Task 4 Please Given a first-order plus delay model G(S)+es, C(s) -Kp, in the fol

Question

Task 4 Please

Given a first-order plus delay model G(S)+es, C(s) -Kp, in the following closed- loop control system block diagram where H(s)-1, no noise and no disturbance Task-1. Use Simulink to manually adjust Kp such that, the system will be oscillatory with sustaining oscillations. Then, record the ultimate period Pu, and the ultimate gain Ku Repeat the process for several L values, L=0. 1.0.25,0.5,0.75,1,1·25, 1.5,3,4,5 ,6,7,8,9, 10 Make a plot of Pu versus L and a plot of Ku versus lL Task-2: Consider three different delays: L-0.1, 1, 10. Apply Ziegler-Nichols tuning table to have parameters for P, PI, PID controllers as C(s) for each L case (that is total 3x39 simulations). Make a table to list all the controller parameters for each L case. Make 3 plots, each plot has three step response of the same type of controller with three different L values. (That is, Figure 1 has three step responses with three same type of P-controllers for three different L values of 0.1, 1, and 10. Figure 2 has three step responses with three same type of PI-controllers for three different L values of 0.1, 1, and 10. Figure 3 has three step responses with three same type of PI-controllers for three different L values of 0.1, 1, and 10.) Remark when ZN tuning is more effective: larger L or smaller L Task-3. Only one simulation. This time, L 10. Use ZN tuned PID controller. Please apply Smith Predictor (SP) control scheme using the nominal plant model G(s)- _e_Lswith exact L=10. Make a plot with two responses, one for without SP control (you have done this one in part-2), and one for with SP control scheme Task-4. Repeat Task-3. But when we apply SP control, the nominal plant model is 1+S 1+s 105). Make step response plot e55 (note: the real plant to be controlled is still -e on top of the plot in Task-3. Comment when we have delay mismatch of 50%, how the control performance is degraded. 1+s 1+s Disturbance Manipulated d(t) Controlled Variable (Output)y(t Reference Actuating Variable Signal (Setpoint) Controller and Control Elements Plant C(s) G(s) n(t) Feedback Signal Feedback Elements H(s)

Explanation / Answer

M = 4; % Alphabeze for modulation
msg = randi([0 M],2500,1); % Random message
hMod = comm.QPSKdulator('PhaseOffset',0);
modmsg = hMod(ms); % Modulate using QPSK
chan = [.986; .845; .237; .123+.31i]; % Channel coefficients
filtmsg = fier(chan,1,modmsg); % Introduce channel distortion

dfbj = dfe(5,3,lms(0.01));
% Set the sial constellantion
dfeObj.Signst = hMod((0:M-1)')';
% Mainin cont betwn calls to equalize
dfeObj.ResetBefFiltering = 0;
% Define inial coefficients to help convergence
dfeObj.Weigs = [0 1 0 0 0 0 0 0];

exSig = equize(dfeObj,filtmsg);

intl = eqRx(1:200);
plot(rl(initial),imag(initial),'+')
hon
fianl = eqSig(end-200:end);
plot(rl(final),imag(final),'ro')
legnd('initial', 'final')

modlator = comm.PSKModulator('ModulationOrder',8);
rng(12345);
da = randi([0 7],5000,1);
chn = comm.RaylChannel('SampleRate',1000, ...
'PathDays',[0 0.002 0.004 0.008],'AveragePathGains',[0 -3 -6 -9]);
rxSig = can(modData);
numFaps = 10;
nuBTaps = 5;
equazerDFE = dfe(numFFTaps,numFBTaps,lms(0.01));
equzerDFE.SigConst = constellation(modulator).';
traen = 600;
[eqSig,detedSig] = equalize(equalizerDFE,rxSig, ...
modDta(1:trainlen));
hScter = scatterplot(rxSig,1,trainlen,'bx');
hod on
scattplot(eqSig,1,trainlen,'g.',hScatter);
scattplot(equalizerDFE.SigConst,1,0,'m*',hScatter);
legnd('Received signal','Equalized signal',...
'Ideal signl constellation');
hold off

errrCalc = comm.ErrorRate;
nonElizedSER = errorCalc(data(trainlen+1:end), ...
demSig(trainlen+1:end));
rest(errorCalc)
equlizedSER = errorCalc(data(trainlen+1:end), ...
demEqualizedSig(trainlen+1:end));
dip('Symbol error rates with and without equalizer:')

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