1, state equation: describes the changing law of the internal state of the system. It is usually a set of first-order differential equations, which represents the relationship between the change rate of system state and the current state and input.
2. Output equation: describes the relationship between the output of the system and the internal state and input. It defines which state variables can be used as the output of the system, and gives the functional relationship between output and state and input.
3. A complete state space model can be expressed in the following mathematical form: dx/dt=Ax+Bu, y=Cx+Du, where X is the state vector, U is the input vector, Y is the output vector, and A, B, C and D are the corresponding coefficient matrices. The model includes state equation and output equation, which provides a powerful tool for us to deeply analyze and control the system.
4. The state equation describes the changing law of the internal state of the system, which is usually a differential equation or difference equation about the state variables of the system. In the state space model, state variables represent the internal state of the system, and its changing law is described by the state equation.
5. The output equation describes the relationship between system output and system state, which is usually an equation about system output variables. In the state space model, the output variable represents the information output by the system through a specific output channel, and its value is determined by the output equation.
6. Through the state equation and output equation, the dynamic behavior and output response of the system can be described comprehensively. These equations play an important role in the analysis and design of control system, which can help us understand and predict the behavior of the system and design appropriate control strategies to control the behavior of the system.
The role of state space model
1. State space model is a mathematical model to describe dynamic systems. Based on the concept of state space, it describes the dynamic behavior of the system by describing its state variables and output variables.
2. Analysis and synthesis: State space model is the basis of analyzing and synthesizing the system by applying modern control theory. By establishing the state equation and output equation of the system, we can fully understand the dynamic characteristics of the system, analyze the stability and controllability of the system, and design an appropriate controller to control the system behavior.
3. Control and optimization: The state space model can be conveniently used for the design and analysis of the controller. By modeling the state variables of the system, we can design a controller that meets specific performance indicators, such as an optimal controller. In addition, there are many control design methods based on state space model, such as state feedback control and optimal control.
4. System simulation: By establishing the state space model of the system, the system can be simulated and analyzed. By simulating the dynamic behavior of the system, we can predict the response of the system under different conditions, evaluate the performance of the system and optimize the design of the system.
5. Fault diagnosis and prediction: State space model can be used for fault diagnosis and prediction of the system. By monitoring and diagnosing the state variables of the system, we can identify the failure modes and causes of the system and predict the future performance and behavior of the system.
6. Modeling of nonlinear systems: State space model can be used for modeling and analysis of nonlinear systems. Through proper linearization or approximate treatment of nonlinear system, the state space model can be established, and then analyzed and synthesized.