%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % This file specifies the F in y'=F(t,y) for the stable indirect adaptive controller function dzdt=sindwingrockc(t,z) % Define variables to be global from associated program global a1 a2 a3 a4 a5 b tau beta0 beta1 thetam global pbeta R palpha global c global sigma global k1 k0 gamma global Walpha Wbeta global Am global etaalpha etabeta % Define the various subvectors of the overall closed-loop system state vector x=z(1:3); ym=z(4:7); thetaalpha=z(length(x)+length(ym)+1:length(x)+length(ym)+palpha); thetabeta=z(length(x)+length(ym)+palpha+1); % Controller % Define the phi vector for the alpha approximator % Next, use only x(1) an x(2) as inputs to the premise for i=1:R mu(i,1)=exp(-0.5*((x(1)-c(1,i))/sigma)^2)*exp(-0.5*((x(2)-c(2,i))/sigma)^2); end denominator=sum(mu(i,1)); xi=(1/denominator)*mu(:,1); % To use all of the state of the plant to the consequents: phi=[ xi', x(1)*xi', x(2)*xi', x(3)*xi']'; % Next, specify the estimates of alpha and beta alphahat=thetaalpha'*phi; betahat=thetabeta; % Next, compute the nu signal yddot=a1*x(1)+a2*x(2)+a3*(x(2)^3)+a4*(x(1)^2)*x(2)+a5*x(1)*(x(2)^2)+b*x(3); es=(ym(3)-yddot) + k1*(ym(2)-x(2)) + k0*(ym(1)-x(1)); %es=(ym(3)-x(4)) + k1*(ym(2)-x(2)) + k0*(ym(1)-x(1)); esbar=k1*(ym(3)-yddot) + k0*(ym(2)-x(2)); nu=ym(4)+gamma*es+esbar; % Certainty equivalence controller uce=(1/betahat)*(-alphahat+nu); % Sliding mode term usi=(1/beta0)*(Walpha+Wbeta*abs(uce))*sgn(es); % Form the control input to the plant u=uce+usi; %u=0; % Use to see how the wing will rock (oscillate) if you use no controller % Plant calculations dxdt=x; % Just to force it to be a column dxdt(1)=x(2); dxdt(2)=a1*x(1)+a2*x(2)+a3*(x(2)^3)+a4*(x(1)^2)*x(2)+a5*x(1)*(x(2)^2)+b*x(3); dxdt(3)=-(1/tau)*x(3)+(1/tau)*u; % Reference model calculations %dymdt=ym; % Just to force it to be a column dymdt=Am*ym; % Parameter update for adaptation % Set adaptation gains % Next, do parameter updates with projection. Here, we place % no restrictions on the parameters thetaalpha. We do, however restrict all % the parameters of thetabeta to >= beta0 and <= beta1 dthetaalphadt=-etaalpha*phi*es; thetabetaud=-etabeta*es*uce; % The update normally used when projection is not used if (thetabeta>=beta1 | thetabeta<=beta0) & (thetabetaud*(thetabeta-thetam)>=0) dthetabetadt=0; % Don't update since will not put in valid range else dthetabetadt=-etabeta*es*uce; end % Normally this last line would be: dthetabetadt=-etabeta*phi*es*uce; % but here we remove the phi since we are only using a constant for the % approximator % Form the output vector dzdt=[dxdt; dymdt; dthetaalphadt; dthetabetadt]; %----------------- function value=sgn(x) if x>0, value=1; end if x<0, value=-1; end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%