文章目录
1. 简单传递函数2. 零极点模型3. 状态空间模型4. 反馈系统5. 多环路系统主要通过MATLAB控制系统工具箱的内置函数实现。
1. 简单传递函数
栗子1:
>> num1=[25];>> den1=[1 1 25];>> G1=tf(num1,den1)G1 =25------------s^2 + s + 25Continuous-time transfer function.>> G2 = tf(den1,num1)G2 =s^2 + s + 25------------25Continuous-time transfer function.>> bode(G2)>> hold on;>> bode(G1)>> bode(G1*G2)>> grid
栗子2:
>> num =[5*0.1,1];>> f1=[1,0];f2=[0.5,1];>> f3=[1/2500,0.6/50,1];>> den=conv(f1,conv(f2,f3));>> bode(num,den)
2. 零极点模型
>> KGain=5; %系统增益K>> Z=[1; 2; 3]; %零点>> P=[4; 5; 6]; %极点>> G=zpk(Z,P,KGain)G =5 (s-1) (s-2) (s-3)-------------------(s-4) (s-5) (s-6)Continuous-time zero/pole/gain model.
3. 状态空间模型
>> A=[A];>> B=[B];>> C=[C];>> D=[D];>> G=ss(A,B,C,D)
4. 反馈系统
>> G1=tf(3,[1,4,4]);>> G2=tf(1,[1,3]);>> G=feedback(G1,G2); %第三个参数默认为-1,表示负反馈 1正反馈G =3 s + 9-----------------------s^3 + 7 s^2 + 16 s + 15Continuous-time transfer function.
5. 多环路系统
栗子1:
sumblk
:实现记录信号的线性叠加,类似于Simulink中的ADD模块,使用时需指明信号名称,sumblk(output, input, input,..., input,Signs)
;connect
:完成各个传递函数的连接,注意需提前指定各sys的输入输出名称,并对应起来;
%构建前馈+反馈C1 = tf([1],[1]);C2 = tf([1],[1]);G = tf([1],[1,1]);B1 = sumblk ('e','r','y','+-');B2 = sumblk ('u','u1','u2 ','++');C1.InputName='r';C1.OutputName='u2';C2.InputName='e';C2.OutputName='u1';G.InputName='u';G.OutputName='y';T=connect(C1,C2,B1,B2,G,'r','y');
栗子2:
% 建立各子系统G1=tf([1],[1 10]);G2=tf([1],[1 1]);G3=tf([1 0 1],[1 4 4]);numg4=[1 1];deng4=[1 6];G4=tf(numg4,deng4);H1=zpk([-1],[-2],1);numh2=[2];denh2=[1];H3=1; %先将H2移至G4之后nh2=conv(numh2,deng4);dh2=conv(denh2,numg4);H2=tf(nh2,dh2);%计算由G3、G4和H1回路组成的子系统模型sys1=series(G3,G4);sys2=feedback(sys1,H1,+1);%计算由H2构成反馈回路的子系统模型sys3=series(G2,sys2);sys4=feedback(sys3,H2);%计算由H3构成反馈主回路的系统闭环传递函数sys5=series(G1,sys4);sys=feedback(sys5,H3)%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% sys = %% %% 0.083333 (s+1)^2 (s+2) (s^2 + 1) %% --------------------------------------------------------- %% (s+10.12) (s+2.44) (s+2.349) (s+1) (s^2 + 1.176s + 1.023) %% %% Continuous-time zero/pole/gain model.%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
参考文献:
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