残差法定出系统的阶数(系统辨识)
系统辨识与自适应控制实验报告
——定阶
姓名:李岱
专业:电气[专研]
学号:[1**********]01
某线性系统的一组输入输出数据 实验要求:定出系统的阶数
数据(300组):
Y(0)-Y(299):
(0,1.09,0.45,0.86,2.26,2.57,2.11,2.81,3.41,2.77,3.48,3.25,3.06,4.9,3.55,4.13,5.33,4.17,4.97,5,3.63,3.63,4.01,4.12,3.21,4.31,4.86,3.21,3.22,3.88,3.51,4.06,4,3.77,3.39,4.28,2. 28,4.56,2.72,3.49,4,4.34,2.39,3.76,2.65,3.33,3.2,2.42,4.52,2.67,4.3,3.49,2.93,4.38,3.53,4.75,4.22,3.87,3.7,3.27,4.53,4.57,2.42,5.31,4.98,3.09,6.05,5.12,5.56,5.89,4.37,6.24, 4.48,3.55,3.97,5.26,3.93,4.4,4.94,4.12,4.93,4.58,3.77,3.78,4.18,2.88,3.89,4.43,3.62,3. 78,6.08,4.82,4.51,5.54,6.38,4.04,3.83,5.27,3.15,3.58,4.99,3.13,3.31,3.32,2.82,3.98,3.06,3.01,4.6,2.55,2.65,4.9,2.32,4.97,4.35,3.52,3.77,5.37,2.9,3.71,5.02,3.72,2.98,5.35,3.34,3.42,3.11,3.44,3.75,3.6,4.25,4.45,3.99,4.12,3.41,5.1,3.72,3.59,3.84,3.02,3.79,3.6,4,4.01,3.32,4.39,2.57,3.38,4.38,2.84,2.99,4.03,3.06,2.57,4.48,2.37,4.18,5.03,2.25,5.05,4. 91,3.75,3.68,6.05,5.34,4.97,4.67,5.25,3.26,2.89,4.04,3.51,4.53,3.67,4.08,4.92,5.38,2.88,6.18,4.61,4.41,6.57,4.96,5.8,6.28,5.36,5.66,4,5.14,5,3.1,3.81,3.9,3.79,3.19,2.86,5.2, 4.42,4.88,4.83,6.39,4.9,6.12,6.32,5.05,6.97,5.41,5.97,5.24,6.43,4.58,6.3,6.21,5.12,6.05,5.78,6.42,6.14,7.21,4.82,6.5,5.91,4.68,7.02,4.31,4.93,6.48,4.46,3.85,6.47,4.43,5.41, 4.65,4.1,4.19,3.73,4.41,3.36,3.91,2.91,3.64,3.84,4.98,3.05,5.41,4.21,2.99,5.07,5.4,4.1, 4.63,5.93,5.13,3.48,5.06,5.67,3.43,5.07,6.22,4.02,5.18,5.49,3.51,5.06,4.44,4.28,5.31,4.46,4.26,4.5,4.64,3.95,3.95,4.49,3.49,4.56,4.81,3.44,3.11,3.96,4.46,4.49,5.1,4.99,3.44, 4.87,4.85,4.08,4.96,3.57,4.86,5.32,5.49,6.03,5.88,6.36,5.27,4.74,5.81,5.59)
U(0)-U(299)
(0.45,0.49,0.48,1.61,1.86,1.02,0.74,0.73,1.14,1.25,0.62,0.8,1.91,0.81,1.23,1.27,1.02,1.67,1.26,0.47,0.57,1.26,1.15,1.11,1.42,1.63,0.26,0.46,0.54,0.93,1.31,0.74,0.84,0.3,1.23,0.16,1.8,0.07,1.02,1.24,1.72,0.17,0.6,0.28,1.16,1.2,0.44,1.94,0.71,1.89,0.91,0.02,1.21,1.27,1.44,1.47,0.26,0,0.47,1.76,1.47,0.2,1.59,1.61,0.61,1.96,1.74,1.96,1.34,0.47,1.79, 0.66,0.15,0.5,1.82,1.2,0.74,1.07,0.71,1.21,1.52,0.59,0.06,0.72,0.04,1.25,1.24,0.69,0.77,1.95,1.27,1,1.13,1.99,0.6,0.05,0.93,0.18,0.66,1.3,0.4,0.39,0.57,0.79,1.49,0.91,0.4,1. 77,0.29,0.31,1.98,0.21,1.93,1.08,0.66,0.58,1.7,0.75,0.94,1.79,0.64,0.36,1.58,0.33,0.8, 0.21,0.4,1.33,1.01,1.29,1.33,0.68,0.81,0.31,1.8,0.45,0.7,0.28,0.47,1.56,1.14,1.74,1.21, 0.56,1.09,0.03,0.32,1.69,0.44,0.25,1.33,0.93,0.4,1.5,0.02,1.84,1.49,0.09,1.37,1.2,1.08, 0.36,1.87,1.95,1.5,0.4,0.43,0.18,0.1,1.29,1.23,1.87,0.56,0.65,1.66,1.88,0.22,1.95,0.83, 1.22,1.98,0.73,1.38,1.39,0.94,0.91,0.16,1.16,1.53,0.14,0.39,0.63,1.19,0.47,0.33,1.91,1.84,1.72,0.98,1.91,1.26,1.48,1.97,0.42,1.89,0.98,1.08,0.72,1.59,0.9,1.54,1.67,0.56,1.63,1.19,1.88,1.95,1.98,0.29,1.44,1.23,1.14,1.99,0.26,0.84,1.82,0.57,0.61,1.48,1.12,1.84,0.33,0.17,0.27,0.94,1.25,0.8,0.69,0.15,0.49,0.93,1.97,0.42,1.47,0.55,0.11,1.15,1.93,0. 81,1.19,1.69,1.78,0.31,0.97,1.54,0.86,1.14,1.69,0.42,1.57,0.84,0.47,1.13,1.11,0.86,1.76,0.85,0.67,0.58,0.99,0.89,0.22,1.55,0.21,1.76,1.52,0.61,0.11,1.08,1.91,1.77,1.94,0.96,0.09,1.08,1.85,1.19,0.9,0.32,0.93,1.86,1.85,1.87,0.84,1.8,0.5,0.21,1.57,1.51,1.33)
按照品质指标“残差平方总和”定出系统的阶数: (一)一阶系统
clear all;
y=[0,1.09,0.45,0.86,2.26,2.57,2.11,2.81,3.41,2.77,3.48,3.25,3.06,4.9,3.55,4.13,5.33,4.17,4.97,5,3.63,3.63,4.01,4.12,3.21,4.31,4.86,3.21,3.22,3.88,3.51,4.06,4,3.77,3.39,4.28,2.28,4.56,2.72,3.49,4,4. 34,2.39,3.76,2.65,3.33,3.2,2.42,4.52,2.67,4.3,3.49,2.93,4.38,3.53,4.75,4.22,3.87,3.7,3.27,4.53,4.57,2.42,5.31,4.98,3.09,6.05,5.12,5.56,5.89,4.37,6.24,4.48,3.55,3.97,5.26,3.93,4.4,4.94,4.12,4.93,4.58,3.77,3.78,4.18,2.88,3.89,4.43,3.62,3.78,6.08,4.82,4.51,5.54,6.38,4.04,3.83,5.27,3.15,3.58,4.99,3.13,3.31,3.32,2.82,3.98,3.06,3.01,4.6,2.55,2.65,4.9,2.32,4.97,4.35,3.52,3.77,5.37,2.9,3.71,5.02,3.72, 2.98,5.35,3.34,3.42,3.11,3.44,3.75,3.6,4.25,4.45,3.99,4.12,3.41,5.1,3.72,3.59,3.84,3.02,3.79,3.6,4, 4.01,3.32,4.39,2.57,3.38,4.38,2.84,2.99,4.03,3.06,2.57,4.48,2.37,4.18,5.03,2.25,5.05,4.91,3.75,3.68,6.05,5.34,4.97,4.67,5.25,3.26,2.89,4.04,3.51,4.53,3.67,4.08,4.92,5.38,2.88,6.18,4.61,4.41,6.57,4. 96,5.8,6.28,5.36,5.66,4,5.14,5,3.1,3.81,3.9,3.79,3.19,2.86,5.2,4.42,4.88,4.83,6.39,4.9,6.12,6.32,5.05,6.97,5.41,5.97,5.24,6.43,4.58,6.3,6.21,5.12,6.05,5.78,6.42,6.14,7.21,4.82,6.5,5.91,4.68,7.02,4.31,4.93,6.48,4.46,3.85,6.47,4.43,5.41,4.65,4.1,4.19,3.73,4.41,3.36,3.91,2.91,3.64,3.84,4.98,3.05,5.41,4.21,2.99,5.07,5.4,4.1,4.63,5.93,5.13,3.48,5.06,5.67,3.43,5.07,6.22,4.02,5.18,5.49,3.51,5.06,4.44, 4.28,5.31,4.46,4.26,4.5,4.64,3.95,3.95,4.49,3.49,4.56,4.81,3.44,3.11,3.96,4.46,4.49,5.1,4.99,3.44,4.87,4.85,4.08,4.96,3.57,4.86,5.32,5.49,6.03,5.88,6.36,5.27,4.74,5.81,5.59];
