Extreme automatic control systems. Extremum search methods. Extreme project management: new in modern project management Chaos theory is a mathematical field dedicated to the description and study of the behavior of nonlinear dynamical
There are many books out there that are helpful. But there are books - breakthroughs, books - revelations, books - bombs. They excite the mind, awaken the intellect exhausted by routine, create hope, you want to return to them again and again. One of these books, in my opinion, is the book by Doug DeCarlo " Extreme project management».
In 2005, I was working as a PM on a fairly complex project with high risks. The company where I worked had a traditional project management culture based on document templates, Gantt charts, fairly tight budgets, standard reports. This culture is based on the premise that performance requirements, budget and schedule must be approved once, and any changes to them are undesirable. In this paradigm, the project manager must invent a plan at the very beginning and strictly follow it, as if fulfilling the plan is an end in itself. If you manage to stay on track, then you are an experienced project manager, if not, you still have a lot to learn. I understood that something was wrong here, but I could not find like-minded people. Much of the literature has been on the side of formulaic management.
And now a powerful blow has been dealt to dogma. It was very unexpected and just as pleasant to meet a like-minded person who took the risk of writing an entire book about an emerging new approach, where common sense and entrepreneurial logic prevailed. I really want many to read this book. If the book helps you shift the old paradigm, a lot will change in your life and work. Doug DeCarlo's views are quite consistent with Lean principles.
Doug DeCarlo says that you do not need to close yourself off from reality with formal plans, budgets, approved procedures, that it is important not to achieve the initially set goal, but to find and obtain the desired result. He presents an extreme project like shooting at a moving target, like a homing missile that searches for a target in real time. Reality rules! - says Doug DeCarlo. Extremely managing a project does not mean doing the project “on your knees”, it is, on the contrary, aerobatics. It's like F1 in auto racing. Extreme control projects require special skills and abilities, flexibility, speed of decision-making, breadth of coverage.
“People would like the world to be a beautiful, tidy place where everything is already certain and predictable. We all know it's not real, but we act like it is, and that's why we get in trouble. In project management, for example, we roughly determine how much time we will spend on solving a particular problem, then we include our calculations in the program for planning the progress of work, and as a result we get a drawn up work plan using the critical path method, to which we already we treat it as something conditioned. This is absolute nonsense, because the program in the minds of senior managers creates the illusion that we have a certainty that does not exist, and these false expectations in the long run create problems for all of us. "
“We live in a world of quantum projects, in which change and uncertainty is the norm... What, then, is project management in light of these circumstances?
“What I'm really convinced is that this book will either create a huge stir in the project management world, or it will be considered heretical. It can also be the source of a paradigm shift. In any case, you will not remain the same after reading this book. You will no longer be able to find solace in your clear work plan using the critical path method, so elegant in its illusion of certainty. ”
“The world of project management has changed dramatically and irreversibly lately. Today's projects simply do not bear even the slightest resemblance to those of yesterday. The very world in which the project management took place has irrevocably sunk into the past. "
"Here the main signs of an extreme project:
Requirements change overnight.
The project requires the use new technology and new methods that have not been tested by anyone before.
The project completion time (in comparison with a conventional project) has been reduced by half.
The quality of life during the work on the project is more like nothingness.
In the midst of a project, the customer suddenly decides that he needs a different end result.
The environment in which the project exists can be described as chaotic, unpredictable, and randomly changing. "
“Traditional project management deals with something famous. Extreme projects deal with the unknown. Traditional projects develop slowly and steadily, their planning is methodical. Extreme projects are chaotic, chaotic and unpredictable; speed and innovation are critical, and planning is done at the last moment. "
“Extreme projects are messy. This is reality. And reality exists independently of the plans made, and we cannot prevent it. She has her own plans. "Reality rules!" ... And we can only react to changes. This position is so fundamental and so important to remember that if you are involved in an extreme project, I strongly recommend that you write on your forehead the phrase “ Reality rules!"And do it in a mirror image."
“If you take the time to carefully plan each step, the project is likely to become irrelevant when you complete it. During this time, the very problem or opportunity that you studied can change beyond recognition. And since for extreme projects constant change is the rule (and stability is the exception), yesterday's plans will be no fresher than a month old fish sandwich».
“Innovation is extremely important for extreme projects. They are the very essence of extreme projects. Here, first of all, it requires the creation of innovative processes and project management methods, as a result of which there are advanced products and services. You can't cut your project time in half if you work twice as hard. This is a hopelessly outdated worldview. "
« Extreme project is the process of finding the desired result by trial and error. His can be compared to a missile looking for a target by thermal radiation... An extreme project is a self-correcting phenomenon, and you will not have time to discuss each decision with upstream management. But even if you find one, the people at the top of the hierarchy won't always be available. Project teams need to make urgent and immediate decisions in light of rapidly changing requirements and circumstances. The goal of traditional projects, on the other hand, is to achieve the desired result with maximum efficiency while minimizing deviations from the original plan. Optimization and efficiency are the goal. Project teams move towards their goals by following predefined processes and rules. Often, strict control principles are introduced to ensure that the project does not deviate from the established values in terms of cost, quality or implementation schedule. The traditional approach to an extreme project can be compared to trying to drive a car at full speed on the freeway, looking in the rearview mirror. "
“In the case of extreme projects that are messy in nature, we will focus on performance rather than efficiency... We are trying achieve the desired result, which can only remotely resemble the original goal. The golden triangle of traditional project management - done on time, efficiently and within budget - will not help in extreme conditions. Why? Yes, because itself the definition of timing, quality and budget is constantly changing in the course of the work on the project».
« Traditional project is like a waterfall- with its smoothly descending, sequential Gantt charts and eight levels of detail. Waterfall project management is appropriate in an environment of relatively low speed and low uncertainty. This model is well suited for traditional civil engineering projects that have clear purpose and a proven plan to achieve it. The process of closing a nuclear power plant and a new McDonald's restaurant project can be well represented using a waterfall model.
The mental model of a traditional project
In contrast, extreme projects, characterized by changing requirements and completion times, unpredictability, chaos, speed, and innovation, do not fit into this model. An extreme project is more like a twisted, overcooked pasta.».
Extreme project mental model
“I usually offer my clients the following definition of an extreme project: An extreme project is a complex, high-speed, self-correcting enterprise, during which people interact in search of the desired result under conditions of extreme uncertainty, constant changes and severe stress ».
"Traditional projects follow the classic scheme" prepare, aim, fire”. On the contrary, in extreme projects we first we shoot, and then we change the trajectory of the bullet... This is the reality in which businessmen, project managers and professional teams live. The bureaucracy, rigid rules, and mechanistic approach that characterize traditional projects do not apply to extreme projects, where uncertainty, improvisation, and spontaneity crowd out predictability, command, and control. It follows that we must take a completely different approach when planning and managing extreme projects - acceptable and adaptable to change».
“When managing extreme projects, we understand that the plan must change in accordance with the state of the outside world. If tomorrow the world changes, then our plan will also change. Change is the norm. The uncertainty is obvious. Stability is deviation from the norm. Traditional project management is focused on the past. Extreme project management is future-oriented ».
