Engineers often face many challenges when designing control algorithms, such as:
With so many different control algorithms available, which one should I choose, or which algorithm is best suited for my application?
Is it necessary to master all these control algorithms so that they can be used at any time? But control theory seems to consist of a lot of complex mathematical formulas, which looks boring and difficult to learn.
Even if I learn these control algorithms, how will I use them in practice, or will I even be able to actually use them? Maybe PID is still the best choice.
Regarding the above issues, let me first state the author's personal opinion:
No single control algorithm is suitable for all situations; each control algorithm was initially developed to address a specific type of problem. Therefore, it's crucial to first carefully analyze your controlled object to determine which specific problem(s) it falls under. Then, understand which control algorithm is best suited for your specific problem, allowing you to quickly select the appropriate algorithm.
In my opinion, it's unnecessary for engineers to master the mathematical derivations behind every control algorithm, and they typically don't have the time or energy for it. Engineers only need to understand the purpose of each control algorithm, the problem it addresses, the assumptions made, the basic ideas and framework, and typical applications. This is also the goal of the Control Algorithm Notes series.
While PID control achieves relatively reasonable performance in over 90% of applications due to its simplicity and universally applicable principles, it is also too crude. For some high-performance applications, PID may simply fail to meet performance requirements, making it essential to surpass PID. In practice, many advanced control algorithms have been successfully applied, with performance indicators far exceeding those of PID. Therefore, understanding other types of control algorithms remains necessary, helping engineers recognize which design approaches can surpass PID and truly achieve high-performance control systems.
When selecting a suitable control algorithm, before delving into the technical details of the algorithm design, the first step is to understand, accurately describe, and analyze the controlled system. Then, summarize the main/critical problems of the controlled system, identify its category, and determine how to mathematically describe them. In other words, first create a problem description and statement, then perform formulation. If your problem, after formulation, can be transformed into a standard problem of a certain type, the remaining task is to use mathematical tools to solve it.
Intuitive and clear description of the controlled system
It should be recognized that control algorithm design involves the entire controlled system. This controlled system encompasses a series of factors, including the specific working process, mechanical, electrical, signal (acquisition, transmission, and processing), numerical calculation, and software implementation. Therefore, control algorithm design is not merely the responsibility of control algorithm engineers but should be viewed from a system-level perspective. Often, the hardware of the controlled system determines the performance ceiling achievable by the control algorithm at the software level. For example, some controlled systems with large inertia/long time delays cannot achieve rapid dynamic response, and low-performance controller hardware is unlikely to implement computationally intensive, high-performance control algorithms. Based on this understanding, the analysis of the controlled system should involve all of the above levels.
What is it—what is the working process of the controlled system?
What is the working/process of the controlled system? Is it a physical (mechanical, electrical, hydraulic, magnetic, acoustic, optical, temperature, etc.) or chemical (reaction) process? How is this process implemented? What is its position in the overall working process/device (does it interact with other subsystems and receive signals from other systems? Is it affected/interfered with by external systems)?
What do you want—what do you want the controlled system to do?
To ensure the automation of this process, what does the controlled system need to do? Is it to control position/force, or temperature/liquid level? Are the control commands fixed or variable, and what are the specific control indicators (tracking or disturbance rejection? Is steady-state accuracy required, dynamic response, or interference rejection, consistency, and repeatability)?
What is included? What components make up the controlled system, and how are they connected?
Generally speaking, a complete control system comprises four parts: the controlled object, the actuator, the sensing system, and the controller (hardware), as shown in Figure 1. The solid lines represent the actual physical hardware, while the dashed lines represent various control and signal processing algorithms and logic flows at the software level. Each component in Figure 1, the connections between components, and the interaction with the environment all present multiple possibilities in reality and must be carefully described and analyzed.
Figure 1. Composition of the controlled system
Controlled object
This refers to specific physical/chemical processes. For example, in a robotic arm control system, the controlled object is a mechanical motion system composed of multiple links; in a temperature control system, the controlled object is a process of heat conduction/convection/radiation. Engineers should possess relevant knowledge of system dynamics analysis and modeling to analyze the characteristics of the controlled object: whether the system is low-order or high-order (generally, the number of independent energy storage elements in a system is the system order), whether it changes rapidly or slowly, what the dominant (dynamic) characteristics are under different operating conditions, whether there are unknown parts or dynamics that are difficult to describe accurately in mathematical language; whether it is a single-input single-output system, a multi-input multi-output system, or an infinite-dimensional system (such as some physical field control problems); whether different inputs and outputs affect each other; whether the relationship between inputs and outputs is linear or nonlinear (dead zone, hysteresis, etc.), whether it is a minimum-phase system, whether the relationship parameters change with time (if so, whether they change rapidly or slowly); whether there are external disturbances affecting the controlled object, how they affect it, whether the disturbance is deterministic or has a certain pattern (such as periodicity), or whether it is unknown/complex nonlinear.
