Thus the upper limit of increases by a positive quantity of . In other words, the stability limits of the process increases by introducing a secondary loop.

One may put some reasonable values to the controller gain and simulate the system. However it will generate some offset for obvious reasons. To get an offset free control action, one needs to assign the master controller with a Gain-Reset setting.

V.2.3 : Example of a relevant MATLAB code

Let us try to find out how y₁ behaves if there is a step disturbance in d₂. Let us take a pure-gain slave controller and PI master controller . In absence of secondary loop, one has,                                                                                              V.31

In presence of secondary loop, one has,                     V.32

One can write the following simple program in MATLAB to find the result:

gp1=tf(1,[1 2 1]);

gp2=tf(1,[1 1]);

gc1=2*tf([3 1],[3 0]);

gc2=5;

cewsl=1+gc2*gp2+gc1*gc2*gp1*gp2;

cewos=1+gc1*gp1*gp2;

[y1,t1]=step(gp1/cewsl);

[y2,t2]=step(gp1/cewos);

plot(t1,y1,t2,y2)

xlabel('Time')

ylabel('Y1')

legend('Cascade','PI')

And the result should look like the following figure: