execution schedule. A traditional approach in relation to an extreme project can be compared with an attempt to conduct a machine on a high-speed freeway, looking at the rear-view mirror. "
"In the case of extreme projects that are messy in nature, we will pay attention to performance, not efficiency. We are trying achieve the desired resultwhich can only remotely resemble the initial goal. The golden triangle of traditional project management is to make on time, qualitatively and within the budget - will not help in extreme conditions. Why? Yes because itself definition of deadlines, quality and budget is constantly changing during the work on the project».
« Traditional project looks like a waterfall - With its smooth downward, consistently walking Ganta diagrams and eight levels of detail. Project management on the principle of "Waterfall" is appropriate in conditions of relatively low speed of work and low uncertainty. This model is well suited for traditional engineering construction projects that have a clear goal and a proven plan for its achievement. The process of closing the nuclear power plant and the project of creating a new restaurant McDonalds can be well submitted using a "waterfall" model.
Mental model of traditional project
On the contrary, extreme projects characterized by changing demands and deadlines, unpredictability, rawness, speed and innovation, do not fit into this model. Extreme project more like a twisted doused macaronin».
Mental model of an extreme project
"To its customers, I usually offer the following definition of an extreme project: Extreme project is a complex, high-speed, self-correcting enterprise, while working on which people interact in search of the desired result in the conditions of extreme uncertainty, constant changes and severe stress ».
"Traditional projects adhere to the classic scheme" get ready, goal, fire". On the contrary, in extreme projects we first we shoot, and then change the trajectory of bullets. This is a reality in which businessmen live project managers and team teams. Bureaucracy, clear rules and mechanical approach, characteristic of traditional projects, are not applicable to extreme projects, where uncertainty, improvisation and spontaneity disappointed predictability, teams and controls. It follows from this that we must use a completely different approach when planning and managing extremal projects - acceptable and adapting to change».
"When managing extreme projects, we understand that the plan should change, corresponding to the state of the outside world. If tomorrow the world changes, then our plan will change. Changes is the norm. Uncertainty is obvious. Stability is a deviation from the norm. Traditional project management is focused on the past. Extreme project management is focused on the future ».
"The" prepare-goal-fire approach "characterizes a high-speed, rapid process. The focus is on the customer whose active participation in the project is invaluable. The customer is the main stakeholder and, together with the project manager, constantly directs the progress of the project to the target, which continuously changes and becomes more and more clear with each iteration. "
"If you do not know the future, why spend time on his planning? Extreme project management does not do this.
Traditional project management makes people serve as a process. Extreme project management causes the process to serve people.
Traditional project management is a set of practices, approaches and methods that make people the servants of the process. Charts Gantt, Protocols, Reports and other processes are designed to limit people's activities. Extreme project management is based on the situation that people are a guarantee of success: thoughts, emotions and interpersonal contacts are the basis of creativity. If the team is demoralized, the project will break from the chart, exceed the budget and worsen the result. Thus, extreme project management pays serious attention to the quality of life and gives participants to the project control over the process, and not vice versa.
Traditional project management centrally controls people, processes and tools. In extreme projects, control is distributed evenly.
Traditional management seeks to minimize changes and establish hard control over processes. The head of extreme projects is aware that it is impossible to manage something unknown and unpredictable the same methods as before. Try to force reality to match the project plan - it means vain to spend time. In a properly organized extreme project, no one is controlled. On the contrary, everything is controlled.
Traditional management challenges the whole world (objects, people, time). In extreme projects, the challenge rushes primarily to itself, its own relation to the world.
Traditional project management seeks to force people, budget and schedule to fit the plan. Extreme project management anticoins changes using a minimalist planning approach and distributing control.
Traditional project management - manages. Extreme project management - leads to ".
"Traditional control stamps - work according to plan, minimizing changes, strict control - are purely administrative functions. The leaders of traditional projects resemble the warders and are only suitable for managing stable processes. In the world of extreme projects, where planning is minimized, and the changes are constant and unpredictable, the project manager performs the role of the leader. As will be visible later, a good leader leading the extremal project will allow people to find the optimal solution and perform permanent self-correction. "
"From the point of view of modern high-speed, prone changes to projects, the traditional world of project management is a remnant of the past."
"Two squares on the left side of the picture display world of traditional project management - Disciplines, which was born in the engineering and construction industry. Here, the approach to project management is closely related to the scientific world of Newton's physics.. Newton's worldview is based on determinism and reductionism - a paradigm, according to which the world can be dismanded on a predictable set of causal relations between its individual parts. This is a logical and linear thinking of the left hemisphere in all its glory. It is analytical. This so-called mechanical approach gave rise to the view that projects can be planned with a great degree of confidence. He marked the project management on the model of the waterfall. But on the other hand, there is a right hemisphere that works nonlinearly. The principle of its work is relative and arbitrarily, and it solves the task using systemic thinking. "
« In the world of extreme projects Plan - not dogma. And, unlike the world of Newton, extreme projects are subject to the laws of new science: the world of quantum physics, self-organizing systems and chaos theory. "
"Many companies have only recently realized the importance of the right organization of the process called" Project Management ", and now in a hurry they are trying to master traditional approaches submitted by organizations such as Software Engineering Institute (SEI), PMI and others. Unfortunately, these organizations seem to be in vain spend their time. Bob Kulin, the winner of the RMR (Project Management Professional), made the following statement: "I have always believed that the representatives of the profession of the project leader have a bad service if they do not understand that many, if not most projects do not meet the fundamental principles, PMI installed in Project Management Body of Knowledge (PMBOK) standard. It's time to discover the eyes to the realities of modern business conditions and find a way to survive and succeed in these new circumstances. "
"The model of extreme projects of projects consists of sets of rules, values, skills, tools and practices based on the principle of changes and uncertainties, and the components of the software and hardware of the extreme projects of projects:
Accelerator - Principles that give freedom of motivation and innovation.
Shared values \u200b\u200b- a set of values \u200b\u200bestablishing confidence between stakeholders.
Business issue - Questions, answers that help often and quickly issue valuable results.
Critical success factors - skills and tools, as well as organizational support that play a key role in achieving success. "
« For an extreme project, there is only a general idea of \u200b\u200bthe ultimate goal., and practically nothing about its achievement methods. It's obvious that traditional, linear approach to project management just does not work. Standard tools, templates and traditional control processes have no practical benefit for the head of the extreme project. Instead, the project manager, together with the Customer, chooses one or more probable areas of work, studies what is happening and prepares for the next stage. This cycle is repeated several times, while the project manager and the customer are in search of the convergence point of the current result with a given goal, which most likely has already changed in the light of new knowledge and discoveries made during previous iterations. The extreme project management can be a gambling and inspiring challenge for the team when it comes to the championship in the market, the destruction of the main competitor, re-attracting a large client or resuming the dying production line. Extreme project management does not necessarily have to be destroying the exhaust work of the reality, of course, of course, if you refuse traditional management methods, and accept the new quantum image of thinking. "
"The adoption of the world of extreme projects requires us primarily to make changes in our worldview."