“The“ prepare-aim-fire ”approach characterizes a high-speed, fast-paced process. The main 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 guides the progress of the project towards the set goal, which is constantly changing and becoming clearer with each iteration. "
“If you don't know the future, why waste time planning it? Extreme project management doesn't do that.
Traditional project management forces people to serve the process. Extreme project management forces the process to serve the people.
Traditional project management is a set of practices, approaches and methods that make people the servants of the process. Gantt charts, protocols, reports and other processes are designed to restrict the activities of people. Extreme project management is based on the belief that people are the key to success: thoughts, emotions and interpersonal contacts are the foundation of creativity. If the team is demoralized, the project will run out of schedule, over budget and worsen the outcome. Thus, extreme project management places serious emphasis on quality of life and gives project participants control over the process, rather than the other way around.
Traditional project management centrally controls people, processes, and tools. In extreme projects, control is evenly distributed.
Traditional management seeks to minimize changes and establish tight control over processes... The leader of extreme projects realizes that it is impossible to manage something unknown and unpredictable with the same methods as before. Trying to make reality fit the project plan is a waste of time... In a properly organized extreme project, no one is under control. On the contrary, everyone is in control.
Traditional management challenges the whole world (objects, people, time). In extreme projects, the challenge is thrown down primarily to oneself, one's attitude, one's approach to the world.
Traditional project management strives to get people, budget, and schedule to align with plan. Extreme project management anticipates change by taking a minimalist approach to planning and distributing control.
Traditional project management - leads. Extreme Project Management - Leads. "
“The stamps of traditional governance — working according to plan, minimizing change, tight control — are purely administrative functions. Traditional project leaders are like overseers and are only suitable for managing stable processes. In a world of extreme projects where planning is minimal and change is constant and unpredictable, the project manager is more of a leader. As you will see later, a good leader leading an extreme project will allow people to find the optimal solution and perform constant self-correction. "
“For today's high-speed, change-prone projects, the traditional world of project management is a relic of the past.”
“The two squares on the left side of the figure represent the world of traditional project management- a discipline that was born in the engineering and construction industry. Here, the project management approach is closely related to the scientific world of Newtonian physics.... Newton's worldview is based on determinism and reductionism - a paradigm according to which the world can be divided into a predictable set of cause-and-effect relationships between its separate parts. This is the logical and linear thinking of the left hemisphere in all its glory. It is analytical. This so-called mechanistic approach has given rise to the notion that projects can be planned with a high degree of certainty. He pioneered waterfall project management. But on the other side is the right hemisphere, which does not work linearly. Its principle of operation is relative and arbitrary, and it solves problems using systems thinking. "
« In the world of extreme projects, the plan is not a dogma... And, unlike Newton's world, extreme projects obey the laws of a new science: the world of quantum physics, self-organizing systems and chaos theory. "
“Many companies have only recently realized the importance of correct organization process called "project management", and now in a hurry are trying to master the traditional approaches presented by organizations such as the Software Engineering Institute (SEI), PMI and others. Unfortunately, these organizations seem to be wasting their time... Bob Kulin, a PMP (Project Management Professional), made the following statement: “I have always believed that the project manager profession is doing themselves a disservice if they don’t realize that many, if not most, projects are inadequate. fundamental principles established by the PMI in the Project Management Body of Knowledge (PMBOK) standard. It's time to open our eyes to the realities of today's business environment and find a way to survive and thrive in these new circumstances. ”
“The extreme project management model consists of a set of rules, values, skills, tools and practices based on the principle of change and uncertainty, and that make up the software and hardware part of extreme project management:
Accelerators - principles that give freedom of motivation and innovation.
Shared Values - A set of values that establish trust between stakeholders.
Business Questions - Questions, answers that help to deliver valuable results to the customer often and quickly.
The critical success factors are skills and tools, as well as organizational support, which play a key role in achieving success. "
« For an extreme project, there is only a general idea of the ultimate goal., and practically nothing is known about the methods of achieving it. It's obvious that the traditional, linear approach to project management just won't work here... The standard tools, templates, and processes of traditional management are of no practical use to the extreme project manager. Instead, the project manager, together with the customer, selects one or more likely areas of work, examines what is happening and prepares for the next stage. This cycle repeats several times, while the project manager and the customer are looking for a point of convergence of the current result with the set goal, which, most likely, has already undergone changes in the light of new knowledge and discoveries made during previous iterations. Extreme project management can be a challenging and inspiring team challenge when it comes to dominating the market, killing a major competitor, re-engaging a major customer, or reopening a dying production line. Extreme project management doesn't have to be destructive grueling work against reality - of course, if you abandon traditional management methods and embrace a new quantum way of thinking. "
“Accepting the world of extreme projects requires us to make a change in our worldview in the first place.”
“Like any software, our brains have“ default settings, ”which is a way of thinking. By a mindset, I mean a set of assumptions and assumptions about how the world works. And this is our internal program. "
“Here's a short list of key ideas to keep in mind:
By quantum thinking, I mean a worldview that accepts change and unpredictability. Quantum thinking assumes that change is the norm.
The Newtonian or linear worldview considers stability to be a given norm.
Extreme projects should be managed primarily in terms of quantum thinking.
Trying to use a quantum approach in managing traditional projects will lead to disastrous results.
Applying Newtonian thinking to an extreme project will completely ruin it. "
“Unlike Newton's causal mindset, extreme project management implies that while the ultimate goal of a project is achievable, it is impossible to predict how we will achieve it. Hence, adaptability is more important than predictability».
“The good news is that sooner or later the leadership of the organization realizes that the old approach does not work. The bad news is that the wrong methods are often chosen to correct the situation. Typically, this process begins with the conclusion that not all employees have mastered the new software and the required design methodology. On the this stage Newtonian thinking concludes that if everyone followed the set rules, then the company could finally achieve clear and predictable results. “We need to tighten up the discipline,” they say. In other words, the prevailing philosophy of traditional management is summed up in the following words: “ If the method doesn't work, let's tighten it up. ”».
“Millions of dollars are wasted on training programs and certification of employees in the traditional approach to project management, which only hinders the implementation of extreme projects. As the instability of the project grows, the desire to light all the way to a linear model becomes just an obsession and inevitably leads to what I call “linear madness”. "
“The reality is that the extreme project is a winding line... It looks like the rolled, overcooked pasta I mentioned earlier. But many project managers who have gone through the school of classical management hold, even unconsciously, completely different views about how a project should be carried out. They want the project to look like this:
This ponderous, linear mindset of the left hemisphere is the underlying cause of Newtonian neurosis: striving to build an extreme project along a straight line... Tim Lister, senior consultant at the Cutter Consortium, calls managers who think this way "straight line." These would-be leaders are ruthlessly trying to subdue every changing element of the project by overusing design tools, rules, patterns, policies and procedures. ”
“They also readily admit their own mistakes. If you could overhear the thoughts of a desperate project manager, his self-talk would look something like “ The world is not according to my plans. I must be not as good a leader as I thought. I have to get through extra education on project management. I will try and promise to use more generic templates and tools ”».
