%------------------------------------- 1. feladat -----------------------------------------------

s=tf('s');
display('<<< Continuous-time process: >>>')
P=zpk(1/(1+5*s)/(1+10*s))
Ts=1;
display('<<< Discretized process with Ts=1 sec: >>>')
G=zpk(c2d(P,Ts))
z=tf('z',Ts);
display('<<< Decompose and normalize as G(z)=Gm(z)Gp(z) with Gm(1)=1: >>>')
pause;
display('<<< Gm(z): >>>')
Gm=1
display('<<< Gp(z): >>>')
Gp=G
display('<<< Specify the design polynomial Rr(z)=Rn(z)=1/z: >>>')
pause;
Rr=1/z;
Rn=1/z
display('<<< Calculate the C(z) controller: >>>')
pause;
C=minreal(Rn/Gp/(1-Rn*Gm),0.0001)
display('<<< Find the loop transfer function L(z)=C(z)G(c): >>>')
pause;
L=minreal(C*G,0.0001)
display('<<< Show the transfer function T(z)=Y(z)/Yr(z) : >>>')
pause;
T=minreal(L/(1+L),0.0001)
display('<<< The transfer function form reflects the numerical conditions): >>>')
pause;
T=tf(T)
display('<<< Compare with the theoretical value (Gm/z): >>>')
pause;
tf(Gm/z)
display('<<< Show the servo input-output records: >>>')
pause;
y=step(T,10); t=0:10; subplot(211),plot(t,y,'*'),grid;
u=step(minreal(C/(1+L)),10); subplot(212),stairs(t,u),grid;
pause;
display('<<< Check the disturbance rejecion: >>>')
pause;
S=minreal(1/(1+L))
tf(S)
display('<<< Compare with the theoretical value (1-Rn/Gm): >>>')
pause;
tf(1-Rn*Gm)
display('<<< Show the disturbance rejecion input-output records: >>>')
pause;
y=step(S,10); t=0:10; subplot(211),plot(t,y,'*'),grid;
u=step(minreal(-C/(1+L)),10); subplot(212),stairs(t,u),grid;
display('<<< Check the steady-state properties: >>>')
dcgain(T)
dcgain(S)
pause;
display('<<< Decompose G(z) with Gm=(z+0.9048)/(1+0.9048): >>>')
Gm=(z+0.9048)/(1+0.9048)/z
display('<<< Gp(z): >>>')
Gp=minreal(G/Gm,0.0001)
display('<<< Calculate the C(z) controller: >>>')
pause;
C=minreal(Rn/Gp/(1-Rn*Gm),0.0001)
display('<<< Find the loop transfer function L(z)=C(z)G(c): >>>')
pause;
L=minreal(C*G,0.0001)
display('<<< Show the transfer function T(z)=Y(z)/Yr(z) : >>>')
pause;
T=minreal(L/(1+L),0.0001)
display('<<< The transfer function form reflects the numerical conditions): >>>')
pause;
T=tf(T)
display('<<< Compare with the theoretical value (Gm/z): >>>')
pause;
tf(Gm/z)
display('<<< Show the servo input-output records: >>>')
pause;
y=step(T,10); t=0:10; subplot(211),plot(t,y,'*'),grid;
u=step(minreal(C/(1+L)),10); subplot(212),stairs(t,u),grid;
pause;
display('<<< Check the disturbance rejecion: >>>')
pause;
S=minreal(1/(1+L))
tf(S)
display('<<< Compare with the theoretical value (1-Rn/Gm): >>>')
pause;
tf(1-Rn*Gm)
display('<<< Show the disturbance rejecion input-output records: >>>')
pause;
y=step(S,10); t=0:10; subplot(211),plot(t,y,'*'),grid;
u=step(minreal(-C/(1+L)),10); subplot(212),stairs(t,u),grid;