"Like any software, our brain has" default settings ", that is, the way of thinking. In the image of thinking, I mean a set of assumptions and assumptions about how the world is arranged. And this is our internal program. "
"Here is a brief list of key ideas that you should not forget:
Under quantum thinking, I mean the worldview that is a meal of change and unpredictability. Quantum thinking assumes that changes are the norm.
Newtonian or linear worldview considers the stability of a given norm.
Extreme projects should be controlled mainly from the point of view of quantum thinking.
Attempting to use a quantum approach when managing traditional projects will lead to deplorable results.
The use of newtonian thinking in relation to an extreme project fully destroyed it. "
"Unlike the Newtonian causal thinking, the management of extreme projects implies that, although the ultimate goal of the project is achievable, it is impossible to predict what methods we reach it. Hence, adaptability is more important than predictability».
"The good news is that the management of the organization sooner or later understands that the old approach does not work. Bad news is that erroneous methods are often selected to correct the situation. Usually this process begins with the withdrawal that not all employees have mastered the new software and the necessary design methodology. At this stage, Newtonian thinking concludes that if everyone had followed the established rules, then the company was finally able to achieve clear and predictable results. "We must tighten the discipline," they say. In other words, the prevailing philosophy of traditional management is concluded in the following words: " If the method does not work, let's tighten it "».
"Millions of dollars are being wrapped in training programs and certification of employees in the field of traditional project management, which only inhibit the implementation of extreme projects. As the nestability of the project is grown, the desire of Sveti all to the linear model becomes just an intrusive idea and inevitably leads to what I call "linear madness".
"Reality is that that the extremal project is a winding line. It looks like a twisted doused macaronin, which I mentioned earlier. But many project managers who have passed the school of classical management are adhered to even unique, completely different views on how the project should be implemented. They want the project to look like this:
This heavy, linear image of the thinking of the left hemisphere is a fundamental cause of occurrence. newtonian neurosis: the desire to build an extreme project along a straight line. Tim Lister, the Senior Consultant of the Cutter Consortium, calls managers who think in a similar way, "direct line adherents". These world-leaders are ruthlessly trying to subjugate each varying element of the project by excessive use of project instruments, rules, templates, policies and procedures. "
"They are also readily recognize their own mistakes. If you managed to overhear the thoughts of the desperate project manager, his conversation with himself would look like this. " The world does not match my plans. I must be, I'm not so good leader, as it seemed to me. I must pass additional project management training. I will try and promise to use more typical templates and tools "».
"The world does not correspond to my plans. Let's think about it. And why should the world match the plans of your project? What could be more ridiculous? Newtonian neurosis leads to fruitless attempts to change the world according to your plansthat in itself is a fiction. Who can come to mind to change reality in accordance with the fiction? People suffering from Newtonian neurosis. "
"Do not misunderstand me. I believe that certification in the field of project management provides a valuable service when a device for work and, undoubtedly, adds weight to your resume. So you can proudly demonstrate your certificate of RMR others. If you want - Take a tattoo. But do not think that those tools and concepts you have mastered during training have universal use. In extreme projects, most of them are practically useless. "
"Newtonian neurosis in no way is a specific disease of the leaders of extreme projects. This cunning disease is widespread among the sponsors of the project, customers and senior management, which insists on the use of a linear Newtonian approach in order to stabilize the unpredictably changing world.
I met quite a few project managers who believe that the quantum thinking is adhered to, although they act in accordance with the Newtonian model. Their behavior does not correspond to their views, although their intentions are completely noble. This phenomenon, known as "unconscious Newtonianism," underlies Newtonian neurosis. "
« Extreme projects are similar to jazz. An inexperienced jazz listener may seem random and chaotic, but it is not. In jazz, there is a structure, and jazz musicians have a huge opportunity for improvisation. Jazz does not have clear installations. They also do not exist in the management of extreme projects. "
"Traditional projects are more reminded by classical music. They are cooled. You must stick to the score, otherwise the conductor will turn to you with his wand. Nevertheless, in some organizations the light is already beginning. There they understand that the most difficult projects tend to decline when using rigid methods, excessive amounts of proven templates, practices and policies. "
"I am not trying to say that there is no place for tough classical or Newtonian principles in an extreme project. Some components of the extremal project require unconditional stiffness, for example, when testing software or conduct a scientific experiment. It is necessary to use both Newtonian and quantum methods. But for the successful implementation of an extreme project in all aspects of the enterprise, a quantum image of thinking should prevail. "
« Newtonian thinking is based on fear of changes, fear to allow an error. Its main task is the desire to not give badly. He is trying to change the reality in accordance with whose ideas about what should be. It trying to win by the power methods. An attempt to apply a traditional approach in unpredictability conditions can be dangerous for both the project itself and for your health and well-being. "
"Manage extreme projects means see the world as it is in his current state, and do not fight him at every step. In the end, when something happens, it is already becoming a reality. Attempting to change reality is equivalent to an attempt to change the story. It's useless. Instead, we forgive past mistakes, we look into the face of reality and change our plan in accordance with it, and nothing else. There is no "Cancel Reality" button on your computer. In conditions of compressed terms, permanent changes, strong uncertainty and high complexity, the use of a traditional approach is equivalent to incapacity. "
"Extreme project management is a new type of thinking and management, which corresponds to the nature of the projects implemented in the conditions of" high turbulence ", rapid changes and constant uncertainty. It is preserving control and achievement of results in a rapidly changing environment. "
"Choosing a stable type of thinking, you choose a system of worldview, which is" synchronized "with chaos and unpredictability, and make a basic bet on people and relationships between them, and not on tools and processes.
The head of the extreme project should direct thoughts of thoughts, emotions and relations to achieve valuable results. "
« I propose to consider the project as a lively variable organism:
Thoughts Find your expression in the form of ideas, solutions, new facts, data and achievements. When thoughts and emotions converge at the convergence point, they find their expression in meetings using simple charts, in conversations for a cup of coffee, in the preparation of simple, informal schemes. They break into life in the form of physical prototypes, drawings, memos, presentations made in the PowerPoint program, design plans, project documentation and final design solutions.
