The development of modern control theory, what is the difference between modern control theory and a

1. Differences: 1. The development time is different.

Modern control theory was developed under the impetus of the rapidly emerging space technology in the mid-50s of the 20th century.

2. The content is different.

Modern control theory can be divided into two types: conventional control and computer control according to the type of control device. Analog controllers (see control instruments) are used for conventional control, and electronic digital computers are used for computer control.

Automatic Control Theory: Linear System Theory, Nonlinear System Theory, Optimal Control Theory, Stochastic Control Theory and Limb Fiber Adaptive Control Theory.

2. Optimal control theory (optimal control theory) is a major branch of modern control theory, focusing on the study of the basic conditions and comprehensive methods to optimize the performance indicators of the control system. Optimal control theory is a discipline that studies and solves the problem of finding the optimal solution from all possible control schemes. It is an important part of modern control theory.

1. It is different in terms of mathematical models.

Classical control theory mainly uses ordinary differential equations, transfer functions and dynamic structure diagrams, which only describe the relationship between the input and output of the system, but cannot describe the internal structure of the system and the changes in the system, and ignores the initial conditions. Information about the internal state of the system cannot be fully described.

The mathematical model of modern control theory is usually described by state-space expressions or state variable diagrams, which are also called "internal descriptions" of the system, which can fully reveal the entire motion state of the system.

2. The foundation of the establishment is different.

Classical control theory is a branch of automatic control theory, which is based on the frequency response method and the root locus method. Modern control theory is a kind of control theory based on the state space method, which is a major component of automatic control theory.

3. The system is different.

The research object of the classical control-friendly group system theory is the automatic control system with single input and single output, especially the linear stationary system. The characteristics of classical control theory are to use the input-output characteristics (mainly transfer function) as the mathematical model of the system, and use the frequency response method and the root trajectory method to analyze the system performance and design the control device.

In modern control theory, the analysis and design of the control system is mainly carried out through the description of the state variables of the system, and the basic method is the time domain method. Modern control theory can deal with a much wider range of control problems than classical control theory, including linear and nonlinear systems, stationary and time-varying systems, univariate systems and multivariable systems.

4. Different methods.

The mathematical basis of classical control theory is the Laplace transform, and the dominant analysis and synthesis method is the frequency domain method. Modern control theory, the methods and algorithms it employs, are also more suitable for being carried out on digital computers. Modern control theory also opens up the possibility of designing and constructing an optimal control system with specified performance indicators.

5. The characteristics are different.

Classical Control TheoryThe research object of classical control theory is the automatic control system with single input and single output, especially the linear stationary system. Classical control theory is characterized by a mathematical model based on input-output characteristics.

Modern control theory contains a wide range of disciplines, including linear system theory, nonlinear system theory, optimal control theory, stochastic control theory and adaptive control theory.

There are differences between "modern control theory" and "classical control theory" in terms of research objects, mathematical modeling, and application fields.

Differences between classical and modern control theories:

First, in terms of research objects.

The control objects of classical control theory are mainly simple single-input-single-output linear stationary control systems. It is not possible to represent time-varying systems, nonlinear systems, and linear stationary systems under non-zero initial conditions.

Compared with classical control theory, modern control theory has a wider range of applications. Modern control theory uses a direct analysis method in the time domain to design an optimal control system for a given performance or comprehensive index.

Second, in terms of mathematical models.

Classical control theory mainly uses ordinary differential equations, transfer functions and dynamic structure diagrams, and only describes the relationship between the input and output of the lead oak system, but cannot describe the internal structure of the system and the changes in the system, and ignores the initial conditions. Information about the internal state of the system cannot be fully described.

The mathematical model of modern control theory is usually described by state-space expressions or state variable diagrams, which are also called "internal descriptions" of the system, which can fully reveal the entire motion state of the system.

Third, in terms of application fields.

Classical control theory is mainly used to solve various control problems in engineering technology, especially in aerospace technology, advanced control, communication technology, etc.

The current generation control theory considers the problem more comprehensively and more complexly, which is mainly manifested in the coupling between the system and the interference outside the system, but it conforms to the law from simple to complex. It can be said that the application field of automatic control covers many aspects of science and technology and life.

Summary. Modern control theory is based on mathematical theories, especially on mathematical methods such as linear algebra, calculus, ordinary differential equations, Laplace transform, and Fourier transform. These mathematical methods are applied to establish and study mathematical models of control systems in order to analyze and design the performance of control systems.

Some important concepts in modern control theory, such as state-space models, observer design, controller design, adaptive control, robust control, etc., are based on mathematical theories. Therefore, mastering mathematical knowledge is an important prerequisite for understanding and applying modern control theory.

Modern control theory is based on mathematical theories, especially on mathematical methods such as linear algebra, calculus, ordinary differential equations, Laplace transform, and Fourier transform. These mathematical methods are applied to establish and study mathematical models of control systems in order to analyze and design the performance of control systems. Some important concepts in modern control theory, such as the spatial model of the banquet state, observer design, controller design, adaptive control and concealment, robust control, etc., are all based on mathematical theories.

Therefore, mastering mathematical knowledge is an important prerequisite for understanding and applying modern control theory.

Can you elaborate on that a little bit more?

When we design a control system, we usually need to build a mathematical model to describe the behavior of the controlled object. This mathematical model can be in the form of differential dust equations, difference equations, state-space models, etc., and different forms of Pai Huijing models are suitable for different control problems. For example, differential equations are often used to describe continuous-time systems, difference equations are often used to describe discrete-time systems, and state-space models are more general and can describe continuous-time or discrete-time systems.

In control systems, it is often necessary to monitor the state changes of the controlled objects in real time, which requires the design of observers. The role of the observer is to estimate the state of the system through known input and output data, so as to realize the monitoring and control of the system. The controller is the core of the control system, and its role is to calculate the control signal and control the output of the controlled object.

The design of the controller can be based on classical control theory or modern control theory, and the commonly used controllers are proportional-integral derivative (PID) controllers, linear quadratic regulation (LQR) controllers, etc. Adaptive control is a control method for system parameter changes and external interference, and its advantage is that it can adaptively adjust the uncertainties of the system. Robust control emphasizes the robustness to uncertain factors, that is, it can still maintain a good control effect without knowing the system parameters.

The above are some of the important concepts of modern control theory, and the mathematical foundation is important because these theories are developed based on mathematical theories.