Products
Rewards
from HOLOOLY

We are determined to provide the latest solutions related to all subjects FREE of charge!

Enjoy Limited offers, deals & Discounts by signing up to Holooly Rewards Program

HOLOOLY

HOLOOLY
TABLES

All the data tables that you may search for.

HOLOOLY
ARABIA

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

HOLOOLY
TEXTBOOKS

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

HOLOOLY
HELP DESK

Need Help? We got you covered.

## Q. 20.8

In Section 20.6.1, MPC was applied to the Wood-Berry distillation column model. A MATLAB program for this example and constrained MPC is shown in Table E20.8. The design parameters have the base case values (Case B in Fig. 20.14) except for $P=10$ and $M=5$. The input constraints are the saturation limits for each input $(-0.15$ and $+0.15$ ). Evaluate the effects of control horizon $M$ and input weighting matrix $R$ by simulating the set-point change and the first disturbance of Section 20.6.1 for the following parameter values:

(a) Control horizon, $M=2$ and $M=5$

(b) Input weighting matrix, $R =0.1 I$ and $R = I$ Consider plots of both inputs and outputs. Which choices of $M$ and $R$ provide the best control? Do any of these MPC controllers provide significantly better control than the controllers shown in Figs. $20.14$ and 20.15? Justify your answer.

 Table E20.8 MATLAB Program (Based on a program by Morari and Ricker (1994)) g11=poly2tfd(12.8,[16.7 1],0.1); % model g21=poly2tfd(6.6,[10.9 1],0,7); g12=poly2tfd(−18.9,[21.0 1],0,3); g22=poly2tfd(−19.4,[14.4 1],0,3); gd1=poly2tfd(3.8,[14.9 1],0,8.1); gd2=poly2tfd(4.9,[13.2 1],0,3.4); tfinal=120; % Model horizon, N delt=1; %Sampling perio ny=2; %Number of outputs model=tfd2step(tfinal,delt,ny,g11,g21,g12,g22) plant=model; %No plant/model mismatch dmodel=[ ] %Default disturbance model dplant=tfd2step(tfinal,delt,ny,gd1,gd2) P=10; M=5; % Horizons ywt=[1 1]; uwt=[0.1 0.1];%Q and R tend=120; % Final time for simulation r=[0 1]; %Set-point change in XB a=zeros([1,tend]); for i=51:tend a(i)=0.3∗2.45; %30 %step in F at t=50 min. end dstep=[a′]; ulim=[−.15 −.15 .15 .15 1000 1000];%u limits ylim=[ ]; %No y limits tfilter=[ ]; [y1,u1]=cmpc(plant,model,ywt,uwt,M,P,tend,r, ulim,ylim, tfilter,dplant,dmodel,dstep); figure(1) subplot(211) plot(y1) legend(′XD′,′XB′) xlabel(′Time (min)′) subplot(212) stairs(u1)% Plot inputs as staircase functions legend(′R′,′S′) xlabel(′Time (min)′)

## Verified Solution

(Use MATLAB Model Predictive Control Toolbox)

a) $M=5$ vs. $M=2$

b) $R =0.1 I . . vs \quad R = I$

Notice that the larger control horizon $M$ and the smaller input weighting $R$, the more control effort is needed.