Emotions Constantly find their expression in physical and bodily forms: when people frown or smile when they send an angry email email, or celebrate the victory associated with the advent of the first successful results of experimental work. On the contrary, traditional management is mainly relying on mechanistic (read Newtonian) approach and refuses to pay attention to the human factor. Its intellectual foundation consists of practices, procedures and policies making people servants of the process. Is it possible to afford to determine the project? No, not in the quantum world.
Relationship They are a complex web of communication arising from the emergence of new information, including thoughts and emotions, which are exchanged among themselves project participants. When you look at the project results, you see the sum of thoughts, emotions and relationships that have found an embodiment in physical form. "
"Thus, the project is a process, as a result of which thoughts and emotions take a certain form. You can look at the desired result of the project as a kind of creature at the stage of its formation. And with an increase in the volume of thoughts and emotions, which are exchanged among themselves the project participants, the final result acquires increasingly distinct outlines. "
"One of the most important tasks of extreme project management is the compression of the time periodnecessary to ensure that thoughts, emotions and relationships make their embodiment in physical form. "
"Project management, extreme or traditional, is not just a process of developing and implementing a new product or an increase in the productivity of the service that the customer has sought. It is also not to create all sorts of artifacts (chart of Ganta, magazines, reporting and other countless documentation). This is something much more: project management is the science and art of sending thoughts, emotions and relationships to achieve significant results. "
"If projects are people (their thoughts, emotions and relationships), then management is becoming the main task of the head of the extreme project. People are a key factor in the success of an extreme project. "
"Anyone who participates in the project or is experiencing its influence (before or after completion) is its member. The project participants provide it with vital products and services, including guidelines, the performance of other projects, information, reviews, labor, cooperation, decisions, approval and advice. Projects depending on your project are also its participants. "
"In addition, you will have to deal with the internal factors of the organization. They include systems, policies and procedures (of course, based on Newtonian thinking), with whom you have to live until you find a keeper angel who will help you avoid these annoying interference. Organizational culture - a way to perform work in a particular organization - can also have a significant impact on you. If you find yourself in an administrative and command organization, you can hardly count on collective decision-making, which is a key success factor for an extreme project. "
« Make friends with change . Changes have a negative impact on the project. They violate the order of things. Usually, changes are wary, and for this reason, traditional management gives such great importance to changes in change. Extreme project management requires a different attitude to change - this in which changes are perceived as a new opportunity , And the adoption of changes increases the chances of achieving the desired result (which can differ significantly from the planned). "
« Play on people's passions . I do not think that in the morning many people leads to the delight of the idea that they need to return to work on the project. In fact, the word project contains a certain oppressive subtext. People will work with great enthusiasm if they know that they fulfill a certain mission; If they consider the project not as a "project", but as the cause of their actions. You must show people that their work is part of something more, giving them a clear idea of \u200b\u200bthe objectives and means. "
« Do not complicate the process . For an extreme project, an old good principle "The smaller the better" is not an empty sound. This is very serious. In practice, the smaller becomes greater: fewer processes, less management, less policies and standard procedures. "
"The main task of the extreme project manager is the achievement and preservation of the commitment of the project mission. You can safely talk about the establishment of commitment when the team members have a strong motivation and most of the community of the project participants provide you with support. "
"When a commitment is weakened or disappears, the energy field of the project comes into decline and the project falls into a gloomy mood. Immediately the risk of non-compliance with the time frame, loss of quality, the breakdown of financial expectations and the full failure of the project ".
"Self-discipline is the first critical success factor in extreme project management. In the case of an extreme project, this means the ability to self-government in hostile terms. It is impossible to stabilize the world around us, you can only stabilize your condition. This is your only opportunity. And when you stabilize yourself, the world around you, as if by magic, it turns out more stable. If you do not adhere to self-discipline when working in hostile conditions, you doomize yourself to suffering. "
"Commitment is a positive energy, an elevated feeling that permeates the project and moves it towards success. Indifference or ridicule is a negative energy that trading the development of the project. "
"Nine reasons for the failure of the head of the extreme project.
The leaders of extreme projects fail when they look at their eyes inside the project and focus on the technical details and development of the product (content), forgetting about the environment surrounding the project: the general economic situation, the expectations of participants and the emotional state of the project. In this regard, unresolved conflicts arise, as a result of which the loss of commitment and the inability to create an acceptable end product or service occurs. The factors below for error project managers are primarily associated with the project environment. They are found in all projects, but acquire special importance in extreme conditions:
1. The absence of benefactor is the inability to find a suitable sponsor, which would have champion their qualities and ability to crush obstacles.
2. Weak communication skills (communication, negotiation, conflict resolution, support and influence).
3. Cancer Cancer Syndrome: The project manager is sitting in front of the computer screen, instead of sitting in front of the key participants.
4. Syndrome of a good soldier: excessive softness; worship before manual and passing their positions; Simple execution of orders.
5. Loss of business orientation: improper application of four business issues (which will be disclosed in the next chapter):
Invasion to someone else's territory: an attempt to answer the first business issue (" Who needs it and why?"). This question should answer the sponsor of the project.
Escape from the battlefield: fear take responsibility for the answer to the second issue of the business (" What should I do for this?"), Allowing the project sponsor to manage the budget. This is the prerogative of the project manager.
Excessive timidity: the inability to get what the project will lead to success (the third business issue - " Can we handle it?"). We must be able to negotiate.
Maliciousness: the project manager continues to perform work, having a negative response to the fourth business issue (" It's worth it?"). This is the same thing that it is known to initiate a project or continue its implementation, knowing that he has no chance for success. At the same time, accusing the project manager in errors, forget about the real reason for the failure: the economic substantiation of the project turned out to be non-visual.
6. Incorrect methodology: the use of anti-productive project implementation methodology.
7. Totalitarianism (or template management): The project manager believes that it will be able to manage the dynamics of an extreme project, forcing people to fill out reporting forms, instead of focusing on the disclosure of motivation, creating innovation and establish confidence relations, which requires the application of a control style based on values \u200b\u200band principles.
8. Naive waters: the inability to understand that the project does not solve the problem.
9. Not in its plate: No understanding that extreme project management (A, perhaps any project management) is a job on which you can best use your congenital talents and motivated abilities. "
"The key to conducting effective group meetings lies in your ability to manage the energy of the participants, not the time. "Let's forget about feelings and emotions," said one project manager at the height of the meeting. It was an incorrect offer. As a professional mediator with thirty years of experience, I can say that my most important skill is in the ability to openly handle the feelings of participants. Model " Feelings -\u003e Facts -\u003e Solutions"Plays an important role throughout the meeting. If the group participants are in a bad mood, you should not count on progress while you do not consult their feelings. "
"People are often mistaken, believing that the difference between the management of traditional and extreme projects is the presence or absence of planning. Such a representation is far from the truth. The management of both types of projects includes planning, and in both cases its goal is to maintain control over the project. "
"Another fundamental distinction between traditional and extreme project management is that traditional project management begins with the project development stage and ends at the implementation stage, and the extreme project management covers the project much more - from the idea to getting the economic effect».