u=[0.45,0.49,0.48,1.61,1.86,1.02,0.74,0.73,1.14,1.25,0.62,0.8,1.91,0.81,1.23,1.27,1.02,1.67,1.26,0.47,0.57,1.26,1.15,1.11,1.42,1.63,0.26,0.46,0.54,0.93,1.31,0.74,0.84,0.3,1.23,0.16,1.8,0.07,1.02,1. 24,1.72,0.17,0.6,0.28,1.16,1.2,0.44,1.94,0.71,1.89,0.91,0.02,1.21,1.27,1.44,1.47,0.26,0,0.47,1.76,1.47,0.2,1.59,1.61,0.61,1.96,1.74,1.96,1.34,0.47,1.79,0.66,0.15,0.5,1.82,1.2,0.74,1.07,0.71,1.21,1.52,0.59,0.06,0.72,0.04,1.25,1.24,0.69,0.77,1.95,1.27,1,1.13,1.99,0.6,0.05,0.93,0.18,0.66,1.3,0.4,0.39,0.57,0.79,1.49,0.91,0.4,1.77,0.29,0.31,1.98,0.21,1.93,1.08,0.66,0.58,1.7,0.75,0.94,1.79,0.64,0.36,1.58,0.33,0.8,0.21,0.4,1.33,1.01,1.29,1.33,0.68,0.81,0.31,1.8,0.45,0.7,0.28,0.47,1.56,1.14,1.74,1.21,0.56,1.09,0.03,0.32,1.69,0.44,0.25,1.33,0.93,0.4,1.5,0.02,1.84,1.49,0.09,1.37,1.2,1.08,0.36,1.87, 1.95,1.5,0.4,0.43,0.18,0.1,1.29,1.23,1.87,0.56,0.65,1.66,1.88,0.22,1.95,0.83,1.22,1.98,0.73,1.38,1. 39,0.94,0.91,0.16,1.16,1.53,0.14,0.39,0.63,1.19,0.47,0.33,1.91,1.84,1.72,0.98,1.91,1.26,1.48,1.97, 0.42,1.89,0.98,1.08,0.72,1.59,0.9,1.54,1.67,0.56,1.63,1.19,1.88,1.95,1.98,0.29,1.44,1.23,1.14,1.99, 0.26,0.84,1.82,0.57,0.61,1.48,1.12,1.84,0.33,0.17,0.27,0.94,1.25,0.8,0.69,0.15,0.49,0.93,1.97,0.42, 1.47,0.55,0.11,1.15,1.93,0.81,1.19,1.69,1.78,0.31,0.97,1.54,0.86,1.14,1.69,0.42,1.57,0.84,0.47,1.13,1.11,0.86,1.76,0.85,0.67,0.58,0.99,0.89,0.22,1.55,0.21,1.76,1.52,0.61,0.11,1.08,1.91,1.77,1.94,0. 96,0.09,1.08,1.85,1.19,0.9,0.32,0.93,1.86,1.85,1.87,0.84,1.8,0.5,0.21,1.57,1.51,1.33]; h=zeros(2,1); h(:,1)=0;
p=10^6*eye(2,2); lambda=1; Q=0;
for i=1:300
N(:,i)=[(-1)*y(i) u(i)]'; end
for i=1:297
K(:,i+1)=(p*N(:,i+1))/(lambda+N(:,i+1)'*p*N(:,i+1));
p=(p-(p*N(:,i+1)*N(:,i+1)'*p)/(1+N(:,i+1)'*p*N(:,i+1)))/lambda; h(:,i+1)=h(:,i)+K(:,i+1)*(y(i+2)-N(:,i+1)'*h(:,i)); ipsn(i+1)=y(i+2)-N(:,i+1)'*h(:,i); a(i)=ipsn(i)^2;
Q=Q+a(i); end
a1=h(1,:);b1=h(2,:); subplot(2,1,1) plot(a1),xlabel('a1'); subplot(2,1,2) plot(b1),xlabel('b1'); a1(298) b1(298)
程序运行结果:
(二)二阶系统 clear all;
y=(同一阶) u=(同一阶) h=zeros(4,1); h(:,1)=0; p=10^6*eye(4,4); lambda=1; Q=0;
for i=1:299
N(:,i)=[(-1)*y(i+1) (-1)*y(i) u(i+1) u(i)]'; end
for i=1:297
K(:,i+1)=(p*N(:,i+1))/(lambda+N(:,i+1)'*p*N(:,i+1)); p=(p-(p*N(:,i+1)*N(:,i+1)'*p)/(1+N(:,i+1)'*p*N(:,i+1)))/lambda; h(:,i+1)=h(:,i)+K(:,i+1)*(y(i+3)-N(:,i+1)'*h(:,i)); ipsn(i+1)=y(i+3)-N(:,i+1)'*h(:,i); a(i)=ipsn(i)^2; Q=Q+a(i); end
a1=h(1,:);a2=h(2,:);b1=h(3,:);b2=h(4,:); figure(1) subplot(2,1,1)
plot(a1),xlabel('a1'); subplot(2,1,2) plot(a2),xlabel('a2'); figure(2)
subplot(2,1,1)
plot(b1),xlabel('b1'); subplot(2,1,2) plot(b2),xlabel('b2'); a1(298) a2(298) b1(298) b2(298)
程序运行结果:
(三)三阶系统 clear all;
y=(同一阶) u=(同一阶) h=zeros(6,1); h(:,1)=0; p=10^6*eye(6,6); lambda=1; Q=0;
for i=1:298
N(:,i)=[(-1)*y(i+2) (-1)*y(i+1) (-1)*y(i) u(i+2) u(i+1) u(i)]'; end
for i=1:296
K(:,i+1)=(p*N(:,i+1))/(lambda+N(:,i+1)'*p*N(:,i+1)); p=(p-(p*N(:,i+1)*N(:,i+1)'*p)/(1+N(:,i+1)'*p*N(:,i+1)))/lambda; h(:,i+1)=h(:,i)+K(:,i+1)*(y(i+4)-N(:,i+1)'*h(:,i)); ipsn(i+1)=y(i+4)-N(:,i+1)'*h(:,i); a(i)=ipsn(i)^2; Q=Q+a(i); end
a1=h(1,:);a2=h(2,:);a3=h(3,:);b1=h(4,:);b2=h(5,:);b3=h(6,:); figure(1) subplot(3,1,1)
plot(a1),xlabel('a1'); subplot(3,1,2) plot(a2),xlabel('a2'); subplot(3,1,3) plot(b1),xlabel('a3'); figure(2) subplot(3,1,1) plot(b2),xlabel('b1'); subplot(3,1,2) plot(b2),xlabel('b2'); subplot(3,1,3) plot(b2),xlabel('b3'); a1(297) a2(297) a3(297) b1(297) b2(297) b3(297)
程序运行结果:
(四)四阶系统 clear all;
y=(同一阶) u=(同一阶) h=zeros(8,1); h(:,1)=0;
p=10^6*eye(8,8); lambda=1; Q=0;
for i=1:297
N(:,i)=[(-1)*y(i+3) (-1)*y(i+2) (-1)*y(i+1) (-1)*y(i) u(i+3) u(i+2) u(i+1) u(i)]'; end
for i=1:295
K(:,i+1)=(p*N(:,i+1))/(lambda+N(:,i+1)'*p*N(:,i+1)); p=(p-(p*N(:,i+1)*N(:,i+1)'*p)/(1+N(:,i+1)'*p*N(:,i+1)))/lambda; h(:,i+1)=h(:,i)+K(:,i+1)*(y(i+5)-N(:,i+1)'*h(:,i));
ipsn(i+1)=y(i+5)-N(:,i+1)'*h(:,i); a(i)=ipsn(i)^2; Q=Q+a(i); end
a1=h(1,:);a2=h(2,:);a3=h(3,:);a4=h(4,:);b1=h(5,:);b2=h(6,:);b3=h(7,:);b4=h(8,:); figure(1)
subplot(4,1,1)
plot(a1),xlabel('a1'); subplot(4,1,2) plot(a2),xlabel('a2'); subplot(4,1,3) plot(a3),xlabel('a3'); subplot(4,1,4) plot(a4),xlabel('a4'); figure(2)
subplot(4,1,1)
plot(b1),xlabel('b1'); subplot(4,1,2) plot(b2),xlabel('b2'); subplot(4,1,3) plot(b3),xlabel('b3'); subplot(4,1,4)
plot(b4),xlabel('b4'); a1(296) a2(296) a3(296) a4(296) b1(296) b2(296) b3(296) b4(296)
程序运行结果:
(五)五阶系统 clear all;
y=(同一阶) u=(同一阶)
