Please use Simulink block diagram (MATLAB). EDIT: Below is what function you can use, and also how the block diagram may look like

Question Two (20 marks) -6s The transfer function of a process unit in a resource company is described by: G(S) = (s + 1)(8 + 8)2 Design a PID controller with filter to control this time delay system. 1. (10 marks) You may use the MATLAB program pidplace.m to find the PID controller parameters or you may choose to find the PID con- troller parameters analytically. Present the PID controller parameters for the three cases where all the desired closed-loop poles are at -1, -0.2 and -0.1, respectively. 2. (10 marks) Assuming that the reference signal to the system is 1, sim- ulate the closed-loop responses for all the three cases. In the simulation of the PID control system, the derivative control is implemented on the output only. Present the control signals and output signals graphically. State your sampling interval and simulation time. Tsim BE Normal PIDController_cascade PID Controller_cascade u control time Run Section NAVIGATE EDIT Breakpoints Run Run and Advance Run and Advance Time BREAKPOINTS RUN function [Kc, taul, taus, tauf]=pidplace (al, ao, b1,bo, Acl) Spole-assignment controller design ac_3-Acl (2); changed the coefficient ac_2=Acl (3); changed the coefficient ac_l=Acl (4); $changed the coefficient ac_0=Acl (5); $changed the coefficient $for Sylvester matrix S_matrix=(1 bl o 0; al bo bi 0; a0 O bo bl; O O O bo]; Vec=[ac_3-al;ac_2-a0; ac_l;ac_0]; contr_p=inv (S_matrix) *Vec; Lo=contr_p(1); c2=contr_p(2); cl=contr_p (3); co=contr_p(4); SPID controller parameters tauf=1/LO; taul=cl/c0-tauf; *Kc=cl*c0/L0-c0/L0^2; Kc=taul*tauf*co; tauD=(c2*taul*tauf-Kc*taul*tauf) / (Kc*taul); PID controller example solution for 3.2 (1) bl=1; bo=-1; al=1; a0=0; num=[1 -1]; den=[1 1 0]; xi=0.707; wn=3; Acl=[1 2*xi*wn wn^2]; Acl=conv (Acl, Acl); [Kc, taul, tauD, tauf]=pidplace (al, a0, b1, b0, Acl); $define the simulation parameters deltat=0.01; Tsim=60; sim('PIDController'); figure (1) plot(t,y) $figure (2) sim('PDController_A'); sfigure (2) Splot(t,y) xlabel('Time (sec)') vlabel('Output') figure (2) plot(t, u) xlabel ('Time (sec)') ylabel('Control') e u Y(s) US) Y() U(s) Y(S) U(s) r output PI Controller PI Inner plant num(s) den(s) Derivative term Question Two (20 marks) -6s The transfer function of a process unit in a resource company is described by: G(S) = (s + 1)(8 + 8)2 Design a PID controller with filter to control this time delay system. 1. (10 marks) You may use the MATLAB program pidplace.m to find the PID controller parameters or you may choose to find the PID con- troller parameters analytically. Present the PID controller parameters for the three cases where all the desired closed-loop poles are at -1, -0.2 and -0.1, respectively. 2. (10 marks) Assuming that the reference signal to the system is 1, sim- ulate the closed-loop responses for all the three cases. In the simulation of the PID control system, the derivative control is implemented on the output only. Present the control signals and output signals graphically. State your sampling interval and simulation time. Tsim BE Normal PIDController_cascade PID Controller_cascade u control time Run Section NAVIGATE EDIT Breakpoints Run Run and Advance Run and Advance Time BREAKPOINTS RUN function [Kc, taul, taus, tauf]=pidplace (al, ao, b1,bo, Acl) Spole-assignment controller design ac_3-Acl (2); changed the coefficient ac_2=Acl (3); changed the coefficient ac_l=Acl (4); $changed the coefficient ac_0=Acl (5); $changed the coefficient $for Sylvester matrix S_matrix=(1 bl o 0; al bo bi 0; a0 O bo bl; O O O bo]; Vec=[ac_3-al;ac_2-a0; ac_l;ac_0]; contr_p=inv (S_matrix) *Vec; Lo=contr_p(1); c2=contr_p(2); cl=contr_p (3); co=contr_p(4); SPID controller parameters tauf=1/LO; taul=cl/c0-tauf; *Kc=cl*c0/L0-c0/L0^2; Kc=taul*tauf*co; tauD=(c2*taul*tauf-Kc*taul*tauf) / (Kc*taul); PID controller example solution for 3.2 (1) bl=1; bo=-1; al=1; a0=0; num=[1 -1]; den=[1 1 0]; xi=0.707; wn=3; Acl=[1 2*xi*wn wn^2]; Acl=conv (Acl, Acl); [Kc, taul, tauD, tauf]=pidplace (al, a0, b1, b0, Acl); $define the simulation parameters deltat=0.01; Tsim=60; sim('PIDController'); figure (1) plot(t,y) $figure (2) sim('PDController_A'); sfigure (2) Splot(t,y) xlabel('Time (sec)') vlabel('Output') figure (2) plot(t, u) xlabel ('Time (sec)') ylabel('Control') e u Y(s) US) Y() U(s) Y(S) U(s) r output PI Controller PI Inner plant num(s) den(s) Derivative term