为无人驾驶汽车设计控制器

Question

我正在尝试解决与我的系统有关的一些问题（控制器和观察器设计），如下图所示：

问题是：

  

  

1. 设置阶跃响应的要求，例如建立时间，输出超调和静态误差。

  

2. 根据您的要求选择所需的极数。如果可能，请计算反馈矩阵K，以将极点放置在所需的极点上。

  

3. 模拟反馈系统的阶跃响应并计算参数   包括超调，建立时间和静态错误。如果系统不满足要求，请返回步骤2。

  

4. 系统的设计状态观察器。观测极的大小必须是系统极的2〜5倍。选择不同的观察者极点并比较观察者的表现。

  

我已经实现了解决这些问题的代码，但是不确定我的过程是否正确。您能检查我的实施吗？

MATLAB实现：

close all;
clear all;
clc
%% 1) Set a requirement for step response, like settling time, overshoot 
%and static error of output.
A=[0,1,0,0;0,-42.44,212.24,0;0,0,0,1;0,0,0,-42.44];
B=[0;106.12;0;78.6];
C=[1,0,0,0;0,1,0,0;0,0,1,0;0,0,0,1];
D=0;
sys = ss(A, B, C, D)
t=0:0.1:10;
figure;
step(sys,t,'r')

%The parameters including overshoot, settling time and static error.
S = stepinfo(sys)

%% 2)Select the desired poles according to your requirements. If possible, 
%calculate the feedback matrix K to place the poles to the desired poles.

eig(sys)
% Now we check the stability
rank(ctrb(sys))
%The desired poles
P = [-1; -2; -3; -3.2850]
K = place(A,B,P)

%% 3) Simulate step response of the feedback system and calculate the parameters
%%including overshoot, settling time and static error. If the system does not satisfy the
%%requirement, go back to step 2).

Acl = A-B*K
syscl = ss(Acl,B,C,D)
figure;
step(syscl,'g')
%The parameters including overshoot, settling time.
S = stepinfo(syscl)
title('Step response of feedback control system')
grid on

%% 4) Design state observer of the system. The magnitude of observer poles must be 2~5
%times of system poles. Select different observer poles and compare the performance
%of observers.

sys=ss(A,B,C,D)
eig(sys)
rank(obsv(sys))
% Observer pole placement at  -10 and -9
% This observer will lead to a fast approximation of the states
L_T=place(A',C',[-10,-9,-8,-7])
L=L_T'
% Observer pole placement at  -1 and -2
% This observer will lead to a slower approximation of the states
% L_anastrofos=place(a',c',[-1,-2])
% L=L_anastrofos'
% State observer Feedback
sys=ss(A,B,C,D)
eig(sys)
rank(obsv(sys))
rank(ctrb(sys))
K=place(A,B,[-5 -6 -7 -8])