question about the LPV-model in simulink

[Hanmi Xu]

hello,

i am trying to compare the nomal MPC method and the minmax MPC based LMI (kothare,Balakrishnan,Morari 1996) with simulink.
The plant is a LPV model. so in the nomal MPC i set a nominal Acn and Bcn.
After simulation, at t=0, the first value u after optimization is not reached 230 (u_max).
as my mind, the value u at t=0 should be 230 so that it can reach the reference value as fast as possible.
And the minmax MPC dosen't show the advantages to the nomal MPC in my simulation.
Could you give me some advice about my simulink model and the definition of the function?
thanks a lot

best regards
xu

[Johan Löfberg]

Not sure what you are asking, doesn't sound like it is YALMIP related. Sounds like you basically don't like the solution of Kothare as it is conservative and doesn't exploit the control authority to the fullest.

[Hanmi Xu]

Dear Johan,

Thank you for the reply.

I would like to ask you, did I correctly define the function of Kothare's method with Yalmip ? 

xs is the current value x and r is the reference value.

here is the function

 uout=rmpcKBM96(xs,r,t)

persistent Controller

if t==0

   

    

Ts=0.0001;

    

% Vertex

   

    Ad{1}=[0.9998,0;0 0.9998];

    Ad{2}=[0.9975 0;0 0.9975];

    

    Bd{1}=[0.0017 0;0 0.0017];

    Bd{2}=[0.0069 0;0 0.0069];

    

    nx=size(Bd{1},1);

    nu=size(Bd{2},2);

    nv=size(Ad,1);

    u_max=[230;230];

    

    

    

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    

% Define data for MPC controller

    

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    

    

Q=[1 0;0 1];

R=0.01*eye(2);

   

   

    

% ZERO-Tolerance of strict LMIs

    

ZERO = 1e-6;

    

    

%-----------------------

    

% Controller

    

%-----------------------

    

% Aviod explosion of internally defined variables in YALMIP

  

  

yalmip('clear')

    

   

% variables

  

  

S=sdpvar(nx);

    

Y=sdpvar(nu,nx,'full');

    

gamma=sdpvar(1);

    

xk=sdpvar(nx,1);

 

% LMI Definition and Constraints

    

Constraints=[];

    

    

Constr_S=[S>=ZERO];

    

    

lmi1=[1 xk';xk S];

    

Constr_lmi1=[lmi1>=ZERO];

   

 

    

Constr_lmi2=[];

    

for v=1:nv

        

lmi2_constr=[[S, (Ad{v}*S+Bd{v}*Y)', S*sqrtm(Q), Y'*sqrtm(R);...

            

(Ad{v}*S+Bd{v}*Y), S, zeros(nx), zeros(nx,nu);...

            

sqrtm(Q)*S, zeros(nx), gamma*eye(nx), zeros(nx,nu);...

            

sqrtm(R)*Y, zeros(nu,nx), zeros(nu,nx), gamma*eye(nu)]>=ZERO];

        

        

Constr_lmi2=Constr_lmi2+lmi2_constr;

    

end

    

   

    

% inputs Constraints

    

lmi_in=[diag(u_max.^2) Y;Y' S];

    

Constr_in=[lmi_in>=ZERO];

    

    

% outputs Constraints

    

Constr_out=[];

               

 % Controller design

    

    

Constraints=Constr_S+Constr_lmi1+Constr_lmi2+Constr_in+Constr_out;

    

options=sdpsettings('solver','sedumi');

   

Controller=optimizer(Constraints,gamma,options,xk,{Y,S})

 

   

    

sol=Controller{{xs-r}};

    

uout=sol{1}*inv(sol{2})*(xs-r);

else

    

sol=Controller{{xs-r}};

    

uout=sol{1}*inv(sol{2})*(xs-r);

end

[Johan Löfberg]

You are doing several X >= smallnumber where you really want to do X >= smallnumber*eye(n)