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Contents of this article IView:

• 1,OKX app Discreteization of state equations of continuous time systems
• 2, How to discrete and how to derive continuous functions
• 3, The steady-state error remains unchanged after the continuous system is discrete
4, The difference and connection between theoretical mechanics continuous system and discrete system

Discreteization of the state equation of continuous time system

discrete the continuous time signal, that is, after sampling and quantification, it is inevitable that there will be an overlapping phenomenon. Overlay means that after sampling and quantification, signal components higher than half of the sampling frequency will appear in the frequency range lower than half of the sampling frequency, resulting in overlapping of mutual interference.

The system loses stability. According to the query operation group, the continuous system is controlled by the continuous time controller. In the continuous control system, the controller and the controlled object are continuous, but in the discrete control system, the controller and the controlled object are time-discrete. Therefore, the system loses stability after the continuous system is discrete.

In order to further explain the continuous time signal and its discreteThe relationship between time representation can represent the transformation from continuous time to discrete time as a periodic sampling process, followed by a link that maps the shock string into a sequence, as shown in the figure below.

How to discrete and how to derive continuous functions

1. The first step : Discrete the definition domain.Divide the definition domain into several small intervals, and select a discrete point in each interval as the representative point of this interval. These discrete points are usually equidistant or randomly sampled. Step 2: Determine the function value at each discrete point.

2. Sampling the continuous signal can achieve continuous signal discrete. The continuous signal changes in some way in time (or space), while the sampling process measures the value of the continuous signal in time (or space) at intervals in T. T is called the sampling interval.

3. Step 1: Understand the definition of derivatives. The derivative represents the rate of change of the function. For a function f(x), its derivative at a point x can be expressed as f(x) or dy/dx. Step 2: Use the limit definition function f(x) The derivative at a point x can be obtained by the limit definition.

4. Derivation method: Derivation method is a method of derivation by using the basic derivation rules of a function to represent the function as an operation combination of basic functions. According to the basic derivative law, the fundamental function is derived.

5. Use numerical methods: For functions that cannot be solved by analytic methods, numerical methods (such as finite difference method and Newton-Lafson method) can be used to derive. These methods approximate the solution of derivatives by discrete function values and derivative values, which are suitable for complex nonlinear functions.

The steady-state error remains unchanged after the continuous system is discrete

1. When the system is overflowed from a steady state to a new steady state, or the system is disturbed and rebalanced, the system may have a deviation, and this bias The difference is called the steady-state error.A measure of the control accuracy of the automatic control system in steady state. The change of the output response of the control system after the transition process is called steady state.

2. Stability is the primary condition for the normal operation of the system. The stability of the system is completely determined by the structure and parameters of the system itself, and has nothing to do with the input of the system. The steady-state error of the system is the steady-state performance index of the system, which marks the control accuracy of the system. The time domain response of the system can be qualitative or quantitative. Analyze the dynamic performance of the system.

3. The first step: discrete the definition domain. Divide the definition domain into several small intervals, and select a discrete point in each interval as the representative point of this interval. These discrete points are usually equidistant or randomly sampled. Step 2: Determine the function value at each discrete point.

The difference and connection between the continuous system and the discrete system in theoretical mechanics

The input and output of the system are different. A continuous system is a type of system in which the input and output signals are the same at both ends. In discrete systems, both input and output signals are discrete signals. Variables change different nodes.

Discreteness: The state of the system only changes at the discrete time point, and the state remains unchanged between the two time points. Discontinuity: The state transition of the discrete time system occurs instantly, and there is no continuous state change.

The main aspects of the study of the differences between the two: the establishment and solution of mathematical models. The system performance analysis system realization principle. The continuous time system focuses on the study of one-dimensional variables, and the discrete time system pays more attention to the study of two-dimensional, three-dimensional or multi-dimensional technologies.

Same point: amplitude-frequency characteristic is an even function of frequency, and phase-frequency characteristic is an odd function of frequency. The difference is like the heart follows the floating clouds.