"Extreme projects are developing in" flexible organizations ", i.e. In organizations with an adapted to change, a culture friendly, which recognizes and satisfies the special needs of various projects - from extreme to traditional.
"Projects are similar to colors. If the soil is poisoned, one or two flower will survive, but the rest will die sooner or later. "
"Bureaucracy, clear rules and mechanistic Newtonian approach, characteristic of traditional projects, are not applicable to extreme projects, where uncertainty, improvisation and spontaneity disappoint predictability and control. Extreme projects require a new worldview and a new management model, which will allow project managers and businessmen to maintain control over the situation in volatile conditions. The management model must be focused on profitability, and do not lose sight of the quality of life. "
"The leaders, the worldview of which aims to strengthen the mechanics of the project, permiss a serious mistake. They seek to develop a hard plan and strictly perform it. But in the world of extreme projects that are subject to influence from competitors, government orders, a change in consumer preferences and new technologies, yesterday's plans will be no more relevant than the newspaper, released a month ago.
"The reasons for the success of extreme projects are, first of all, competent management of the dynamics, not mechanics of the project."
"The situation is exacerbated even more after sending employees, sometimes in very large quantities, training courses and certification in the field of project management, where traditional project management techniques are taught, which lead only to a decrease in the productivity of volatile and complex extreme projects. As a result, there is a waste of time and money. "
"The combination of newtonian thinking, totalitarianism and design bureaucracy leads to the fact that the project is concluded in the strait shirt. Such practice suppresses motivation and innovation, which is the vital force of an extreme project. Instead of the desired productivity growth, the organization faces incapacity, as people start working on the system, and not vice versa. "
"In the world of traditional project management, success is determined by the obsolete principles of compliance with the schedule of work, budget framework and all the requirements established at the planning stage. In the world of extreme projects, these indicators of success do not make sense. What is the only sense of compliance with all criteria if the project becomes unprofitable after its implementation? Of course, the leaders of extreme projects are worried about graphics, budget, purposes and quality, but they also understand that these factors do not determine the success of the project. "
"Quantum leader sees its project as follows:
The main secret of preserving control over the extremal project is to do not try to stretch it along a straight line. This desire is erroneous in essence. Instead, it is necessary to establish the project implementation boundaries and create many checkpoints. The boundaries make it possible to improvise in the specified limits. "
"The Newtonian leader wants to see his project as follows:
This type of thinking takes us away from reality, because it contradicts her. Newtonian thinking calls us to adhere to the established plan at any cost and contributes to the creation of practices and systems that confront changes or seek them to minimize them. Newtonian leader trying to change the reality in accordance with the plan and manages people on the principle of submission. But the reality rules. For a Newtonian personality, effectiveness is more important than the result (read, profits). He asks himself: "Does the project be coming out for temporary and budgetary frames?".
"Traditional indicators are not enough, since they are tied to schedule, budget, requirements and quality, and not to the compliance of the results of the project's values \u200b\u200bof the business. If the project is performed on time and does not go beyond the budget, but it does not bring profit and does not meet the basic requirements, its practical value is close to zero. "
"Extreme projects do not live in complete isolation. They are associated with other projects and global business issues. "
"This is a book on how to change the surrounding world ... disguised as a book about the extreme project management. And this is the main concept of project management: a change in the surrounding world with each new project. When it comes to changes, whatever position you occupied - the project manager, sponsor, or the executive director of the organization, the extreme project management equalizes the situation. When reality changes, she is not doing to your post, place of residence or amount of money in the bank account. The changes arrange other priorities. "
"The world in which we live has long been considered extreme. No one can change reality. It remains to hope that the most important thing we can do in an extreme world for themselves and the people around change of our type of thinking and adoption of a new worldview, new quantum reality».
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The need for adaptive (adaptable) control systems arises due to the complication of management tasks in the absence of a practical possibility of a detailed study and description of the processes occurring in control objects in the presence of changing external perturbations. The adaptation effect is achieved due to the fact that some of the functions for obtaining, processing and analyzing processes in the control object is performed during the operation of the system. Such a separation of functions contributes to a more complete use of information about the flowing processes in the formation of control signals and allows you to significantly reduce the impact of uncertainty on the quality of management. Thus, adaptive management is necessary in cases where the effect of uncertainty or "incompleteness" of a priori information about the operation of the system becomes essential to ensure the specified quality of management processes. Currently, there is the following classification of adaptive systems: self-adjusting systems, systems with adaptation in special phase states and study systems.
The class of self-adjustable (extreme) automatic control systems has widespread in mind a fairly simple technical implementation. This class of systems is associated with the fact that a number of control objects or technological processes have extreme dependencies (minimum or maximum) of the operating parameter from the control influences. These include powerful DC electric motors, technological processes in the chemical industry, various types of furnaces, jet engines of aircraft, etc. Consider the processes flowing in the furnace when burning fuel. With insufficient air supply, the fuel in the furnace burns not completely and the amount of heat released decreases. With overpressing air, part of the heat is carried away along with air. And only with a certain ratio between the amount of air and heat, the maximum temperature in the furnace is achieved. In the turbojet engine of the aircraft, the change in fuel consumption can be obtained to obtain the maximum air pressure behind the compressor, and consequently, the maximum motor thrust. With a small and large fuel expenditures, air pressure behind the compressor and thrust drops. In addition, it should be noted, the fact that the extreme points of control objects are "floating" in time and in space.
In general, we can argue that there is an extremum, and under what values \u200b\u200bof the control exposure it is achieved - a priori is unknown. Under these conditions, the automatic control system during operation should form a control effect, which leads an object into an extreme position, and hold it in this state in conditions of perturbations and the "floating" nature of extreme points. The control device is an extreme regulator.
By a method for obtaining information about the object of the object of the object, extreme systems are messed and search. In universal systems, the best control is determined by the use of analytical dependencies between the desired value of the operating parameter and the parameters of the regulator. In search engines that are slow, finding extremum can be performed in various ways. The greatest distribution was obtained by the method of synchronous detection, which reduces to the estimate of the DY / DU derivative, where Y is an adjustable (working) parameter of the control object, U is the control effect. The structural diagram illustrating the method of synchronous detection is shown in Fig. 6.1.
