How to manage cross-border complexity

List of contents of this article:

• 1,How to manage cross-border complexity What mathematical expression does the system mathematical model refer to
2, Commonly used What are the mathematical models of continuous systems
• 3, What does the mathematical model of the system mean
• 4, What are the mathematical models of discrete systems
• 5, What are the functions and common forms of mathematical models in the automatic control system
• 6, What does the mathematical model of the system mean? Mathematical expression

What does the system mathematical model mean?Mathematical expression

Systematic mathematical model, also known as mathematical simulation, refers to the evaluation of various environmental elements and processes involved on the basis of an objectively existing environmental system and a set of mathematical expressions between them.

The mathematical model of the control system is a mathematical expression that describes the relationship between physical quantities (or variables) within the system. Under static conditions (that is, the derivative of each order of a variable is zero), the algebraic equation that describes the relationship between variables is called a static mathematical model; and the differential equation that describes the relationship between the derivatives of each order of a variable is called a mathematical model.

The mathematical model of the control system is a mathematical expression that describes the internal physical quantities or variables of the system. To establish a mathematical model of the control system, please refer to the blogger's specific explanation in Signal and Linear System Analysis.

Time domain model - a mathematical expression that regulates the differential equation of the object and describes the relationship between the variables of the system, which is called the mathematical model of the system. It is expressed by t differential equations, differential equations and equations of state.

The mathematical model is a mathematical expression that describes the dynamic relationship between the physical quantities within the system. Commonly used mathematical models include: differential equations, transfer functions, frequency characteristics, differential equations and statespace expressions, etc.

What are the commonly used mathematical models of continuous systems

1. Normal distribution model: a continuous distribution whose shape is like a bell curve, which can describe the distribution of many phenomena in nature, such as height, body Wait again. Markov Chain Model: DrawingDescribe the evolution of state in time and is used in various applications, such as natural language processing, financial market analysis, etc.

2. The differential equation model is generally suitable for dynamic continuous models. When describing the process of the evolution of certain characteristics of the actual object with time or space, analyzing its laws of change, predicting its future nature, and studying its control means, it is usually necessary to establish a dynamic model of the object. Probability statistical model.

3. Continuous systems can be described by a set of differential equations. When the coefficient of a differential equation is constant, it is called a constant system, and when the coefficient changes with time, it is called a time-variable system. Mathematical models of this kind of system include continuous models (diferential equations, etc.), discrete time models (diferential equations, etc.) and continuous-discrete hybrid models.

4. NervousNetwork model: Neural network is a mathematical model that simulates the nervous system of the human brain, which can be used to simulate and predict complex nonlinear systems. Neural network models are widely used in image processing, speech recognition, intelligent control and other fields.

What does the mathematical model of the system mean

1. Systematic mathematical model, also known as mathematical simulation, refers to the evaluation of various environmental elements and processes involved and a set of mathematical expressions based on the objectively stored environmental system.

2. Static and dynamic models. Static models refer to the relationship between the quantities of the system to be described does not change with time, and is generally expressed by algebraic equations. A dynamic model refers to a mathematical expression that describes the laws that change over time between the quantities of the system, which is generally represented by differential equations or differential equations.

3. Mathematical modeling is to establish a mathematical model, and the process of establishing a mathematical model is the process of mathematical modeling. Mathematical modeling is a mathematical thinking method. It is a powerful mathematical means that can approximate and "solve" practical problems through abstraction and simplification by using mathematical language and methods.

What are the mathematical models of discrete systems

1. In the discrete model, there are hierarchical analysis model, benefit distribution model, gray evaluation model, election rule model, etc.

2. Discrete model: algebraic equations and differential equations, integer planning, graph theory, countermeasure theory, network theory, continuous system VS discrete system definition continuous system: the change of system state is continuous in time. Discrete system: Changes in system state only occur at a certain point in time.

3. The expressions of discrete systems include differential equations, state space method, Z transformation and Fourier transform (DTFT) of discrete time, etc. A discrete system refers to a system in which both input and output are discrete time signals, and its mathematical model is usually described by differential equations.

What are the functions and common forms of mathematical models in the automatic control system

Differential equation model: This is the most common automatic control system model, which uses differential equations to describe the system The relationship between input, output and state variables. For example, a simple first-order system can be expressed as dx/dt=ax+b, where x is a state variable and a and b are constants.

The equation of motion (also known as the mathematical model) of the control system is written according to the dynamic characteristics of the system, that is, through the laws of physics that determine the characteristics of the system, such as the basic laws of mechanics, electricity, heat, hydraulics, pneumatics, etc.

Using mathematical languages such as differential equations to describe the relationship between the output and the corresponding input is called establishing a mathematical model.The function of the mathematical model is to describe the characteristics of the accused object itself; the design and correction link quantitatively according to the characteristics of the accused object; it is used to analyze the performance indicators of the whole system as a criterion for judging whether the system meets the standard.

It is called a static model. There are many forms of dynamic mathematical models. The mathematical models commonly used in the time domain include differential equations and differential equations; there are transfer functions and structure diagrams in the complex domain; there are frequency characteristics in the frequency domain, etc.

A mathematical model of an electromechanical control system can have a variety of expressions, but usually chooses the form that best describes the dynamic characteristics of the system. In the electromechanical control system, commonly used mathematical models include transfer functions, state equations, frequency responses, etc.

What mathematical expression does the mathematical model of the system refer to?

The mathematical model of the system, also known as mathematical simulation, refers to the evaluation of various environmental elements and processes involved on the basis of the objective environmental system and the interconnection and action of a set of mathematical expressions between them.

The mathematical model of the control system is a mathematical expression that describes the internal physical quantities or variables of the system. To establish a mathematical model of the control system, please refer to the blogger's specific explanation in Signal and Linear System Analysis.

The definition is as follows. Time domain model - the differential equation that regulates the object, a mathematical expression that describes the relationship between the variables of the system, is called the mathematical model of the system. It is expressed by t differential equations, differential equations and equations of state.