Gitlab Runner Update from orc-aux-files/master:Add code for for 16_3, 17_1, 17_2

ORC/exercise-files/Exercise_material_SoSe_2021/code/E_16_3_waterbed.m

+% ORC 16.3  :: Waterbed effect
+%
+% TUHH :: Institut for Control Systems :: Optimal and Robust Control
+% Last update: 30.06.2020
+
+% The following example is borrowed from:
+% Skogestad, S. & Postlethwaite, I. 
+% "Multivariable Feedback Control - Analysis and Design"
+% John Wiley & Sons, Ltd. , 2001
+
+clear
+clc
+close all
+%% Sub-problem a) and b)
+% G = tf( 2, [1 1 0] );
+% K1 = 0.1;   K2 = 1;     K3 = 10;
+
+%% Sub-problem c)
+G = tf( [-1 2],[1 2 0] );
+K1 = 0.1;   K2 = 0.5;   K3 = 1.5;
+
+
+%% Open loop transfer function L
+L1 = G*K1;     L2 = G*K2;     L3 = G*K3;
+
+figure()
+margin(L1)
+hold on
+margin(L2)
+margin(L3)
+legend(['K1=' num2str(K1)], ['K2=' num2str(K2)], ['K3=' num2str(K3)])
+
+figure()
+nyquist(L1,'r')
+hold on
+nyquist(L2,'g')
+nyquist(L3,'b')
+legend(['K1=' num2str(K1)], ['K2=' num2str(K2)], ['K3=' num2str(K3)])
+
+
+%% Frequency response Analysis: loop transfer functions
+
+S1 = feedback( 1, L1 );     T1 = feedback( L1, 1 );
+S2 = feedback( 1, L2 );     T2 = feedback( L2, 1 );
+S3 = feedback( 1, L3 );     T3 = feedback( L3, 1 );
+
+% Plot sensitivity and complementary sensitivity for different designs
+figure()
+subplot(211)
+sigma( S1,'r-', S2,'g-', S3,'b-');  title('S');
+subplot(212)
+sigma( T1,'r-', T2,'g-', T3,'b-');  title('T')
+legend(['K1=' num2str(K1)], ['K2=' num2str(K2)], ['K3=' num2str(K3)])
+
+figure()
+sigma(S1,'r-', S2,'g-', S3,'b-',T1,'r-', T2,'g-', T3,'b-');  
+title('S&T in one plot')
+
+%% Time domain analysis
+
+% Step response of the closed loop (Without input disturbance)
+figure()
+step(T1,'r-',T2,'g-',T3,'b-');
+legend(['K1=' num2str(K1)], ['K2=' num2str(K2)], ['K3=' num2str(K3)]) 
+
+%% Sine tracking of the closed loop without input disturbance
+t=0:0.1:100;             % time 
+u=sin(0.05*t);               % Step input    
+
+figure()
+lsim(T1,u',t,'r')
+hold on
+lsim(T2,u',t,'g')
+lsim(T3,u',t,'b')
+legend(['K1=' num2str(K1)], ['K2=' num2str(K2)], ['K3=' num2str(K3)])
+%%
+
+% Sine tracking of the closed loop with input disturbance
+t=0:0.1:100;             % time 
+u=sin(0.05*t);           % Step input
+d=0.05*sin(1.9*t);         % Input disturbance
+ud=(u+d)';              % input=step+noise
+
+figure()
+lsim(T1,ud,t,'r')
+hold on
+lsim(T2,ud,t,'g')
+lsim(T3,ud,t,'b')
+legend(['K1=' num2str(K1)], ['K2=' num2str(K2)], ['K3=' num2str(K3)])
+
+