There are many types of automatic control systems, and the completion of the function is more different, and some are used to control the temperature change, and some have to track the flight trajectory of the aircraft. However, all systems have a common feature to work normally, that is, to meet the requirements of stability. What is stability? We can understand the concept of stability through a simple example. As shown in the figure below, a steel ball is placed on different two wooden blocks, and a diagram is placed on top of the wooden block, and the B is placed on the bottom of the wooden block. If a force is applied to the steel ball in the figure, the steel ball will leave the original position. The steel ball of the A figure will fall down, and it will not return to the original position. The steel ball in the B figure will be rolled back and forth in the bottom of the wood block. When the time is long enough, the ball is ultimately returned to the original position. Stability can be defined: when one When the actual system is in a balanced state (it is equivalent to the state of the ball placed on the wooden block) If it is affected by the external effect (equivalent to the force applied to the ball in the above example), the system has passed a transition process It is still able to return to the original balance, we call this system stable, otherwise the system is unstable. A control system must be stable if you want to achieve the required control functions. In actual applications, there is an energy storage element in the system, and each component is inertia. This is when the input of a given system, the output is generally swung between the desired output. The system will absorb energy from the outside world. For stable system oscillations, the oscillation is an increased oscillation for unstable systems. The former will balance in a state, but the latter will continue to increase until the system is damaged. Since stability is very important, how can you know if the system is stable? Controllers give us a lot of determination theorem for stability or not. These theorems are based on the system's mathematical model. According to the form of the mathematical model, it can conclude that the conclusions of stable or not, these theorems are known: Rolls criterion, Helsuditz criterion, Li Yacuf husband three theorem. These stability discriminant methods are respectively suitable for different mathematical models, and the prior to determine whether the system is stable by determining whether the feature value of the system is less than zero, the latter is mainly determined by examining whether the system energy is attenuated. Stability. Of course, the stability of the system is only a basic requirement for the system, and one other satisfactory control system must also meet many other indicators, such as transition time, ultra-demand, steady-state error, adjustment time, and the like. A good system is often a comprehensive consideration of these aspects.