“The world is not in line with my plans. Let's think about it. Why on earth should the world match your project plans? What could be more ridiculous? Newtonian neurosis leads to fruitless attempts to change the world according to your plans, which in itself is fiction. Who can think of changing reality in accordance with fiction? People suffering from Newtonian neurosis. "
"Do not misunderstand me. I believe that certification in project management is a valuable service when applying for a job and will surely add weight to your resume. So you can proudly showcase your PMP certificate to those around you. Get a tattoo if you want. But don’t assume that the tools and concepts you’ve mastered while learning have universal application. In extreme projects, most of them are practically useless. "
“Newtonian neurosis is by no means a specific disease of extreme project managers. This insidious affliction is widespread among project sponsors, customers, and senior management who insist on using a linear Newtonian approach to stabilize an unpredictably changing world.
I have met quite a few project leaders who believe they have a quantum mindset while acting in accordance with the Newtonian model. Their behavior does not correspond to their views, although their intentions are quite noble. This phenomenon, known as "unconscious Newtonianism", is at the heart of Newtonian neurosis. "
« Extreme projects are like jazz... To an inexperienced listener, jazz may seem random and chaotic, but it is not. Jazz has structure and jazz musicians have a tremendous opportunity to improvise. Jazz has no clear guidelines. They also do not exist in the management of extreme projects. "
“Traditional projects are more like classical music. They are well managed. You have to stick to the score, otherwise the conductor will reach you with his baton. However, some organizations are already starting to see the light. They understand that the most difficult projects tend to decline when using rigid methods, an excessive number of proven patterns, practices and policies. "
“I am not trying to argue that there is no room for rigid classical or Newtonian principles in an extreme project. Some components of an extreme project require unconditional rigidity, for example, when testing software or conducting a scientific experiment. It is necessary to use both Newtonian and quantum methods. But for an extreme project to succeed, a quantum mindset must prevail in all aspects of the enterprise. ”
« Newtonian thinking is based on a fear of change, a fear of making a mistake.... Its main task is to strive to prevent bad things from happening. He is trying to change reality in accordance with someone's idea of what should be. He trying to win by force... Trying to apply the traditional approach in an unpredictable environment can be dangerous both for the project itself and for your health and well-being. "
“Managing extreme projects means see the world as it is, in its current state, and not fight it at every step... In the end, when something happens, it already becomes reality. Trying to change reality is tantamount to trying to change history. It's useless. Instead, we forgive past mistakes, face reality and change our plan to match it, and nothing else. There is no Reality Cancel button on your computer. In the face of tight deadlines, constant change, high uncertainty and high complexity, using the traditional approach is tantamount to incapacity. "
“Extreme project management is a new type of thinking and management that matches the nature of projects being implemented in an environment of 'high turbulence', rapid change and constant uncertainty. It's about maintaining control and achieving results in a rapidly changing environment. ”
“By choosing a mindset that is resistant to change, you choose a worldview system that is 'in sync' with chaos and unpredictability, and you rely on people and relationships between them, rather than on tools and processes.
The leader of an extreme project must direct the streams of thoughts, emotions and attitudes towards the achievement of valuable results. "
« I propose to consider the project as a living variable organism:
Thoughts find their expression in the form of ideas, solutions, new facts, data and achievements. When thoughts and emotions converge at a point of convergence, they find expression in meetings using simple diagrams, in conversations over coffee, in drawing up simple, informal diagrams. They break into life in the form of physical prototypes, drawings, memos, presentations made in PowerPoint, project plans, project documentation and final design decisions.
Emotions constantly find expression in physical and bodily forms: when people frown or smile, when they send an angry email, or celebrate the victory associated with the appearance of the first successful results of experimental work. In contrast, traditional management relies heavily on a mechanistic (read Newtonian) approach and refuses to pay attention to the human factor. Its intellectual foundation consists of practices, procedures and policies that make people the servants of the process. Can you afford to dehumanize the project? No, not in the quantum world.
Relationship are a complex web of communication that arises when new information appears, including thoughts and emotions that are exchanged between project participants. When you look at the results of a project, you see the sum of thoughts, emotions and relationships that have been embodied in physical form. "
“Thus, a project is a process by which thoughts and emotions take shape. You can look at the desired result of the project as a kind of creature in the stage of its formation. And with the growth of the volume of thoughts and emotions, which are exchanged between the project participants, the final result takes on more and more distinct outlines. "
“One of the most important tasks of extreme project management is time period compression necessary for thoughts, emotions and relationships to take shape in physical form. "
“Project management, extreme or traditional, is not just the process of developing and implementing a new product or increasing the performance of a service that a customer has been seeking. It also does not mean creating all sorts of artifacts (Gantt charts, journals, reports and other countless documentation). It's much more than that: project management is the science and art of channeling the streams of thoughts, emotions and relationships towards meaningful results. ”
“If projects are people (their thoughts, emotions and relationships), then relationship management becomes the main task of the extreme project manager. People are a key factor in the success of an extreme project. "
“Anyone who participates in or is influenced by a project (before or after completion) is a participant. Project participants provide vital products and services, including leadership, other projects, information, feedback, labor force, cooperation, solutions, approvals and advice. Projects that depend on your project are also participants in it. "
“Moreover, you will have to deal with internal factors organizations. These include the systems, policies, and procedures (based on Newtonian thinking, of course) that you will have to live with until you find a guardian angel to help you avoid these annoying hindrances. Organizational culture is a way of doing work in specific organization- can also have a significant impact on you. Once you find yourself in an administrative-command organization, you can hardly count on the collective decision-making, which is a key success factor for an extreme project. "
« Make friends with change ... The changes have a negative impact on the project. They disrupt the order of things. Change is usually viewed with caution, which is why traditional management places such a high value on change management. Extreme project management requires a different attitude towards change - one in which changes are perceived as new opportunity and the adoption of changes increases the chances of achieving the desired result (which may differ significantly from the planned). "
« Play on people's passions ... I don't think many people get excited about getting back to work on a project in the morning. In fact, the word project contains some depressing connotation. People will work with great enthusiasm if they know they are on a mission; if they see the project not as a “project” but as a reason for their actions. You have to show people that their work is part of something bigger., giving them a clear idea of the goals and means ”.
« Don't over complicate the process ... For an extreme project, the good old principle “less is more” is not an empty phrase. It is very serious. In practice, less is more: fewer processes, less governance, fewer policies and less standard procedures. ”
“The main task of an extreme project manager is to achieve and maintain commitment to the project mission. You can safely talk about building commitment when team members are highly motivated and a large part of the project community is supporting you. ”
“When commitment wanes or disappears, the project's energy field declines and the project falls into a gloomy mood. Immediately there is a risk of non-compliance with the time frame, loss of quality, failure of financial expectations and complete 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-govern in hostile conditions. You cannot stabilize the world around you, you can only stabilize your condition. This is your only opportunity. And when you stabilize yourself, the world around you, as if by magic, is more stable.... If you do not practice self-discipline when working in hostile conditions, you will condemn yourself to suffering. "
“Commitment is positive energy, a sublime feeling that permeates the project and drives it towards success. Indifference or ridicule is a negative energy that hinders the development of a project. "
“Nine reasons for the failure of the leader of an extreme project.
