Create a gain surface with one scheduling variable and evaluate the gain at a list of scheduling-variable values.

When you create a gain surface using tunableSurface, you specify design points at which the gain coefficients are tuned. These points are the typically the scheduling-variable values at which you have sampled or linearized the plant. However, you might want to implement the gain surface as a lookup table with breakpoints that are different from the specified design points. In this example, you create a gain surface with a set of design points and then evaluate the surface using a different set of scheduling variable values.

Create a scalar gain that varies as a quadratic function of one scheduling variable, t. Suppose that you have linearized your plant every five seconds from t = 0 to t = 40.

t = 0:5:40;
domain = struct('t',t);
shapefcn = @(x) [x,x^2];
GS = tunableSurface('GS',1,domain,shapefcn);

Typically, you would tune the coefficients as part of a control system. For this example, instead of tuning, manually set the coefficients to non-zero values.

GS = setData(GS,[12.1,4.2,2]);

Evaluate the gain surface at a different set of time values.

tvals = [0,4,11,18,25,32,39,42];   % eight values
GV = evalSurf(GS,tvals)

GV = 8×1

    9.9000
   10.0200
   10.6150
   11.7000
   13.2750
   15.3400
   17.8950
   19.1400

GV is an 8-by-1 array. You can use tvals and GV to implement the variable gain as a lookup table.

Evaluate a gain surface with two scheduling variables over a grid of values of those variables.

When you create a gain surface using tunableSurface, you specify design points at which the gain coefficients are tuned. These points are the typically the scheduling-variable values at which you have sampled or linearized the plant. However, you might want to implement the gain surface as a lookup table with breakpoints that are different from the specified design points. In this example, you create a gain surface with a set of design points and then evaluate the surface using a different set of scheduling-variable values.

Create a scalar-valued gain surface that is a bilinear function of two independent variables, $$\alpha$$ and V.

[alpha,V] = ndgrid(0:1.5:15,300:30:600);
domain = struct('alpha',alpha,'V',V);
shapefcn = @(x,y) [x,y,x*y];
GS = tunableSurface('GS',1,domain,shapefcn);

Typically, you would tune the coefficients as part of a control system. For this example, instead of tuning, manually set the coefficients to non-zero values.

GS = setData(GS,[100,28,40,10]);

Evaluate the gain at selected values of $$\alpha$$ and V.

alpha_vec = [7:1:13];  % N1 = 7 points
V_vec = [400:25:625];  % N2 = 10 points
GV = evalSurf(GS,alpha_vec,V_vec);

The breakpoints at which you evaluate the gain surface need not fall within the range specified by domain. However, if you attempt to evaluate the gain too far outside the range used for tuning, the software issues a warning.

The breakpoints also need not be regularly spaced. evalSurf evaluates the gain surface over the grid formed by ndgrid(alpha_vec,V_vec). Examine the dimensions of the resulting array.

size(GV)

ans = 1×2

     7    10

By default, the grid dimensions N1-by-N2 are first in the array, followed by the gain dimensions. GS is scalar-valued gain, so the dimensions of GV are [7,10,1,1], or equivalently [7,10].

The value in each location of GV is the gain evaluated at the corresponding (alpha_vec,V_vec) pair in the grid. For example, GV(2,3) is the gain evaluated at (alpha_vec(2),V_vec(3)) or (8,450).

Evaluate an array-valued gain surface with two scheduling variables over a grid of values of those variables.

Create a vector-valued gain that has two scheduling variables.

[alpha,V] = ndgrid(0:1.5:15,300:30:600);
domain = struct('alpha',alpha,'V',V);
shapefcn = @(x,y) [x,y,x*y];
GS = tunableSurface('GS',ones(2,2),domain,shapefcn);

Setting the initial constant coefficient to ones(2,2) causes tunableSurface to generate a 2-by-2 gain matrix. Each entry in that matrix is an independently tunable gain surface that is a bilinear function of two scheduling variables. In other words, the gain surface is given by:

where each of the coefficients $$K_0,\dots ,K_3$$ is itself a 2-by-2 matrix.

Typically, you would tune the coefficients of those gain surfaces as part of a control system. For this example, instead of tuning, manually set the coefficients to non-zero values.

K0 = 10*rand(2);
K1 = 10*rand(2);
K2 = 10*rand(2);
K3 = 10*rand(2);

The tunableSurface object stores array-valued coefficients by concatenating them into a 2-by-8 array (see the tunableSurface reference page). Therefore, concatenate these values of $$K_0,\dots ,K_3$$ to change the coefficients of GS.

GS = setData(GS,[K0 K1 K2 K3]);

Now evaluate the gain surface at selected values of the scheduling variables.

alpha_vec = [7:1:13];  % N1 = 7 points
V_vec = [400:25:625];  % N2 = 10 points
GV = evalSurf(GS,alpha_vec,V_vec,'gridlast');

The 'gridlast' orders the array GV such that the dimensions of the grid of gain values, 7-by-10, are last. The dimensions of the gain array itself, 2-by-2, are first.

size(GV)

ans = 1×4

     2     2     7    10