# 控制系统建模

A system can be described as one of the followings:

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

## 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)

### System Analysis

linearSystemAnalyzer(G,T1,T2)

step(sys)

## Reference

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