Extreme project leaders fail when they turn their gaze inside the project and focus on technical details and product development (content), forgetting about the environment surrounding the project: the general economic situation, the expectations of the participants and the emotional state of the project. As a result, unresolved conflicts arise, resulting in a loss of commitment and inability to create an acceptable end product or service. The following error factors for project managers are primarily related to the project environment. They are found in all projects, but acquire special significance in extreme conditions:
1. Absence of a benefactor - the inability to find a suitable sponsor who would have the qualities of a champion and the ability to crush obstacles.
2. Weak communication skills (communication, negotiation, conflict resolution, support and influence).
3. Hermit Cancer Syndrome: The project manager sits in front of a computer screen instead of in front of key stakeholders.
4. Syndrome of the good soldier: excessive softness; admiration for the leadership and surrender of their positions; simple execution of orders.
5. Loss of business orientation: misapplication of four business questions (which will be covered in the next chapter):
Invasion of foreign territory: an attempt to answer the first business question (“ Who needs it and why?”). This question should be answered by the sponsor of the project.
Flight from the battlefield: fear of taking responsibility for answering the second business question (“ What needs to be done for this?”), Allowing the project sponsor to manage the budget. This is the prerogative of the project manager.
Excessive shyness: inability to get what will lead the project to success (the third business question is “ Can we handle this?”). You must be able to negotiate.
Malicious obsequiousness: The project manager continues with the negative answer to the fourth business question (“ It's worth it?”). This is the same as initiating a project or continuing its implementation, knowing that it has no chance of success. At the same time, blaming the project manager for mistakes, they forget about the real reason for the failure: economic justification the project turned out to be unviable.
6. Incorrect methodology: using an anti-productive methodology for project execution.
7. Totalitarianism (or boilerplate management): The project manager believes he can manage the dynamics of an extreme project by forcing people to fill out reporting forms instead of focusing on uncovering motivation, creating innovation and building trust, which requires a management style based on values and principles.
8. Naive obsequiousness: the inability to understand that the implementation of the project does not solve the problem.
9. Not at ease: lack of understanding that extreme project management (and possibly any project management) is a job where you can make the best use of your innate talents and motivated abilities. "
“The key to having effective group meetings is in your ability to manage the energy of participants, not time... “Let's forget about feelings and emotions,” said one project manager in the midst of the meeting. This was an incorrect proposal. As a professional mediator with thirty years of experience, I can say that my most important skill is being able to openly communicate the feelings of the participants. Model " Feelings -> Facts -> Decisions»Plays an important role throughout the entire meeting. If the members of the group are in a bad mood, you should not count on progress until you reach out to their feelings. "
“People are often mistaken in thinking that the difference between managing traditional and extreme projects lies in the presence or absence of planning. This view is far from the truth. Management of both types of projects involves planning, and in both cases, the goal is to maintain control over the project. "
“Another fundamental difference between traditional and extreme project management is that traditional project management starts at the design stage and ends at the implementation stage, while extreme project management encompasses the project much more broadly - from idea to obtaining economic effect».
“Extreme projects are developed in 'flexible organizations', i.e. in organizations with a change-adapted, project-friendly culture that recognizes and meets the special needs of a variety of projects, from extreme to traditional.
“Designs are like colors. If the soil is poisoned, one or two flowers will survive, but the rest will die sooner or later. ”
“The bureaucracy, rigid rules and mechanistic Newtonian approach that characterize traditional projects do not apply to extreme projects, where uncertainty, improvisation and spontaneity supplant predictability and control. Extreme projects require a new worldview and a new management model that will allow project managers and business people to maintain control in a changing environment. The management model should focus on profitability and not overlook the quality of life. "
“Leaders whose worldview is aimed at strengthening the mechanics of the project, make a serious mistake. They strive to develop a tough plan and execute it rigorously.... But in a world of extreme projects that are influenced by competitors, government orders, changing consumer preferences and new technologies, yesterday's plans will be no more relevant than a newspaper published a month ago. ”
"The reasons for the success of extreme projects are, first of all, competent management of the dynamics, not the mechanics of the project."
“The situation is aggravated even more after sending employees, sometimes in very large numbers, to training and certification in project management, where they teach traditional project management techniques that only lead to a decrease in the productivity of volatile and inherently complex extreme projects. The result is a waste of time and money. "
“The combination of Newtonian thinking, totalitarianism and project bureaucracy leads to the fact that the project is enclosed in a straitjacket. This practice stifles the motivation and innovation that are the lifeblood of an extreme project. Instead of the desired productivity gains, the organization faces a disability as people begin to work for the system, and not vice versa. ”
“In the world of traditional project management, success is determined by outdated principles of adherence to schedule, budget and all requirements set during the planning stage. In a world of extreme projects, these success rates are meaningless. What is the use of meeting all the criteria if the project becomes unprofitable after its implementation? Of course, extreme project managers worry about schedule, budget, goals and quality, but they also understand very well that these factors do not determine the success of a project. "
“A quantum leader sees his project as follows:
The main secret to maintaining control over an extreme project is to don't try to stretch it along a straight line... This aspiration is inherently flawed. Instead, it is necessary to establish the boundaries of the project implementation and create many control points... Boundaries make it possible to improvise within given limits. "
“The Newtonian leader wants to see his project like this:
This type of thinking takes us away from reality because it contradicts it. Newtonian thinking encourages us to adhere to a set plan at all costs and contributes to the creation of practices and systems that resist or seek to minimize change. Newtonian leader tries to change reality according to plan and manages people according to the principle of submissive submission... But reality rules. For a Newtonian personality, efficiency is more important than the result (read, profit). He asks himself: "Is the project going beyond the time and budget?" "
“Traditional metrics are not enough because they are tied to schedule, budget, requirements and quality, and not to the alignment of project results with business values. If the project is completed on time and does not go beyond the budget, but at the same time does not bring profit and does not meet the basic requirements, its practical value is close to zero. "
“Extreme projects don't live in complete isolation. They relate to other projects and global business issues. "
“This is a book about how to change the world around us ... disguised as a book about extreme project management. And this is the basic concept of project management: changing the world around us with each new project. When it comes to change, whatever position you are in - project manager, sponsor, or Executive Director organizations, extreme project management levels the playing field. When reality changes, it doesn't care about your job., place of residence or the amount of money in the bank account. The changes set different priorities. "
“The world we live in has long been considered extreme. No one can change reality. It remains to be hoped that the most important thing we can do in the extreme world for ourselves and the people around us is changing our type of thinking and adopting a new worldview, a new quantum reality».
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The need for adaptive (adaptable) control systems arises in connection with the complication of control problems in the absence of the practical possibility of a detailed study and description of the processes occurring in control objects in the presence of changing external disturbances. The adaptation effect is achieved due to the fact that some of the functions for receiving, processing and analyzing processes in the control object are performed during the operation of the system. This separation of functions contributes to a more complete use of information about ongoing processes in the formation of control signals and can significantly reduce the influence of uncertainty on the quality of control. Thus, adaptive control is necessary in cases where the influence of uncertainty or "incompleteness" of a priori information about the operation of the system becomes essential to ensure the specified quality of control processes. Currently, there is the following classification of adaptive systems: self-adjusting systems, systems with adaptation in special phase states and learning systems.
The class of self-adjusting (extreme) automatic control systems is widespread in view of the rather simple technical implementation. This class of systems is associated with the fact that a number of control objects or technological processes have extreme dependences (minimum or maximum) of the operating parameter from the control actions. These include powerful DC motors, technological processes in chemical industry, various types of furnaces, jet engines of airplanes, etc. Consider the processes occurring in the furnace during fuel combustion. With insufficient air supply, the fuel in the furnace does not burn completely and the amount of heat generated decreases. With excessive air supply, part of the heat is carried away with the air. And only with a certain ratio between the amount of air and heat, the maximum temperature in the furnace is reached. V turbojet by changing the fuel consumption, it is possible to achieve the maximum air pressure behind the compressor, and, consequently, the maximum engine thrust. At low and high fuel consumption, the air pressure downstream of the compressor and the thrust drop. In addition, it should be noted that the extreme points of control objects are "floating" in time and space.
In the general case, we can assert that there is an extremum, and at what values of the control action it is achieved is a priori unknown. Under these conditions, the automatic control system during operation must form a control action that brings the object to an extreme position, and keep it in this state in conditions of disturbances and the "floating" nature of extreme points. In this case, the control device is an extreme regulator.
According to the method of obtaining information about the weaving state of an object, extreme systems are non-search and search. In search-free systems, the best control is determined by using analytical relationships between the desired value of the operating parameter and the parameters of the regulator. In search engines that are slow, extremum finding can be done in a variety of ways. The most widespread method is synchronous detection, which boils down to estimating the derivative dy / du, where y is the controlled (operating) parameter of the control object, and u is the control action. A block diagram illustrating the method of synchronous detection is shown in Fig. 6.1.
Rice. 6.1 Structure of synchronous detection
At the input of the control plant, which has an extreme dependence y (u), together with the control action U, an insignificant perturbation is applied in the form of a regular periodic signal f (t) = gsinwt, where g is greater than zero and rather small. At the output of the control object, we get y = y (u + gsinwt). The resulting y value is multiplied by the f (t) signal. As a result, signal A will take the value
A = yf (t) = y (u + gsinwt) gsinwt.
Assuming that the dependence y (u) is a sufficiently smooth function, it can be expanded in a power series and, with a sufficient degree of accuracy, is limited to the first terms of the expansion
Y (u + gsinwt) = y (u) + gsinwt (dy / du) + 0.5g 2 sin 2 wt (d 2 y / du 2) +… ...
Since the value of g is small, the higher-order terms can be neglected and, as a result, we obtain
Y (u + gsinwt) "y (u) + gsinwt (dy / du).
Then, as a result of multiplication, the signal A will take the value
A = y (u) sinwt + g 2 sin 2 wt (dy / du).
At the output of the low-pass filter Ф, we get a signal B
.
If the filter time constant T large enough, we get
.
Therefore, the signal B at the filter output is proportional to the derivative dy / du
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The main most common types of extreme systems, in which the static mode of operation of an object is optimized, are extreme systems that ensure the operation of an object at the extreme point of its static characteristics.
The static characteristic should reflect the relationship between the quality function of the object and the operating parameters of the object.
It is advisable to use extreme self-propelled guns:
1. There is an indicator of quality (technical and economic, characterizing the operation of an object, and this dependence has a pronounced extremum) (most often)
2. Benefits from increased quality functionality.
3. There is a possibility of the current definition of the quality functional.
The control device in this case is called an optimizer or extreme regulator.
The quality functional for setting the operating mode is written:, where is the change, which determines the operating mode of the object.
Depending on whether the extreme static characteristic is stable or changes during the operation of the object, extreme systems are divided into two groups: - static; - dynamic.
Static: Here, extreme control is provided, corresponding to the extremum of the static characteristics of the object with constant parameters set for a given extremum point, and the system is similar to a conventional regime stabilization system.
Dynamic: Here the characteristic can shift independently and the extremum point too. In this case, two cases are possible:
It is known how the characteristic is shifted, and program control can be dispensed with;
The displacement of the most extreme characteristic and the extreme point is of a random nature (you must first find the optimal point, then move to it).
In extreme systems, when the extreme characteristic is shifted, there can be an automatic search for the extremum and a shift to it.
In such cases, two operations are carried out:
1. Trial search engine(Determination of the ratio between the current quality index Q and Q extr and determination of the direction of movement. Reduces to the determination of the slope of the characteristic:).
2. Working(works out the found values of changing the regulator setting to ensure the extremum of the function)
You can determine the magnitude and sign of the derivative or use a special stepwise method for finding an extremum.
Depending on whether an additional signal is used to search for an extremum, the systems are divided:
Systems without an additional search signal (depending on whether the slope S 0 is used in the formation of working operations or the sign of the derivative system is divided by proportional and relay(direction of movement is determined by the sign dx slave / dt = h 0 SignS = h 0 Sign, that is, the implementation of "independent search" and RO moves from one state to another and back, leading the object to the extremum of the static character Here the logic device switches when the sign of the derivative changes - this leads to a change in the setpoint of the regulator and the corresponding displacement of the regulator. They are used for low-inertia objects.). For inertial systems, the system is used. stepping type(here, at the command of the command generator through the step Dt, measuring the value of the quality indicator and comparing it with the given Q, as a result, the signal at the input does or does not reverse)
· System with add. Search. signal (a harmonic signal and a signal from a logical device are fed to the input. The search for an extremum is carried out on the basis of the study of the phase shift of the signal X n to the output of the system. The search signal in relation to the main one is the modulating signal.
Based on signal. X is superimposed harmoniously. search signal and if start signal. X resp. position to the left of the extremum point (X 1), then on out. extra. link, an additional search signal will create a harmonic. component Q * with the same f as the search signal and there will be no phase shift. Main signal X 3 - harmonic. state on out extras. link shifted rel. Search. signal at an angle –pi. Main signal X 2 - harmonic. state on out extras. the link will have f 2 times more than the original f. signal. That. by phase shift m.o. define. direction movement.
Multidimensional extreme systems. are constructed for multi-parameter objects that have several inputs and outputs, and one of the outputs has an extreme characteristic, and restrictions are imposed on the other outputs.
To build such extreme systems. use specials. methods of mat. programming and algorithmic. optimization methods.
The condition for an extremal function of several variables is the equality to zero of all its parts. derivatives with respect to parameters
In a particular case, if the generalized quality function Q is represented. extreme. static har-coy, then for design it is multidimensional. sist. m / b used the method of simplex planning, and in this case in the system. centuries device for comput. hail. extreme. har-ki and a device for forming. control signal.
