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
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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).
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(*) 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
- Control Tutorials, Inverted Pendulum: Digital Controller Design, University of Michigan