Simulink Control Design™ - MathWorks

points along the Cref trajectory. Use the tunableSurface object to parameterize each

gain as a quadratic function of Cr. The "tuning grid" is set to the five concentrations CrEQ

and the basis functions for the quadratic parameterization are. Most gains are

initialized to be identically zero.

TuningGrid = struct('Cr',CrEQ);

ShapeFcn = @(Cr) [Cr , Cr^2];

Kp = tunableSurface('Kp', 0, TuningGrid, ShapeFcn);

Ki = tunableSurface('Ki', -2, TuningGrid, ShapeFcn);

Kt = tunableSurface('Kt', 0, TuningGrid, ShapeFcn);

a = tunableSurface('a', 0, TuningGrid, ShapeFcn);

b = tunableSurface('b', 0, TuningGrid, ShapeFcn);

Controller Tuning

Because the target bandwidth is within a decade of the Nyquist frequency, it is easier to

tune the controller directly in the discrete domain. Discretize the linearized process

dynamics with sample time of 0.5 minutes. Use the ZOH method to reflect how the digital

controller interacts with the continuous-time plant.

Ts = 0.5;

Gd = c2d(G,Ts);

Create an slTuner interface for tuning the quadratic gain schedules introduced above.

Use block substitution to replace the nonlinear plant model by the five discretized linear

models Gd obtained at the design points CrEQ. Use setBlockParam to associate the

tunable gain functions Kp, Ki, Kt, a, b with the Lookup Table blocks of the same name.

BlockSubs = struct('Name','rct_CSTR/CSTR','Value',Gd);

ST0 = slTuner('rct_CSTR',{'Kp','Ki','Kt','a','b'},BlockSubs);

ST0.Ts = Ts; % sample time for tuning

% Register points of interest

ST0.addPoint({'Cref','Cr','Tr','TrSP','Tc'})

% Parameterize look-up table blocks

ST0.setBlockParam('Kp',Kp);

ST0.setBlockParam('Ki',Ki);

ST0.setBlockParam('Kt',Kt);

ST0.setBlockParam('a',a);

ST0.setBlockParam('b',b);

11 Gain-Scheduled Controllers