The principle of constructing a device for calculating. hail. in the operation of finding an extremum depends on the method of determining. private derivatives and the type of algorithm used.
The most widely used methods are:
1.of course increments
2.time derivative
3.synchronous detection
4.applying an adaptive model
1. The finite increment method is based on replacing partial derivatives with a finite ratio. increments and defining it. In this case, the cord is alternately changed. control and comput. correspondence. it increments. yavl. components of the gradient of the function.
2. Also, the control actions are changed in turn and the quotient is calculated. derivatives and gradient functions.
Disadvantages 1 and 2: the need to alternately change control. influences and calculation of the gradient for each change of exercise. signal. This requires additional. time for calculation.
3. Control coordinates are modulated by add. harmonious. signals with different. amplitudes a ni and frequencies w ni. Number of detectors def. number independent coordinates defining the extremum of the function Q xi. Sync output signal detector. proportional to private derivative ... Because modulating signals are divided by frequency. spectrum, then made up. gradient def. parallel. With the use of a computer, this time will be MIN.
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1. Extreme control systems
Extreme control systems are such ACS, in which one of the performance indicators must be kept at the maximum level (min or max).
A classic example of an extreme control system is the automatic frequency control system of a radio receiver.
Figure 1.1 - Amplitude-frequency response:
1.1 Statement of the problem of synthesis of extremal systems
Objects are described by equations:
The extreme characteristic drifts in time.
It is necessary to select a control action that would automatically find the extremum and keep the system at this point.
U: extr Y = Y o (1.2)
Figure 1.2 - Static extreme characteristic:
It is necessary to determine such a control action that ensured the performance of the property:
1.2 Extremum condition
A necessary condition for an extremum is the equality to zero of the first partial derivatives.
A sufficient condition for an extremum is the equality to zero of the second partial derivatives. When synthesizing an extreme system, it is necessary to estimate the gradient, but the vector of the second partial derivatives cannot be estimated, and in practice, instead of a sufficient condition for an extremum, the following relation is used:
Stages of synthesis of an extreme system:
Gradient estimation.
Organization of movement in accordance with the condition of movement to an extremum.
System stabilization at the extremum point.
Figure 1.3 - Functional diagram of an extreme system:
1.3 - Types of extreme characteristics
1) Unimodal extreme characteristic of the module type
Rice. 1.4 - Extreme characteristic of the module type:
2) Extreme characteristic of the parabola type
Rice. 1.5 - Extreme characteristic of the parabola type:
3) In the general case, the extreme characteristic can be described by a parabola of the nth order:
Y = 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) Vector-matrix representation:
Y = y T By (1.10)
1.4 Methods for estimating gradient
1.4.1 Method of division of derivatives
Let us consider it on a unimodal characteristic, y is the output of the dynamic part of the system.
yR 1, Y = Y (y, t)
Find the total time derivative:
Drifting slowly this way
Dignity: simplicity.
Disadvantage: at small 0s, the gradient cannot be determined.
Differential filter.
Rice. 1.6 - Partial derivative scoring scheme:
1.4.2 Discrete Gradient Estimation
Rice. 1.7 - Scheme of discrete partial derivative estimation:
1.4.3 Discrete estimate of the gradient sign
With a small sampling step, we replace:
1.4.4 Synchronous detection method
The method of synchronous detection involves adding an additional sinusoidal signal of low amplitude, high frequency to the input signal to an extreme object, and extracting the corresponding component from the output signal. From the phase ratio of these two signals, one can conclude about the sign of the partial derivatives.
Rice. 1.8 - Functional diagram of partial derivative estimation:
Rice. 1.9 - Illustration of the passage of search oscillations to the system output:
y 1 - operating point, while the phase difference of the signals is equal to 0.
y 2 - the phase difference of the signals, as the simplest phase-frequency amplifier, you can use the multiplication block.
Rice. 1.10 - Illustration of the FCU operation:
As a filter, a filter averaging over a period is chosen, which makes it possible to obtain at the output a signal proportional to the value of the partial derivative.
Rice. 1.11 - Linearization of the static characteristic at the operating point:
Therefore, the equation of the extremal curve can be replaced by the equation of the straight line:
The signal at the output of the FPU:
k - coefficient of proportionality - the tangent of the angle of inclination of the straight line.
Filter output signal:
In this way:
The method of synchronous detection is suitable for determining not only one partial derivative, but also the gradient as a whole, while several oscillations of different frequencies are fed to the input. The corresponding output filters highlight the response to a specific search signal.
1.4.5 Custom Gradient Estimator Filter
This method involves the introduction of a special dynamic system into the system, the intermediate signal of which is equal to the partial derivative.
Rice. 1.12 - Scheme of a special filter for estimating a partial derivative:
T- filter time constant:
To estimate the total derivative of Y, a DF - a differentiating filter is used, and then this estimate of the total derivative is applied to estimate the gradient.
1.5 Organization of movement to the extremum
1.5.1 First order systems
We organize the control law in proportion to the gradient:
Let's write the equation of the closed-loop system:
This is a common differential equation that can be investigated using TAU methods.
Consider the equation of statics of the system:
If the stability of the closed-loop system is ensured with the help of the gain k, then automatically in statics we will come to the extremum point.
In some cases, using the coefficient k, in addition to stability, it is possible to provide a certain duration of the transient process in a closed system, i.e. provide the specified time for reaching the extremum.
Where k is stability
Rice. 1.13 - Functional diagram of a first-order gradient extremal system:
This method is only suitable for unimodal systems, i.e. systems with one global extremum.
1.5.2 Heavy Ball Method
By analogy with a ball that rolls into a ravine and overshoots points of local extrema, an AE system with oscillatory processes also overshoots local extrema. To ensure oscillatory processes, we introduce additional inertia into the first-order system.
Rice. 1.14 - Illustration of the "heavy" ball method:
Closed-loop system equation;
Characteristic equation of the system:
The smaller d, the longer the transient process.
Analyzing the extreme characteristic, the necessary overshoot and the duration of the transient are set, from where:
1.5.3 Single-channel systems of general type
Control law:
Substituting the control law into the control of the object, we obtain the equation of the closed-loop system:
In the general case, to analyze the stability of a closed-loop system, it is necessary to use the second Lyapunov method, with the help of which the gain of the controller is determined. Because The second Lyapunov method gives only a sufficient condition for stability, then the chosen Lyapunov function may turn out to be unsuccessful and a regular procedure for calculating the controller cannot be proposed here.
1.5.4 Systems with the highest derivative in control
General case of extremum of objects:
The functions f, B and g must satisfy the conditions for the existence and uniqueness of the solution to the differential equation. Function g - must be multiply differentiable.
С - matrix of derivatives
The synthesis problem is solvable if the product matrix is not degenerate, i.e.
Analysis of the solvability condition for the synthesis problem allows one to determine the derivative of the output variables, which explicitly depends on the control action.
If condition (1.31) is satisfied, then the first derivative is such a derivative, and therefore the requirements for the behavior of the closed-loop system can be formulated in the form of a differential equation for y of the corresponding order.
We will form the control law of the closed-loop system, for which we will form the control law, substituting it into the right side of the control for:
Closed-loop system equation with respect to the output variable.
Consider a situation where
With an appropriate choice of the gain, we get the desired equation and automatic exit to the extremum.
The parameters of the regulator are selected from the same considerations as for conventional ACS, i.e. (SVK) i = (20 * 100), which allows providing the corresponding error.
Rice. 1.15 - Scheme of a system with the highest derivative in control:
In the system, a differentiating filter is introduced into the system to estimate the total time derivative; therefore, it is convenient to use a gradient estimation filter to estimate gradients in such systems. Because Both of these filters have small time constants, then different-tempo processes can arise in the system, which can be distinguished using the method of separation of movements, and slow movements will be described by equation (1.34), which corresponds to the desired at. Fast motions need to be analyzed for stability, and depending on the ratio of the time constant of the DF and the filter for evaluating partial derivatives (FOCP), the following types of motions can be distinguished:
1) The time constants of these filters are comparable.
Fast motions describe the combined processes in these two filters.
2) The time constants differ by an order of magnitude.
In addition to slow motions, the system observes fast and super-fast motions corresponding to the smallest time constant.
Both cases need to be analyzed for sustainability.
2. Optimal systems
Optimal systems are systems in which target quality work is achieved through the maximum use of the facility's capabilities, in other words, these are systems in which the facility operates at the limit of its capabilities. Consider a first-order aperiodic link.
For which it is necessary to ensure the minimum transition time y from the initial state y (0) to the final y k. The transition function of such a system at K = 1 is as follows
Rice. 2.1 - Transient function of the system at U = const:
Let us consider the situation when we apply the maximum possible control action to the input of the object.
Rice. 2.2 - Transient function of the system at U = A = const:
t 1 - the minimum possible transition time y from the zero state to the final one for a given object.
To obtain such a transition, there are two control laws:
The second law is more preferable and allows to provide control in case of interference.
Rice. 2.3 - Block diagram of a system with a feedback-type control law:
2.2 Statement of the problem of synthesis of optimal systems
2.2.1 Mathematical model of the object
The object is described by state variables
Where the function f (x, u) is continuous, differentiable with respect to all arguments, and satisfies the condition for the existence and uniqueness of the solution to the differential equation.
This function is non-linear but stationary. As special cases, the object can be in the form of a nonlinear system with additive control:
Or a linear system
The object must be presented in one of the three forms presented above.
2.2.2 Multiple start and end states
The problem of the optimal transition from the initial state to the final state is the boundary value problem
Where the start and end points can be specified in one of the four ways shown in Fig. 2.4.
a) a problem with fixed ends,
b) a problem with a fixed first end (a fixed starting point and a set of end values),
c) a problem with a fixed right end,
d) a problem with moving ends.
Figure 2.4 - Phase portraits of the system's transition from the initial state to the final state for various tasks:
For an object, the set of initial states can generally coincide with the entire set of states or with the work area, and the set of final states is a subspace of the set of states or the work area.
Example 2.1 - Can an object described by a system of equations be transferred to any point in the state space?
Substituting into the second equation the value of U from the first equation u = x 2 0 - 2x 1 0, we get -5x 1 0 + x 2 0 = 0;
Got a set of final states described by the equation x 2 0 = 5x 1 0;
Thus, the set of final states specified for an object (system) must be realizable.
2.2.3 State and Control Constraints
Rice. 2.5 - General view of the working area of the state space:
The working area of the state space is highlighted, which is discussed. Typically, this area is described by its boundaries using modular conventions.
Fig.2.6 - View of the workspace of the state space, specified by modular conventions:
Also, U is set - the range of permissible values of the control action. In practice, the U region is also specified using modular ratios.
The problem of synthesis of an optimal controller is solved under the condition of constraints on control and a limited resource.
2.2.4 Optimality criterion
At this stage, the requirements for the quality of the closed-loop system are discussed. Requirements are set in a generalized form, namely in the form of an integral functional, which is called the optimality criterion.
General view of the optimality criterion:
Particular types of the optimality criterion:
1) an optimality criterion that ensures the minimum time of the transient process (the problem of optimal performance is being solved):
2) the criterion of optimality, ensuring the minimum energy consumption:
For one of the components:
For all state variables:
One control action:
For all control actions:
For all components (in the most general case):
2.2.5 Result form
It is necessary to stipulate in what form we will look for the control action.
Two variants of optimal control are possible: u 0 = u 0 (t), used in the absence of disturbance, u 0 = u 0 (x), optimal control in the form of feedback (closed-loop control).
General formulation of the problem of synthesis of an optimal system:
For an object described by state variables with given constraints and a set of initial and final states, it is necessary to find a control action that ensures the quality of processes in a closed system that meets the optimality criterion.
2.3 Dynamic programming method
1 Principle of Optimality
Initial data:
It is necessary to find u 0:
Rice. 2.7 - Phase portrait of the transition of the system from the initial point to the final point in the state space:
The trajectory of the transition from the start point to the end point will be optimal and unique.
Formulation of the principle: The final section of the optimal trajectory is also the optimal trajectory. If the transition from the intermediate point to the final one would not be carried out along the optimal trajectory, then it would be possible to find its optimal trajectory for it. But in this case, the transition from the initial point to the final one would pass along a different trajectory, which should have been optimal, and this is impossible, since there is only one optimal trajectory.
2.3.2 Basic Bellman Equation
Consider an arbitrary control object:
Consider a state-space transition:
Rice. 2.8 - Phase portrait of the transition of the system from the initial point to the final point x (t) - current (initial) point, x (t + Дt) - intermediate point.
Let's transform the expression:
Replace the second integral with V (x (t + Дt)):
For a small value of Δt, we introduce the following assumptions:
2) Expand the auxiliary function
Performing further transformations, we get:
Where min V (x (t)) is the optimality criterion J.
As a result, we got:
Divide both sides of the expression by Dt and remove Dt to zero:
We get the basic Bellman equation:
2.2.3 Calculated ratios of the dynamic programming method:
The main Belman equation contains (m + 1) - unknown quantities, since U 0 R m, VR 1:
Differentiating m times, we obtain a system of (m + 1) equations.
For a limited circle of objects, the solution of the resulting system of equations gives an exact optimal control. Such a problem is called the ACOR problem (analytical design of optimal controllers).
The objects for which the ACOR problem is considered must meet the following requirements:
The optimality criterion should 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) according to the optimality criterion:
Having analyzed the object for stability, we get:
U 0 = U 2 = -6x.
2.4 Pontryagin's maximum principle
Let us introduce an extended state vector, which we expand due to the zero component, as which we choose the optimality criterion. zR n + 1
We also introduce an extended vector of the right-hand sides, which we extend due to the function under the integral in the optimality criterion.
We introduce W - a vector of conjugate coordinates:
Let us form the Hamiltonian, which is the scalar product of W and q (z, u):
H (W, z, u) = W * q (z, u), (2.33)
Equation (2.34) is called the basic equation of the Pontryagin maximum principle, based on the dynamic programming equation. The optimal control is the one that delivers the maximum of the Hamiltonian over a given time interval. If the control resource were not limited, then the necessary and sufficient extremum conditions could be used to determine the optimal control. In a real situation, to find the optimal control, it is necessary to analyze the value of the Hamiltonian at the limiting value of the level. In this case, U 0 will be a function of the extended state vector and the vector of conjugate coordinates u 0 = u 0.
To find the conjugate coordinates, it is necessary to solve the system of equations:
2.4.1 The procedure for calculating the system according to the Pontryagin maximum principle.
The equations of the object should be reduced to the form standard for the synthesis of optimal systems:
It is also necessary to stipulate the initial and final states and write down the criterion of optimality.
An extended state vector is introduced
Extended vector of right-hand sides:
And a vector of conjugate coordinates:
We write the Hamiltonian as a dot product:
Find the maximum of the Hamiltonian with respect to u:
By which we determine the optimal control u 0 (Ш, z).
We write down the differential equations for the vector of conjugate coordinates:
Find the conjugate coordinates as a function of time:
6. Determine the final optimal control law:
As a rule, this method allows one to obtain a programmed control law.
Example 2.3 - For the object shown in Fig. 2.9. It is necessary to ensure the transition from the initial point y (t) to the final point y (t) in T = 1c with the quality of the process:
Rice. 2.9 - Object model:
To determine the constants b 1 and b 2, you need to solve a boundary value problem.
Let us write the equation of the closed-loop system
Let's integrate:
Consider the end point t = T = 1s., As x 1 (T) = 1 and x 2 (T) = 0:
1 = 1/6 b 1 + 1/2 b 2
Received a system of equations, from which we find b 2 = 6, b 1 = -12.
Let us write down the control law u 0 = -12t + 6.
2.4.2 Optimal control problem
For a general-type object, it is necessary to ensure the transition from the initial point to the final point in the minimum time with a limited control law.
Features of the problem of optimal performance
Speed Hamiltonian:
Relay control:
This is the case for relay objects.
The theorem on the number of switchings of the control action:
This theorem is valid for linear models with real roots of the characteristic equation.
Det (pI - A) = 0 (2.51)
Л (A) is a vector of real eigenvalues.
Theorem formulation:
In the problem of optimal performance 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 constancy intervals will not be greater than (n-1).
Rice. 2.10 - Type of control action for n = 3:
Example 2.4 - Consider an example of solving the problem of optimal performance:
W = [W 1, W 2]
H b = W 1 x 2 + W 2 (-2dx 2 -x 1 + u)
For - real roots:
The sum of the two exponents is:
If, then the roots are complex conjugate and the solution will be a periodic function. In a real system, switchings are not more than 5 - 6.
2.4.3 Switching surface method
This method allows us to find the control of the state variable functions for the case when the optimal control is of a relay nature. Thus, this method can be used to solve problems of optimal performance, for an object with additive control
The essence of the method is to select points in the entire state space where the control sign changes and combine them into a common switching surface.
Switching surface
The control law will be as follows:
To form the switching surface, it is more convenient to consider the transition from an arbitrary starting point to the origin of coordinates
If the end point does not coincide with the origin, then it is necessary to select new variables for which this condition will be true.
We have an object of the form
We consider the transition, with the criterion of optimality:
This criterion allows you to find a control law of the following type:
With unknown, the initial conditions are also unknown to us.
Consider the transition:
Reverse time method (backward motion method).
This method allows you to define switching surfaces.
The essence of the method lies in the fact that the start and end points are interchanged, while instead of two sets of initial conditions, there remains one for.
Each of these trajectories will be optimal. First, we find the points where the control changes sign and combine them into a surface, and then we change the direction of movement to the opposite.
EXAMPLE The transfer function of an object is:
Optimal performance criterion:
Restriction on control.
Consider the transition:
The optimal control will have a relay character:
Let's go backward (i.e.). In reverse time, the problem will look like this
Consider two cases:
We obtain the equations of the closed system:
We use the method of direct integration, we obtain the dependence on and since -, then we have
Because the start and end points are swapped, then we get the same thing:
Let us construct the result and, using the phase plane method, determine the direction
Applying the direct integration method, we get:
The function will look like:
Changing direction:
Sign change point (switch point).
General analytical expression:
Surface equation:
Optimal control law:
Substituting the equation for the surface, we get:
2.5 Suboptimal systems
Suboptimal systems are systems with properties close to optimal
It is characterized by the criterion of optimality.
Absolute error.
Relative error.
A process close to optimal with a given accuracy is called suboptimal.
A suboptimal system is a system where there is at least one suboptimal process.
Suboptimal systems are obtained in the following cases:
when approximating the switching surface (using piecewise linear approximation, approximation using splines)
When, an optimal process will arise in a suboptimal system.
limiting the workspace of the state space;
3. ADAPTIVE SYSTEMS
3.1 Basic concepts
Adaptive systems are such systems in which the parameters of the controller change following the change in the parameters of the object, so that the behavior of the system as a whole remains unchanged and corresponds to the desired:
There are two directions in the theory of adaptive systems:
adaptive systems with a reference model (ASEM);
adaptive systems with an identifier (ASI).
3.2 Adaptive systems with identifier
Identifier - a device for evaluating the parameters of an object (the evaluation of parameters should be carried out in real time).
AR - adaptive regulator
ОУ - control object
U - identifier
The part that is highlighted with a dotted line can be realized digitally:
V, U, X - can be vectors. The object can be multi-channel.
Let's consider how the system works.
In the case of constant parameters of the object, the structure and parameters of the adaptive controller do not change, the main feedback acts, the system is a stabilization system.
If the parameters of the object change, then they are estimated by the identifier in real time and the structure and parameters of the adaptive controller change so that the behavior of the system remains unchanged. The main requirements are imposed on the identifier (performance, etc.) and on the identification algorithm itself. This class of systems is used to control objects with slow nonstationarities. If we have a general non-stationary object:
;. The simplest responsive view will be as follows:
Requirements for the system:
Where and are matrices of constant coefficients.
In reality, we have:
If we equate, then we get the ratio for determining the parameters of the controller
3.3 Adaptive systems with a reference model
In such systems, there is a reference model (EM), which is placed parallel to the object. BA - adaptation block.
Fig 2 - ASEM functional diagram:
Consider the operation of the system:
In the case when the parameters of the object do not change or the output processes correspond to the reference, the error is:
auto-tuning control programming
The adaptation block does not work and the adaptive regulator is not rebuilt, the system has a smooth feedback.
If the behavior is different from the reference, this happens when the parameters of the object are changed, in which case an error appears.
The adaptation block is turned on, the structure of the adaptive regulator is rebuilt, in such a way as to reduce it to the reference model of the object.
The adaptation block must reduce the error to zero ().
The algorithm embedded in the adaptation block is formed in various ways, for example, using the second Lyapunov method:
If this is true, then the system will be asymptotically stable and.
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