Fig. 6.1 Synchronous Detection Structure
At the input of the control object, which has an extreme dependence Y (U), together with the control exposure U, a slight perturbation in the form of a regular periodic signal F (T) \u003d GSINWT, where G is larger than zero and enough. At the output of the control object, we obtain Y \u003d Y (U + GsinWT). The resulting value of y is multiplied by the signal F (T). As a result, the signal will take a value
A \u003d yf (t) \u003d y (u + gsinwt) GSINWT.
Assuming that the dependence Y (U) is a fairly smooth function, it can be decomposed into a power row and with a sufficient degree of accuracy will be limited to the first member of the decomposition
Y (u + gsinwt) \u003d y (u) + gsinwt (DY / DU) + 0.5G 2 SIN 2 WT (D 2 Y / DU 2) + ... ..
T. K. The value of G is little, then you can neglect the members of the highest order and as a result we get
Y (u + gsinwt) »Y (U) + GSINWT (DY / DU).
Then, as a result of multiplication, the signal will take a value
A \u003d Y (U) SINWT + G 2 SIN 2 WT (DY / DU).
At the output of the low frequency filter f, we get a signal in
.
If the filter time constant T. great enough, then get
.
Consequently, the signal in the outlet of the filter is proportional to DY / DU derivative
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The main most common types of extremal systems in which the static mode of operation of the object is optimized, are extreme systems that ensure the operation of the object in the extreme point of its static characteristics.
The static characteristic should reflect the connection between the object's quality function function and the object parameters of the object.
Extreme SAU It is advisable to apply:
1. There is a quality indicator (technical and economic, characterizing the work of the object, and this dependence has a pronounced extremum) (most often)
2. Benefits from the increase in quality functional.
3. There is a possibility of the current definition of quality functional.
The control device in this case is called an optimizer or an extreme regulator.
Quality functionality To set the operation mode is written:, where - change., Determining the operation mode of the object.
Depending on whether the extremal static characteristic is stable or changes in the process of operating the object, extreme systems are divided into two groups: - static; - Dynamic.
Static: It provides extreme control, corresponding to the extremum of the static characteristics of the object with unchanged parameters installed for this point of extremum, and the system is similar to the usual system stabilization system.
Dynamic: Here, the characteristic can shift independently and the point of extremum too. At the same time, two cases may be:
It is known as the characteristic shifts, and you can do with the software control;
The displacement of the most extreme characteristic and the point of extremum is random character (you need to find the optimal point, then move to it).
In extreme systems, when the extreme characteristic is shifted, there may be an automatic search for extremum and a shift to it.
In such cases, two operations are carried out:
1. Trial search (determining the relationship between the current Q and Q EXTR quality indicator and the determination of the direction of movement. It comes down to the definition of the steepness characteristics :).
2. Working (Extensions the found values \u200b\u200bof the regulator setting change to ensure the extremum function)
You can determine the value and sign of the derivative or use a special step step method of searching for extremum.
Depending on whether an additional signal is used to search for extremum, systems are divided:
· Systems without an additional search signal (depending on whether the operating operations are used when the values \u200b\u200bof the steepness S 0 or the sign of the derivative system are divided into proportional(Determined by the dx crack / dt \u003d H 0 S, i.e. absolutely. The dependent search and the speed moves the slave. The organ depends on the steepness. Depending "setpoint" of the regulator) and relay(Direct. The movement is determined by the sign DX slave / dt \u003d h 0 signs \u003d h 0 sign, i.e. ration. "Independent search" and ro move from one comp. and back, leading an object to extremum static. Har -You. Here is a log. The device switches when the derivative sign changes - this leads to a change in the regulator setting and acc. Note. Reg. Organ. Used for minority. Objects.). System is used for inertial systems. stepping type (Here on the command generator command through the DT step of the DT. Sign. Quality indicator. And comparing. Its with a given Q, as a result, there is no reverse signal at the entrance)
· System with extra. Search. Signal (Harmonic signal and a signal from a logical device are fed to the input. The extremum search is carried out on the basis of the study of the phase shift of the signal x N on the extent. System search signal. To the main - modulating signal.
On the land SIGN. X is superimposed by harmonic. Search signal and if Nach Sign. X acc. The position on the left of the extremum point (x 1), then on the outline. Exp. Room Additional search signal will create harmonic. The component Q * with the same F that the search signal and the phase shift will not be. OSN. Signal x 3 - harmonic. Cost on the exhibition. The link is shifted. Search. Signs at the angle -pi. OSN. Signal x 2 - harmonic. Cost on the exhibition. The link will have f in 2 times more than F is source. Signal. So by phase shift M.O. Def. Directed. Movement.
Multidimensional extreme syst. are built for multi-packet objects that have several inputs and outputs, and one of the outputs has an extremal characteristic, and on dr. Outputs M / m imposed restrictions.
To construct such extremal systems. Use specials. Matthods Mat. Programming and algorithmich. optimization methods.
The condition of the extreme function of many variables is the equality zero of all of it. derivatives by parameters
In a particular case, if the generalized Q quality feature is presented. extremal. Static. Har-Koy, then for the design of multidimensional. Syst. M / B used the simplex planning method and in this case to the syst. explosive Device for calculated. Grad. Extreme. Har-ki and device for formim. Control signal.
The principle of constructing a device for evaluation. Grad. In the exercise of the search for extremum depends on the method determined. private derivatives and types of an applied algorithm.
Methods are most widely used:
1. Of course increments
2. time derivative
3. Simultaneous detection
4. Application of an adaptive model
1. The finite increment method is based on the replacement of private detectional derivatives. increments and definition of it. At the same time, cord changes alternately. Management and calculated. . The increments of them. Yawl. components of the gradient function.
2. Also alternately change the control effects and are calculated privately. Derivatives and gradient function.
Disadvantages 1 and 2: the need for alternate changes to the UPR. The impacts and calculation of the gradient for each change of UPR. Signal. This requires additional. time calculation.
3. Management coordinates are modulated add. Harmonic. Signals with different. A amplitudes and Ni and frequencies W Ni. Number of detectors of ODA. Number of independent. The coordinates of the extremum defining the Q XI function. Output Sync. detector. Proportional to private. derivative. . Because Modulating signals are separated by frequency. Spectra, then composed. gradient determin parallel. Using computer this time will be min.
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1. Extreme control systems
Extreme Su is such sau, in which one of the performance performance indicators must be held at the maximum level (min or max).
A classic example of extremal Su is a system of auto-adjust the frequency of the radio receiver.
Fig.1.1 - amplitude-frequency characteristic:
1.1 Setting the problem of synthesis of extreme systems
Objects are described by equations:
Extreme characteristics drifting over time.
It is necessary to choose such a control effect that allows you to automatically find an extremum and hold the system at this point.
U: extr y \u003d y o (1.2)
Fig.1.2 - Static extreme characteristics:
It is necessary to determine such a control action that ensured the property:
1.2 Condition of Extremum
The required extremum condition is the equality of zero of the first private derivatives.
A sufficient extremum condition is the equality of zero second private derivatives. In the synthesis of an extreme system, it is necessary to estimate the gradient, but the vector of second private derivatives is not possible, and in practice, instead of a sufficient extremma condition, the ratio is used:
Extreme System Synthesis Stages:
Gradient assessment.
Organization of movement in accordance with the condition movement towards extremum.
Stabilization of the system at the point of extremum.
Fig.1.3 - Functional scheme of the extreme system:
1.3 - types of extreme characteristics
1) Emnamed Extreme Characteristics of the Module Type
Fig. 1.4 - Extreme Module Type Feature:
2) Extreme Characteristics of the type of parabola
Fig. 1.5 - Extreme Characteristics of the type of parabola:
3) In the general case, the extreme characteristic can be described by the N-order parabola:
Y \u003d k 1 | y-y o (t) | N + K 2 | Y-Y O (T) | N -1 + ... + K N | Y-Y O (T) | + K n +1 (t). (1.9)
4) Matrix representation:
Y \u003d Y T BY (1.10)
1.4 Ways to estimate the gradient
1.4.1 The method of dividing derivatives
Consider it on an umnamed characteristic, y - output dynamic part of the system.
yr 1, y \u003d y (y, t)
Find a complete time derivative:
With slow drift, so
Dignity: Easy.
Disadvantage: at small 0 it is impossible to determine the gradient.
Differentiation filter.
Fig. 1.6 - Assessment scheme for a private derivative:
1.4.2 Discrete gradient assessment
Fig. 1.7 - Discrete assessment scheme of a private derivative:
1.4.3 Discrete gradient mark
With a small sampling step, we replace:
1.4.4 Method of synchronous detection
The synchronous detection method involves adding to the input to the extremal object of an additional sinusoidal signal of a small amplitude, high frequency and separation from the output signal of the corresponding component. By the ratio of phases of these two signals, it can be concluded that the sign of private derivatives can be concluded.
Fig. 1.8 - Functional scheme for assessing a private derivative:
Fig. 1.9 - Illustration of the passage of search oscillations on the system output:
y 1 is the operating point, while the difference in the phases of signals is equal to 0.
y 2 is the difference in the phases of signals, the multiplication block can be used as the simplest FCU.
Fig. 1.10 - FCC illustration:
As a filter, the filter averaging on the period period is chosen, which allows the signal to be obtained by the output, proportional value of the private derivative.
Fig. 1.11 - Linearization of static characteristics at the operating point:
Consequently, the equation of an extreme curve can be replaced with a straight equation:
FCU output signal:
k - proportionality coefficient - tanglex angle of tilt forward.
Filter output signal:
In this way:
The method of synchronous detection is suitable for determining not only one private derivative, but also the gradient as a whole, and several oscillations of various frequencies are supplied to the input. The corresponding filters at the outlet make the reaction to a specific search signal.
1.4.5 Special gradient estimation filter
This method involves the introduction of a special dynamic system into the system, the intermediate signal of which is equal to a private derivative.
Fig. 1.12 - Diagram of a special filter assessment of a private derivative:
T- Duration of the filter time:
DF is used to estimate the full derivative Y, and then this estimate of the total derivative is used to estimate the gradient.
1.5 Organization of Movement to Extremum
1.5.1 first order systems
We organize the law of the Office proportional to the gradient:
Write the equation of a closed system:
This is a common differential equation that can be explored by Tau methods.
Consider the system statics equation:
If using the gain coefficient K to ensure the stability of the closed system, then automatically in the statics we will come to the extremum point.
In some cases, using the coefficient k, it is possible in addition to stability to provide a certain duration of the transition process in a closed system, i.e. Provide a given time to exit an extremum.
Where k is stability
Fig. 1.13 - Functional scheme of the gradient extremal system of the first order:
This method is suitable only for unimodal systems, i.e. Systems with one global extremum.
1.5.2 Heavy Ball Method
By analogy with the ball, which is rolling into the ravine and skips the points of local extremums, the system of AU with oscillatory processes also slip local extremums. To ensure oscillatory processes into the first order system, we introduce additional inertia.
Fig. 1.14 - Illustration of the "heavy" ball:
Equation of a closed system;
Characteristic equation of system:
The smaller D the longer the transition process.
Analyzing the extreme characteristic, the necessary overshoot and the duration of the transition process are set, from where:
1.5.3 Single-channel general view systems
Control Law:
Substituting the law of management in the management of the object, we obtain the equation of a closed system:
In the general case, to analyze the stability of a closed system, it is necessary to use the second Lyapunov method, which is determined by the regulator gain coefficient. Because The 2nd Lyapunov method gives only a sufficient stability condition, the selected Lyapunov function may be unsuccessful and the regular procedure for calculating the regulator here cannot be offered.
1.5.4 Systems with senior derivative in management
General case of extremum objects:
Functions F, B and G must satisfy the conditions for the existence and uniqueness of solving a differential equation. The function G must be repeatedly differentiated.
C - Matrix derivatives
The problem of the synthesis is solvable if the work matrix is \u200b\u200bnot degenerate, i.e.
Analysis The conditions for solvability of the synthesis problem allows you to determine the derivative of the output variables, which explicitly depends on the control exposure.
If condition (1.31) is satisfied, then such a derivative is the first derivative, and therefore the requirements for the behavior of a closed system can be formed as a differential equation for y corresponding to the order.
We formulate the law of management of a closed system, for which we form the law of management, substituting into the right-hand part of the management for:
The equation of a closed system relative to the output variable.
Consider the situation when
With the appropriate selection of the gain coefficient, we obtain the desired equation and automatic exit to the extremum.
The parameters of the regulator are selected from those considerations as for conventional Sau, i.e. (SVK) i \u003d (20 * 100), which makes it possible to provide an appropriate error.
Fig. 1.15 - System scheme with senior derivative in control:
In the system, a differentiation filter is introduced into the system to assess the full derivative in time, therefore, to estimate the gradients in such systems, it is convenient to use a gradient estimation filter. Because Both of these filters have a small time constant, then in the system there may be multi-empty processes, allocate which can be separated by the method of separation of movements, and slow movements will be described by equation (1.34), which corresponds to the desired when. Fast movements need to be analyzed for stability, and depending on the ratio of the time constant of the DF and the filter of the assessment of private derivatives (Foci), the following types of movements can be distinguished:
1) The constant time of these filters is commensurate.
Fast movements describe the combined processes in these two filters.
2) Distant time differ in order.
The system is observed in addition to slow movements, fast and super fast movements corresponding to the smallest time constant.
For stability, it is necessary to analyze both cases.
2. Optimal systems
Optimal systems are systems in which the specified quality of work is achieved due to the maximum use of the capabilities of the object, in other words, these are systems in which the object works at the limit of its capabilities. Consider the aperiodic link of the first order.
For which it is necessary to ensure the minimum transition time from the initial state Y (0) to the final Y k. The transitional function of such a system at k \u003d 1 looks like this
Fig. 2.1 - the transition function of the system at u \u003d const:
Consider the situation when the maximum possible control effect is submitted to the object input.
Fig. 2.2 - Transitional function of the system at u \u003d a \u003d const:
t 1 is the minimum possible time of the transition y from the zero state to the final for this object.
To obtain such a transition, there are two management laws:
The second law is more preferable and allows for control under interference.
Fig. 2.3 - Structural System System with Feedback Type Control Law:
2.2 Setting the problem of synthesis of optimal systems
2.2.1 Mathematical model of the object
The object is described by the status variables.
Where the function f (x, u) is continuous, differentiable in all arguments and satisfies the condition and uniqueness of the solution of the differential equation.
This feature is non-linear, but stationary. As special cases, the object may have the appearance of a nonlinear system with additive control:
Either a linear system
The object must be represented in one of the three forms presented above.
2.2.2 Many initial and end states
The task of the optimal transition from the initial state to the final is the boundary task
Where the initial and endpoints can be set by one of the four methods presented in Fig. 2.4.
a) task with fixed ends,
b) the task with a fixed first end (fixed starting point and a lot of end values),
c) the task with the fixed right end
d) the task with moving ends.
Fig.2.4 - Phase portraits of the system transition from the initial state in the final for various tasks:
For the object, the set of initial states may generally coincide with the entire set of states or the working area, and the set of finite states is a subspace of a plurality of states or the workspace.
Example 2.1 - In any state of the state space, can we translate an object described by the system of equations?
Substituting into the second equation, the value of U from the first equation U \u003d x 2 0 - 2x 1 0, we obtain -5x 1 0 + x 2 0 \u003d 0;
The sets of finite states described by the equation x 2 0 \u003d 5x 1 0 are obtained;
Thus, the set of finite states specified for the object (system) must be implemented.
2.2.3 Restrictions on state and management
Fig. 2.5 - General view of the workspace of the status space:
It is allocated to the workspace of the space of states, which is negotiated. As a rule, this area is described by its borders using modular agreements.
Fig.2.6 is the type of working area of \u200b\u200bthe space of states specified by modular agreements:
U is the area of \u200b\u200bpermissible values \u200b\u200bof the control exposure. In practice, the U region is also set using modular relations.
The objective of the synthesis of the optimal regulator is solved under the condition of restrictions on control and limited resource.
2.2.4 Optimality Criterion
At this stage, the requirements of the work of the closed system are specified. Requirements are specified in generalized, namely, in the form of an integral functional, which is called the optimality criterion.
General view of optimality criterion:
Private types of optimality criterion:
1) the optimality criterion that provides a minimum of the transition time (the task of optimal speed is solved):
2) the optimality criterion that provides minimum energy costs:
By one of the components:
For all variable states:
According to one control influence:
For all control influences:
For all components (in the general case):
2.2.5 The form of the result
It is necessary to specify in what form will look for the control effect.
Two options for optimal control are possible: U 0 \u003d U 0 (T), used in the absence of perturbation, u 0 \u003d u 0 (x), optimal control in the form of feedback (closed control).
The wording of the synthesis problem of the optimal system in general form:
For an object described by variable states with specified restrictions and a plurality of initial and end states, it is necessary to find the control action that ensures the quality of the processes in the closed system corresponding to the optimality criterion.
2.3 Dynamic programming method
2.3.1 Principle of optimality
Initial data:
It is necessary to find u 0:
Fig. 2.7 - Phase portrait of the system transition from the starting point to the ultimate state in the state space:
The transition trajectory from the starting point to the final will be optimal and only.
The wording of the principle: the end portion of the optimal trajectory is also the optimal trajectory. If the transition from the intermediate point to the final would not be carried out by the optimal trajectory, then for it it would be possible to find its optimal trajectory. But in this case, the transition from the starting point to the final would pass on another trajectory, which would have to be optimal, and this is impossible, since the optimal trajectory is the only one.
2.3.2 BALLMAN BASIC EQUATION
Consider an object of control of an arbitrary type:
Consider the transition in the space of states:
Fig. 2.8 - Phase portrait of the system transition from the starting point to the final X (T) - the current (initial) point, X (T + DT) is an intermediate point.
We transform expression:
Replace the second integral on V (X (T + DT)):
With a small value of DT, we introduce assumptions:
2) Spread the auxiliary function
By performing further transformations, we get:
Where min v (x (t)) is the optimality criterion J.
As a result, received:
We split both parts of the expression on DT and eliminate DT to zero:
We obtain the main equation Bellaman:
2.2.3 Estimated ratio of the dynamic programming method:
The main equation of Belman contains (M + 1) - unknown values, because U 0 R M, VR 1:
Differentizing M times, we obtain the system from (M + 1) equations.
For a limited circle of objects, the solution of the obtained system of equations gives accurate optimal control. Such a task is the name of the task of the ACOR (analytical design of optimal regulators).
Objects for which the Akor task is considered must meet the following requirements:
The optimality criterion must be quadratic:
Example 2.2
For the object described by the equation:
It is necessary to ensure the transition from x (0) to x (t) by the optimality criterion:
After analyzing the object for stability, we get:
U 0 \u003d U 2 \u003d -6x.
2.4 Pontryagin maximum principle
We introduce an extended state vector, which is expanding due to the zero component, which is chosen by the optimality criterion. Zr n + 1
We also introduce an extended vector of right-hand parts, which are expanding due to the function under the integral in the optimality criteria.
We introduce w - vector of conjugate coordinates:
We form a Hamiltonian, which is a scalar product W and C (Z, U):
H (w, z, u) \u003d w * c (z, u), (2.33)
Equation (2.34) is called the primary equation of the Pontryagin maximum principle based on the dynamic programming equation. Optimal is the control that at a specified time interval delivers the maximum of Hamiltonian. If the management resource would not be limited, then it would be possible to use the necessary and sufficient conditions of extremum to determine optimal control. In a real situation to find optimal control, it is necessary to analyze the amount of Hamiltonian with the limit value of the level. In this case, u 0 will be the function of the extended vector of states and the vector of the conjugate coordinates U 0 \u003d U 0.
To find the conjugate coordinates, it is necessary to solve the system of equations:
2.4.1 Procedure for calculating the system on the principle of the maximum Pontryagin.
The object equations must be given to the form, standard for the synthesis of optimal systems:
It is also necessary to specify the initial and end states and write the optimality criterion.
Entered vector status
Advanced vector of right parts:
And vector conjugate coordinates:
Record Hamiltonian as a scalar product:
We find the maximum Hamiltonian on U:
For which the optimal control U 0 (W, Z) is determined.
We write down differential equations for the vector of conjugate coordinates:
We find conjugate coordinates as a function of time:
6. Determine the final optimal management law:
As a rule, this method allows you to get a program of management.
Example 2.3 - for the object presented in Fig. 2. 9. It is necessary to ensure the transition from the starting point y (t) to the final y (t) per t \u003d 1c with the quality of the process:
Fig. 2.9 - Model of the object:
To determine the constants B 1 and B 2, you need to solve the edge task.
Write the equation of a closed system
Integrate:
Consider the final point T \u003d T \u003d 1C., Like x 1 (t) \u003d 1 and x 2 (t) \u003d 0:
1 \u003d 1/6 b 1 + 1/2 b 2
Received a system of equations from which we find b 2 \u003d 6, b 1 \u003d -12.
We write the law of control U 0 \u003d -12T + 6.
2.4.2 Optimal Control Task
For the object of the general view, it is necessary to ensure the transition from the starting point to the ultimate in the minimum time with a limited control law.
Features of the task of optimal speed
Hamiltonian speed:
Relay management:
This feature takes place for relay objects.
Theorem on the number of control exposure switches:
This theorem is valid for linear models with real roots of the characteristic equation.
Det (PI - a) \u003d 0 (2.51)
L (a) - vector of real eigenvalues.
The wording of the theorem:
In the problem of optimal speed with real roots of the characteristic equation, the number of switchings cannot be greater than (n - 1), where N is the order of the object, therefore, the number of control intervals will not be greater than (N-1).
Fig. 2.10 - the type of control exposure at n \u003d 3:
Example 2.4 - Consider an example of solving the problem of optimal speed:
W \u003d [W 1, W 2]
H B \u003d W 1 x 2 + W 2 (-2DX 2 -X 1 + U)
When - the roots are real:
The sum of the two exponential is:
If, the roots are complex and conjugate and the solution will be a periodic function. In the real system, switching no more than 5 - 6.
2.4.3 Switching surface method
This method allows you to find the control of the function variable functions for the case when the optimal control is relay. Thus, this method can be used when solving optimal speed tasks, for an object with additive control.
The essence of the method is that in the entire space of states to highlight the points where the control sign changes and combine them into the general surface of the switching.
Switching surface
The Act of Management will have the following form:
To form the switching surface, it is more convenient to consider the transition from an arbitrary starting point to the beginning of coordinates
If the end point does not coincide with the start of coordinates, it is necessary to select new variables for which this condition will be valid.
We have an object of type
We consider the transition, with optimality criterion:
This criterion allows you to find the law of controlling this type:
With unknown, the initial conditions are also unknown to us.
We consider the transition:
Return time method (method of the way traffic).
This method allows you to define the surfaces of the switching.
The essence of the method is that the initial and endpoints are changing in places, while instead of two sets of initial conditions there is one for.
Each of these trajectories will be optimal. First we find a point where control changes the sign and combine them into the surface, and then the direction of movement changes to the opposite.
Example - the gear ratio of the object is:
Criterion for optimality speed:
Restriction on management.
Consider the transition:
Optimal control will be relay:
Let's turn over the opposite time (i.e.). In the opposite time the task will have such a kind
Consider two cases:
We obtain the equation of a closed system:
We use the method of direct integration, we obtain the dependence on and since -, we have
Because The initial and endpoints changed places, then we obtain similarly:
We will construct the resulting phase plane to determine the direction
Applying the method of direct integration, we get:
The function will look at:
By changing the direction:
Sign change point (switching point).
General Analytical Expression:
Surface equation:
Optimal control law:
Substiving the surface equation, we get:
2.5 Suboptimal systems
Suboptimal systems are systems close by properties to optimal
Characterized by the criterion of optimality.
Absolute error.
Relative error.
Suboptimal call the process close to optimal with a given accuracy.
Suboptimal system - a system where there is at least one suboptimal process.
Suboptimal systems are obtained in the following cases:
in approximation of the switching surface (using piecewise linear approximation, approximation with splines)
When in the suboptimal system, the optimal process will occur.
restriction of the working area of \u200b\u200bthe space of states;
3. Adaptive systems
3.1 Basic concepts
Adaptive systems are called such systems in which the parameters of the regulator are changing after a change in object parameters, so that the behavior of the system as a whole remains unchanged and corresponded to the desired:
There are two directions in the theory of adaptive systems:
adaptive systems with reference model (ASEM);
adaptive systems with identifier (ACI).
3.2 Adaptive Systems with Identifier
The identifier is a device for estimating object parameters (parameter estimates should be carried out in real time).
Ar - adaptive regulator
OU - Control Object
U - Identifier
A part that is highlighted by a dotted line can be implemented in digital form:
V, U, X - can be vectors. The object can be multichannel.
Consider the operation of the system.
In the case of unchanged object parameters, the structure and parameters of the adaptive regulator do not change, the main feedback is valid, the SIS-topic is a stabilization system.
If the object parameters change, then they are estimated by the identifier-rum in real time and the structure and parameters of the adaptive regulator occur so that the behavior of the system remains unchanged. The basic requirements are presented to the identifier (speed, etc.) and the identification algorithm itself. Such a class of systems is used to control objects with slow nonstationarities. If we have a non-stationary object of the general form:
;. The following adaptive appearance will be the following:
Requirements that are presented to the system:
Where and - matrices of permanent coefficients.
Really, we have:
If you equate, then we obtain the ratio to determine the parameters of the regulator
3.3 Adaptive systems with reference model
In such systems there is a reference model (EM), which is placed in parallel to the object. Ba - adaptation unit.
Figure 2 - Functional scheme ASEM:
Consider the operation of the system:
In the case when the object parameters do not change or the output processes correspond to the reference, the error:
auto adjustment Programming management
The adaptation unit does not work and the adaptive regulator is not rebuilt, a smooth feedback operates in the system.
If the behavior is excellent from the reference, this happens when the object parameters change, an error appears in this case.
The adaptation unit turns on, the adaptive regulator structure is rebuilt, so to reduce the object model.
The adaptation unit must reduce the error to zero ().
The algorithm laid in the adaptation unit is formed in various ways, for example, using the second Lyapunov method:
If this is performed, the system will be asymptotically stable and.
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