h=zeros(10,1); h(:,1)=0;
p=1*eye(10,10); lambda=1; Q=0;
for i=1:296
N(:,i)=[(-1)*y(i+4) (-1)*y(i+3) (-1)*y(i+2) (-1)*y(i+1) (-1)*y(i) u(i+4) u(i+3) u(i+2) u(i+1) u(i)]'; end
for i=1:294
K(:,i+1)=(p*N(:,i+1))/(lambda+N(:,i+1)'*p*N(:,i+1)); p=(p-(p*N(:,i+1)*N(:,i+1)'*p)/(1+N(:,i+1)'*p*N(:,i+1)))/lambda; h(:,i+1)=h(:,i)+K(:,i+1)*(y(i+6)-N(:,i+1)'*h(:,i)); ipsn(i+1)=y(i+6)-N(:,i+1)'*h(:,i); a(i)=ipsn(i)^2; Q=Q+a(i); end
a1=h(1,:);a2=h(2,:);a3=h(3,:);a4=h(4,:);a5=h(5,:);b1=h(6,:);b2=h(7,:);b3=h(8,:);b4=h(9,:);b5=h(10,:);
figure(1) subplot(5,1,1)
plot(a1),xlabel('a1'); subplot(5,1,2) plot(a2),xlabel('a2'); subplot(5,1,3) plot(a3),xlabel('a3'); subplot(5,1,4)
plot(a4),xlabel('a4'); subplot(5,1,5)
plot(a5),xlabel('a5'); figure(2)
subplot(5,1,1) plot(b1),xlabel('b1'); subplot(5,1,2) plot(b2),xlabel('b2'); subplot(5,1,3)
plot(b3),xlabel('b3'); subplot(5,1,4) plot(b4),xlabel('b4'); subplot(5,1,5)
plot(b5),xlabel('b5'); a1(295)
a2(295) a3(295) a4(295) a5(295) b1(295) b2(295) b3(295) b4(295) b5(295)
程序运行结果:
(六)六阶系统 clear all;
y=(同一阶) u=(同一阶) h=zeros(12,1); h(:,1)=0;
p=1*eye(12,12); lambda=1; Q=0;
for i=1:295
N(:,i)=[(-1)*y(i+5) (-1)*y(i+4) (-1)*y(i+3) (-1)*y(i+2) (-1)*y(i+1) (-1)*y(i) u(i+5) u(i+4) u(i+3) u(i+2) u(i+1) u(i)]'; end
for i=1:293
K(:,i+1)=(p*N(:,i+1))/(lambda+N(:,i+1)'*p*N(:,i+1)); p=(p-(p*N(:,i+1)*N(:,i+1)'*p)/(1+N(:,i+1)'*p*N(:,i+1)))/lambda; h(:,i+1)=h(:,i)+K(:,i+1)*(y(i+7)-N(:,i+1)'*h(:,i)); ipsn(i+1)=y(i+7)-N(:,i+1)'*h(:,i); a(i)=ipsn(i)^2; Q=Q+a(i); end
a1=h(1,:);a2=h(2,:);a3=h(3,:);a4=h(4,:);a5=h(5,:);a6=h(6,:);b1=h(7,:);b2=h(8,:);b3=h(9,:);b4=h(10,:);b5=h(11,:);b6=h(12,:); figure(1)
subplot(6,1,1) plot(a1),xlabel('a1'); subplot(6,1,2)
plot(a2),xlabel('a2'); subplot(6,1,3) plot(a3),xlabel('a3'); subplot(6,1,4) plot(a4),xlabel('a4'); subplot(6,1,5) plot(a5),xlabel('a5'); subplot(6,1,6)
plot(a6),xlabel('a6'); figure(2)
subplot(6,1,1) plot(b1),xlabel('b1'); subplot(6,1,2) plot(b2),xlabel('b2'); subplot(6,1,3)
plot(b3),xlabel('b3'); subplot(6,1,4) plot(b4),xlabel('b4'); subplot(6,1,5)
plot(b5),xlabel('b5'); subplot(6,1,6)
plot(b6),xlabel('b6'); a1(294) a2(294) a3(294) a4(294) a5(294) a6(294) b1(294) b2(294) b3(294) b4(294) b5(294) b6(294)
程序运行结果:
(六)结果比较:
从上述结果可以看出:
当n
因此,模型阶数的“真值”为3,此模型为三阶系统