1, mathematical model:

The mathematical expression and final model describing the relationship between the output variables and the input variables of the system, regardless of the internal controller.

Modeling methods: analysis and calculation, mechanism modeling: f = ma.m = JW motor, etc. Engineering experiment methods: black box method, tracking point method and least square method.

Linear system: a system that satisfies the superposition principle; Non-linearity: the superposition principle (homogeneous sum and addition f(a+b)=f(a)+f(b), f(kx)=kf(x)) is not satisfied, and the responses to the two inputs cannot be calculated separately.

2. Linearization of nonlinear differential equations;

Determine the working point first. If the input changes in a large range, the small deviation method will inevitably bring greater errors.

Linearized differential equations are usually incremental equations.

3. Transfer function of control system:

The mathematical model of complex number domain is convenient to study the influence of system structure or parameter change on performance.

Transfer function of linear time-invariant system: under zero initial condition (the input of the system is t >；; 0 (when t = 0, the system input and all its derivatives are 0), and the system is in a steady state before the input acts on the system (when t = 0, the output and all its derivatives are 0). The ratio of Laplace transform of system output to Laplace transform of system input. N & gt=m, only zero state response;

4, the nature of the transfer function

Only applicable to linear time-invariant systems, defined under zero initial conditions.

N & gt=m (if m>n, this is a physically infeasible system); All coefficients are real numbers.

The transfer function is a mathematical description of the system; Transfer function representation: the functional relationship between input and output; Multi-input multi-output system can use transfer function matrix;

The transfer function represents the ability of linear time-invariant system to transfer and transform input signals, which is only related to the structure and parameters of the system, and has nothing to do with the form of input action.

5. Transfer function and differential equation

Different physical systems may have the same transfer function, but the same system may have different transfer functions; Similar systems: different physical properties, but the same transfer function;

6, unit pulse signal

Under the zero initial condition, the output under the action of unit pulse input is corresponding. Similarly, there is a unit step response.

In general, the order m of the numerator and the order n of the denominator of the transfer function satisfy n >；; =m

Why m>n is not feasible in practice? The energy is limited and the system has inertia.