%------------------------------------- 2. feladat -----------------------------------------------
s=tf('s');
display('<<< Continuous-time process: >>>')
P=zpk(1/(1+5*s)/(1+8*s)/(1+10*s))
Ts=1;
display('<<< Discretized process with Ts=1 sec: >>>')
G=zpk(c2d(P,Ts))
z=tf('z',Ts);
display('<<< Decompose and normalize as G(z)=Gm(z)Gp(z) with Gm(1)=(z+3.358)/(1+3.358)/z: >>>')
pause;
display('<<< Gm(z): >>>')
Gm=(z+3.358)/(1+3.358)/z
display('<<< Gp(z): >>>')
Gp=minreal(G/Gm,0.0001)
display('<<< Specify the design polynomial Rn(z)=1/z: >>>')
pause;
Rn=1/z
display('<<< Calculate the C(z) controller: >>>')
pause;
C=minreal(Rn/Gp/(1-Rn*Gm),0.0001)
display('<<< Find the loop transfer function L(z)=C(z)G(c): >>>')
pause;
L=minreal(C*G,0.0001)
display('<<< Show the transfer function T(z)=Y(z)/Yr(z) : >>>')
pause;
T=minreal(L/(1+L),0.0001)
display('<<< The transfer function form reflects the numerical conditions): >>>')
pause;
T=tf(T)
display('<<< Compare with the theoretical value (Gm/z): >>>')
pause;
tf(Gm/z)
display('<<< Show the servo input-output records: >>>')
pause;
y=step(T,10); t=0:10; subplot(211),plot(t,y,'*'),grid;
u=step(minreal(C/(1+L)),10); subplot(212),stairs(t,u),grid;
display('<<< Check the disturbance rejecion: >>>')
pause;
S=minreal(1/(1+L))
tf(S)
display('<<< Compare with the theoretical value (1-Rn/Gm): >>>')
pause;
tf(1-Rn*Gm)
display('<<< Show the disturbance rejecion input-output records: >>>')
pause;
y=step(S,10); t=0:10; subplot(211),plot(t,y,'*'),grid;
u=step(minreal(-C/(1+L)),10); subplot(212),stairs(t,u),grid;
display('<<< Check the steady-state properties: >>>')
dcgain(T)
dcgain(S)
pause;
display('<<< Define new Rn=Rr=0.1/(z-0.9) >>>');
Rn=0.1/(z-0.9)
Rr=0.1/(z-0.9)
display('<<< Calculate the C(z) controller: >>>')
pause;
C=minreal(Rn/Gp/(1-Rn*Gm),0.0001)
display('<<< Find the loop transfer function L(z)=C(z)G(c): >>>')
pause;
L=minreal(C*G,0.0001)
display('<<< Show the transfer function T(z)=Y(z)/Yr(z) : >>>')
pause;
T=minreal(L/(1+L),0.0001)
display('<<< The transfer function form reflects the numerical conditions): >>>')
pause;
T=tf(T)
display('<<< Compare with the theoretical value (Gm/z): >>>')
pause;
tf(Rr*Gm/z)
display('<<< Show the servo input-output records: >>>')
pause;
y=step(T,30); t=0:30; subplot(211),plot(t,y,'*'),grid;
u=step(minreal(C/(1+L)),30); subplot(212),stairs(t,u),grid;
pause;
display('<<< Check the disturbance rejecion: >>>')
pause;
S=minreal(1/(1+L))
tf(S)
display('<<< Compare with the theoretical value (1-Rn/Gm): >>>')
pause;
tf(1-Rn*Gm)
display('<<< Show the disturbance rejecion input-output records: >>>')
pause;
y=step(S,10); t=0:10; subplot(211),plot(t,y,'*'),grid;
u=step(minreal(-C/(1+L)),10); subplot(212),stairs(t,u),grid;
pause;
display('<<< Check the steady-state properties: >>>')
dcgain(Rr*Gm/z)
dcgain(S)