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控制系统建模

A system can be described as one of the followings:

  • Differential equation
  • Difference Equation
  • Transfer Function
  • State Space

Differential Equation

Difference Equation

Transfer Function

  • Polynomial

  • Poles and Zeros

State Space

  • x as the state vector,
  • A as the system matrix (square, N x N for N states),
  • B as the input matrix (N rows x 1 column for a single-input, single output (SISO) system,
  • C as the output matrix (one row x N columns for a SISO system),
  • D as the feedforward matrix (1 x 1 for a SISO system).

  • (*) The poles of the transfer function are the eigenvalues of the system matrix A

Matlab Code

sys = ss(a,b,c,d)

sys = ss(a,b,c,d,Ts)

sys_ss = ss(sys)

Matlab functions

Transfer Function

s = tf('s')

feedback(G(s), H(s))

G = zpk(sys)

G = zpk([1],[1],[1])

Poles and Zeros

Find poles of a SISO or MIMO system: pole(sys)

pzplot(sys)

State Space

System Analysis

linearSystemAnalyzer(G,T1,T2)

step(sys)

Reference

  1. Control Tutorials, Inverted Pendulum: Digital Controller Design, University of Michigan