Simulink Control Design™ - MathWorks

beta_vec = -10:5:10; % Beta Range

[alpha,beta] = ndgrid(alpha_vec,beta_vec);

SG = struct('alpha',alpha,'beta',beta);

% Proportional gains

alphabetaBasis = polyBasis('canonical',2,2);

P_PHI = tunableSurface('Pphi', 0.05, SG, alphabetaBasis);

P_ALPHA = tunableSurface('Palpha', 0.05, SG, alphabetaBasis);

P_BETA = tunableSurface('Pbeta', -0.05, SG, alphabetaBasis);

ST0.setBlockParam('P phi',P_PHI);

ST0.setBlockParam('P alpha',P_ALPHA);

ST0.setBlockParam('P beta',P_BETA);

% Integral gains

alphaBasis = @(alpha) alpha;

betaBasis = @(beta) abs(beta);

alphabetaBasis = ndBasis(alphaBasis,betaBasis);

I_PHI = tunableSurface('Iphi', 0.05, SG, alphabetaBasis);

I_ALPHA = tunableSurface('Ialpha', 0.05, SG, alphabetaBasis);

I_BETA = tunableSurface('Ibeta', -0.05, SG, alphabetaBasis);

ST0.setBlockParam('I phi',I_PHI);

ST0.setBlockParam('I alpha',I_ALPHA);

ST0.setBlockParam('I beta',I_BETA);

Note that we initialized each gain surface to a fixed value suggested by the baseline

design. In general, it is not recommended to start from a zero or random initial point

because the difficulty of the problem increases the likelihood of getting stuck in

uninteresting local minima. Instead, a better strategy consists of tuning a fixed (non-

scheduled) set of gains against the full set (or a relevant subset) of design points. Such

"robust design" typically provides a good starting point for gain surface tuning.

You can now use systune to tune the 6 gain surfaces against the three tuning goals.

ST = systune(ST0,[R1 R2 R3]);

Final: Soft = 1.03, Hard = -Inf, Iterations = 42

The final objective value is close to 1 so the tuning goals are essentially met. Plot the

closed-loop angular responses and compare with the baseline design.

T = getIOTransfer(ST,'Demand',{'Phi_deg','Alpha_deg','Beta_deg'});

step(T0,T,6)

legend('Baseline','Tuned','Location','SouthEast')

11 Gain-Scheduled Controllers