While initial uncertainty, confusion, or anxiety are difficult to avoid, their impact on project execution can be minimized through a scientific and systematic approach. Returning to the issue of control algorithm design, these problems stem from two main reasons: firstly, we haven't thoroughly analyzed our primary challenges and lack a deep understanding of the essence of control algorithms within the context of control systems, as well as the fundamental ideas and principles of various control algorithms; secondly, we tend to assume the existence of a standard/reference control value algorithm that can perfectly solve our problems, lying dormant in a sea of literature, simply waiting to be discovered, thus blindly studying relevant materials.
It should be recognized that although there are many types of control algorithms, each algorithm is highly problem-specific and targeted at a specific controlled object. That is, each control algorithm was initially proposed to address a particular type of problem or a particular type of controlled object (which exhibits one or more main dynamic characteristics/problems). A "control algorithm" is essentially a man-made "dynamic system." The purpose of designing such a dynamic system is to ensure that, after interacting with the "controlled object" (the "dynamic system"), the "dynamic behavior" of the "entire controlled system," including the control algorithm, meets the target performance requirements (such as steady-state accuracy, bandwidth/rise time, tracking performance, and anti-interference capability), as shown in Figure 1. If the overall dynamic performance requirements of the controlled system are largely consistent, then it is clearly the main dynamic characteristics/problems exhibited by the controlled object that determine the final design of the control algorithm.
Figure 1 shows how the interaction between the control algorithm and the dynamic system of the controlled object ensures that the dynamic behavior of the entire controlled system meets the requirements.
Figure 2. Complex control theory and algorithms (Source: https://engineeringmedia.com)
Figure 1 offers profound insights into control algorithm design: Firstly, the choice of control algorithm should be based on its popularity and "advanced" status, not on the primary dynamic characteristics of the controlled target and the controlled object (see Control Algorithm Notes – What Makes Control Algorithms Complex?). Different fields (e.g., electromechanical, power electronics, power grids, chemical processes) exhibit different primary dynamic characteristics and face different main problems. A deep understanding of the actual process/operation and its associated dynamic behavior is essential; algorithms effective in one field cannot be easily applied to another. Secondly, the design, analysis, and implementation of control algorithms and the controlled object's (process/operation, structure) must be conducted within the framework of the entire control system, as the ultimate goal is to ensure the overall performance of the controlled system meets expectations. This requires collaborative design at the system level by engineers specializing in control, mechanical, and electrical engineering, and the development of intuition and insight into the impact of each subsystem/component on the overall system performance from a system dynamics perspective (e.g., how the dynamics of each subsystem/component affect the final dynamic performance, whether it dominates, and how to improve dynamic characteristics in advance through design to avoid adverse effects).
Therefore, the importance of system dynamics modeling and analysis must be emphasized in the design, learning, and development of control algorithms and control systems. Unfortunately, this area has long been neglected in China's control theory curriculum. Beginners only memorize concepts like transfer functions/state-space expressions and a bunch of design methods based on them, but they don't know how these formulas are derived in practice, why they are written in these forms, how the solutions relate to system dynamics performance, or how to effectively apply their knowledge to the problems they face, let alone develop new control algorithms to more effectively solve these problems. An unreasonable curriculum and a lack of connection to the real physical world make the learning/design of control theory seem "vague and unclear." So, can system dynamics modeling and analysis solve these problems in the process of designing/learning control algorithms?
Figure 3. First learn system dynamics modeling and analysis.
System dynamics modeling and analysis
Before answering the question above, it's important to note that control algorithms are always linked to dynamics/dynamic changes: the object of control algorithms is the actual dynamic system. These dynamic systems may be in physical fields such as mechanics, electricity, temperature, magnetism, light, sound, and fluid dynamics, or involve chemical reaction processes, exhibiting extremely rich and complex dynamic behaviors. Taming these rich and complex dynamic behaviors depends on a deep understanding and analysis of these behaviors. The goal of control algorithms is to ensure that the final dynamic behavior of the entire controlled system meets the expected requirements (these requirements can generally be described from three dimensions: stability, control accuracy, and dynamic responsiveness), so as to achieve automatic operation of the dynamic system without human intervention (note that this is not autonomous operation).
The implementation of control algorithms generally relies on various hardware platforms capable of numerical calculations. These hardware platforms collect the necessary information in real time in the form of signal sampling, process and calculate it, and then apply the dynamic calculation results/control commands to the controlled object.
Therefore, while control algorithms may seem complex, there are patterns to follow in their in-depth study: grasping the core of the dynamic system. Thus, "system dynamics modeling and analysis," which aims to model and analyze real-world dynamic systems, becomes particularly important. On one hand, it provides a consistent analytical framework for the analysis, design, and implementation of the entire control system (Figure 1), connecting the real physical world and the mathematical world (Control Algorithm Notes—Is Modeling Important?). On the other hand, the analysis results of the dynamic characteristics of the controlled object provide the premise and motivation for the design of control algorithms.
In learning control algorithms, the author believes that the approach should follow the sequence of "system dynamics modeling and analysis - basic control theory and control algorithm design methods - control algorithm implementation," as shown in Figure 3. "System dynamics modeling and analysis" takes actual dynamic systems as the research object, studying how to establish suitable mathematical models (including mechanistic and data models) to describe dynamic changes, how to obtain typical system dynamic behaviors based on these models (the solution of the model and the dynamic behavior are directly related), and how these typical dynamic behaviors affect the final control performance. "Basic control theory and control algorithm design methods" addresses how, for a given actual dynamic system and its typical dynamic behaviors, the design of control algorithms can tame rich/complex dynamic behaviors to meet human expectations and achieve control objectives. "Control algorithm implementation" considers how, in the era of digital computing, control algorithms from the mathematical world can be effectively implemented in the real physical world, and whether this implementation process affects the system dynamic behavior (e.g., sampling-computation delay, discretization effects, etc.).
Figure 3 shows the essential knowledge system, which only outlines the basic control theories, concepts, frameworks, and systems required for learning control algorithms. This lays a solid and accurate foundation for the "selective module knowledge system" (i.e., selective learning based on one's specific field and application scenario). Learning control algorithms should be gradual. Only after a thorough grasp of typical dynamic systems, their behavior, analysis methods, basic control theories, concepts, frameworks, and systems (the essential knowledge system in Figure 3) should one learn some "advanced control algorithms" (many of which do not escape these basic concepts and frameworks). Avoid being greedy and trying to learn everything at once, neglecting a deep understanding and in-depth analysis of real-world dynamic behavior, and plunging alone into the vast ocean of control theory.
Summarize
In the learning and practice of control algorithms, do not rush to learn/apply "advanced control algorithms". Instead, focus on mastering the system of modeling and analysis methods for system dynamics, analyzing the dynamic characteristics and main problems of your controlled object, and designing and deeply understanding any control algorithm, whether based on mechanistic models or data-driven. This is a very necessary step.
[Author Biography] Li Lei holds a PhD in Mechanical Engineering from Zhejiang University and was a visiting scholar at Georgia Institute of Technology (2016-2017). He currently works on the research and development of automation control algorithms. During his doctoral studies, he published several articles in journals such as IEEE TMech and TIE. He currently serves as a reviewer for international mechanical engineering journals such as TMech and IJIRA (International Journal of Intelligent Robotics and Applications).