Actuator
An actuator is a mechanism that executes control commands and applies them to a controlled object. In robot control systems, actuators are typically joint actuators composed of motors/electromagnetic/electrohydraulic actuators and transmission mechanisms. In temperature control systems, actuators may be heating wires, coolers, heat exchangers, etc. Analysis is needed on: how the actuator's output affects the output/controlled variable (directly or through intermediate transmission/transmission mechanisms); what kind of inputs the actuator accepts, its output characteristics, and how the input and output are related (e.g., actuator frequency response/bandwidth, presence of dead zones, saturation, hysteresis, or other nonlinear characteristics, presence of unpredictable interference factors such as friction forces, and changes in specific parameters, etc.).
Sensing system
These are components capable of sensing the system's state/changes in real time, typically various sensors and corresponding signal acquisition, transmission, and processing systems. Analysis is needed to determine: which signals in the controlled system can be acquired, their relationship to the controlled variable (directly controlled variable or correlated variable), and whether all states/changes can be acquired; what sensors are used to acquire signals, where are they installed, what type of signal is acquired, and what are their measurement accuracy/resolution and dynamic response; how are signals sampled (multi-sampling), what is the sampling rate, how are the acquired signals transmitted (bus or I/O), and what is the noise level during acquisition (is it affected by power frequency or random interference), etc.
controller
This refers to the component that runs the control algorithm and calculates control commands in real time, mainly consisting of various control chips (such as microcontrollers, PLCs, DSPs, FPGAs, etc.). Analysis is needed on: the controller's specific hardware configuration and corresponding computing and storage capabilities, such as whether it supports floating-point operations, its processing speed and time; what external signals the controller needs to accept and how it adjusts related operating processes; the specific implementation form of the control algorithm, the language used, and its real-time performance; how it connects to actuators and sensing systems, and whether these connections introduce noise and latency.
Engineers should describe the controlled system intuitively (without any preconceived notions or assumptions) and clearly from the above dimensions (it is recommended to create a checklist document). This is the first and crucial step in designing a suitable control algorithm.
Analyze the characteristics of the controlled system and select a suitable control algorithm.
Based on an intuitive and clear description of the controlled system, the characteristics of the controlled system are analyzed in depth, and the main problems of the controlled system are summarized (i.e., grasping the principal contradiction and the principal aspect of the contradiction). Then, using mathematical language, this main problem is described as having been mathematically reduced to a specific type of problem; further, based on the main problem faced, a suitable control algorithm is selected/designed. The general principle is that the characteristics of the controlled system and the basic ideas and structure of the control algorithm should match.
Unfortunately, due to the wide range of fields involved in control algorithms, the diverse specific situations and main problems of the controlled systems, and the vastly different performance requirements and real-world conditions, it is difficult to strictly declare that a particular control algorithm should be used for a specific type of problem. A rough approach is to categorize control algorithms into two methodologies based on whether an accurate model of the controlled system is readily available: model-based and data-driven. The Control Algorithm Notes series has introduced several typical methods, which the author will continue to update; they will not be discussed in detail here.
Summarize
The first step in control algorithm design should be to understand and deeply analyze the controlled system, and then select/design a suitable control algorithm based on the problem being addressed. In other words, everything should start from the actual problem, rather than the other way around, starting from the complex concepts/algorithms in control theory to assume/simplify the actual problem, which would lead to the embarrassing situation where the designed control algorithm cannot be implemented. In practice, because control algorithms deal with system-level problems, the situations are diverse. Engineers should not be limited by various concepts, designing the algorithm according to the form/structure of the problem, even if there may be no similar concept/use in theory. On the other hand, the value and rigor of theoretical research should not be ignored, nor should the application of mathematical tools and theoretical analysis be downplayed, returning to the idea that control theory is useless and everything is PID. Influenced by my mentor, I believe that good control practice should be a perfect combination of strong physical concepts and mathematical tools, that is, finding appropriate mathematical tools to describe and solve problems based on a deep understanding of the problems in the real physical world. Specifically, in the design of control algorithms, system dynamics analysis and modeling, as tools connecting the physical and mathematical worlds, are particularly important.
Many people find control theory difficult when they first learn it, feeling it's just about memorizing formulas and not knowing how to apply them. I believe a major reason for this is the unreasonable curriculum structure, lacking a prerequisite course in system dynamics. In fact, the difficulty stems from the flawed course design and textbook writing. For example, introducing Laplace transforms, reverse block diagrams, and transfer functions right from the start can easily confuse beginners, turning what should be a technical course into a theoretical one focused on memorizing formulas. Based on my experience studying abroad, the curriculum structure I observed started with System Dynamics, explaining how to describe various dynamic systems (such as electrical, thermal, magnetic, mechanical, and fluid systems), how to model these systems, and how to use the Laplace transform to solve the differential equations involved in the models. After clarifying these concepts, transfer functions, typical transfer functions and time-domain responses, feedback closed-loop systems, and the concept of stability were introduced. Finally, some simple design examples from classical control theory were presented. With this foundation, learning control theory becomes much more logical and natural.
[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).
