custom state estimation -凯发k8网页登录

define plant model

consider the case of a double integrator plant for which all of the plant states are measurable. in such a case, you can provide the measured states to the mpc controller rather than have the controller estimate the states.

the linear open-loop plant model is a double integrator.

plant = tf(1,[1 0 0]);

design mpc controller

create the controller object with a sample time of 0.1 seconds, a prediction horizon of 10 steps, and control horizon of 3 steps.

ts=0.1;
mpcobj = mpc(plant,ts,10,3);

-->"weights.manipulatedvariables" is empty. assuming default 0.00000.
-->"weights.manipulatedvariablesrate" is empty. assuming default 0.10000.
-->"weights.outputvariables" is empty. assuming default 1.00000.

specify actuator saturation limits as manipulated variable constraints.

mpcobj.mv = struct('min',-1,'max',1);

configure the controller to use custom state estimation.

setestimator(mpcobj,'custom');

simulate controller

initialize variables to store the closed-loop responses.

tf = round(5/ts);
yy = zeros(tf,1);
uu = zeros(tf,1);

prepare the plant used in the simulation by converting it to a discrete-time model and setting the initial state.

sys = c2d(ss(plant),ts);
xsys = [0;0];

get an handle to the object that is used to store the controller states.

xmpc = mpcstate(mpcobj);

-->converting the "model.plant" property to state-space.
-->converting model to discrete time.
   assuming no disturbance added to measured output #1.
-->"model.noise" is empty. assuming white noise on each measured output.

iteratively simulate the closed-loop response using the function.

for each simulation step:

for t = 0:tf
    y = sys.c*xsys; % plant equations: output
    yy(t 1) = y;
    xmpc.plant = xsys; % state estimation
    u = mpcmove(mpcobj,xmpc,[],1); % y is not needed
    uu(t 1) = u;
    xsys = sys.a*xsys   sys.b*u; % plant equations: next state
end

plot the simulation results.

figure
subplot(2,1,1)
plot(0:ts:5,yy)
title('y')
subplot(2,1,2)
plot(0:ts:5,uu)
title('u')

simulate closed-loop control of the linear plant model in simulink. for this model, the controller mpcobj is specified in the mpc controller block.

mdl = 'mpc_customestimation';
open_system(mdl)
sim(mdl)

the closed-loop responses for the matlab and simulink simulations are identical.

fprintf('\ndifference between simulations in matlab and simulink is %g\n',norm(uu-u));

difference between simulations in matlab and simulink is 5.92777e-14

close the simulink model.

bdclose(mdl)