What Are Adaptive Systems?

An adaptive system is a control system that can modify its own characteristics to adapt to changes in the dynamic characteristics of objects and disturbances. This adaptive control method can be achieved: in the system operation, by continuously collecting control process information, determining the current actual working state of the controlled object, optimizing performance criteria, and generating adaptive control rules, so as to adjust the controller structure or Parameters, so that the system always works automatically in the optimal or sub-optimal operating state.

"Adaptive" generally refers to a system that adjusts itself in accordance with changes in the environment so that its behavior achieves the best or at least allowable characteristics and functions in a new or changed environment. This kind of adaptive to environmental changes A system of capabilities is called an adaptive system.

In both feedback control and optimal control, it is assumed that the mathematical model of the controlled object or process is known and has the characteristics of linear invariance. In fact, in many projects, the mathematical model of the controlled object or process is difficult to determine in advance. Even if the mathematical model is determined under a certain condition, its dynamic parameters and even the model are changed after the working conditions and conditions have changed. The structure still changes frequently. When these problems occur, conventional controllers cannot get good control quality. To this end, a special control system needs to be designed that can automatically compensate for unpredictable changes in model order, parameters, and input signals. This is

Since the first adaptive control system was proposed by the Massachusetts Institute of Technology in the late 1950s, many different forms of adaptive control systems have appeared. There are:

(1) Gain adaptive control

(2) Model Reference Adaptive Control (MRAC)

(3) Self-correction control (STC)

(4) Direct optimization of objective function adaptive control

(5) Fuzzy adaptive control

(6) Multi-model adaptive control

(7) Adaptive inverse control

Model reference adaptive control (MRAS) and self-tuning control system (self-tuning control system) are currently two mature types of adaptive control systems. One of the main characteristics of this type of adaptive system is to identify the parameters of the mathematical model of the object online, and then modify the parameters of the controller ^[1]

Application of Model Reference Adaptive Control System

One of the most successful applications of the MRAC system in the past is the field of electric drag. For example, the earliest applications were Courtial and Landau's adaptive control of thyristor-powered DC power drag systems. The use of conventional PI regulators for speed feedback control cannot guarantee the required high-performance indicators, but the adaptive control scheme can approximate the object to a second-order system, and only two parameters can be adjusted to ensure the performance indicators when the object parameters change It does not change and can overcome the dead time problem that PI regulator cannot solve when the motor speed crosses zero.

MRAC technology is also very active in automata, which can basically solve the problem of non-linearity and interference between automata. MRAC technology is also very successful in the application of ship autopilot. It can reduce the non-linear model to a second-order linear model. In this way, when the external environment (wind, waves, currents, etc.) changes, the dynamic characteristics of the ship vary with draught and load. When the water depth changes, the autopilot with adaptive control can achieve the required performance, and the operation is safe and reliable. In addition, MRAC technology is also used in other fields, such as internal combustion engines, oxygen-blowing steelmaking furnaces, and hydraulic servo systems.

Application of self-tuning control system

At present, self-calibration control systems are applied much more than MRAC. Except for papermaking, chemical industry, titanium dioxide kiln, cement industry, ore crushing, single crystal furnace cylinder boiler, etc., random interference is overcome in the automatic cruise of super cruise ships and automatic driving of ships, such as Wind, wave, tide, speed, load and water depth also work well. At the same time, there are also successful examples of applications in the atomic energy industry, robotics and artificial heart sectors.

Stability problem

The problem of stability is the core issue of all control systems. The design of adaptive control system should be based on the principle of ensuring the overall stability of the system. It has been found that the existing stability theory cannot deal with some of the adaptive control problems that have been proposed, and a new stability theory system M needs to be established.

Convergence problem

When an adaptive control algorithm is proven to converge, it can increase the credibility of the algorithm in practical applications. Due to the non-linear characteristics of adaptive algorithms, it is difficult to establish convergence theory. At present, only a limited number of simple adaptive control algorithms have obtained certain results. Moreover, the existing convergence results are too limited, and assumptions are too restrictive, which is not convenient for practical application. Even the most basic requirements for ensuring the convergence of parameter estimates may not always be satisfied for actual systems. The theoretical study of convergence needs further study.

Robustness problem

In the presence of disturbances and unmodeled dynamic characteristics, the ability of the system to ensure its stability and certain dynamic performance is called the robustness of the adaptive control system. Disturbances can cause serious drift of system parameters, leading to system instability, especially in the presence of unmodeled high-frequency dynamic characteristics. If the command signal is too large or contains high-frequency components, or there is high-frequency noise, or If the adaptive gain is too large, the adaptive control system may lose stability. At present, several different schemes have been proposed to overcome the instability caused by the above reasons, but they are far from satisfactory. An important theoretical research topic in the future is to design a robust adaptive control system.

Performance and stability issues

The good work of an adaptive control system not only requires the designed system to be stable, but also to meet certain performance requirements. Since the adaptive control system is a non-linear time-varying system, its initial condition changes or is not modeled, and its dynamic existence is bound to change the system's motion trajectory. Therefore, it is extremely difficult to analyze the dynamic quality of adaptive control systems. At present, results in this area are rare ^[2] .