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# Documentation

## Tuning Controller Weights

This example shows how to vary the weights on outputs, inputs, and ECR slack variable for soft constraints in real-time.

The weights specified in the MPC object are overridden by the weights supplied to the MPC Controller block. If a weight signal is not connected to the MPC Controller block, then the corresponding weight is the one specified in the MPC object.

Define Plant Model

Define a multivariable discrete-time linear system with no direct I/O feedthrough, and assume input #4 is a measured disturbance and output #4 is unmeasured.

```Ts = 0.1; % sampling time
plant = tf({1,[1 1],5,2;3,[1 5],1,0;0,0,1,[1 1];2,[1 -1],0,0},...
{[1 1 1],[1 3 4 5],[1 10],[1 5];
[1 1],[1 2],[1 2 8],[1 1];
[1 2 1],[1 3 1 1],[1 1],[1 2];
[1 1],[1 3 10 10],[1 10],[1 1]});
plant = c2d(ss(plant),Ts);
plant.D = 0;
```

Design MPC Controller

Specify input and output signal types.

```plant = setmpcsignals(plant,'MD',4,'UO',4);
% Create the controller object with sampling period, prediction and control
% horizons:
p = 20;                                     % Prediction horizon
m = 3;                                      % Control horizon
mpcobj = mpc(plant,Ts,p,m);
```
```-->Assuming unspecified input signals are manipulated variables.
-->Assuming unspecified output signals are measured outputs.
-->The "Weights.ManipulatedVariables" property of "mpc" object is empty. Assuming default 0.00000.
-->The "Weights.ManipulatedVariablesRate" property of "mpc" object is empty. Assuming default 0.10000.
-->The "Weights.OutputVariables" property of "mpc" object is empty. Assuming default 1.00000.
for output(s) y1 y2 y3 and zero weight for output(s) y4
```

Specify MV constraints.

```mpcobj.MV(1).Min = -6;
mpcobj.MV(1).Max = 6;
mpcobj.MV(2).Min = -6;
mpcobj.MV(2).Max = 6;
mpcobj.MV(3).Min = -6;
mpcobj.MV(3).Max = 6;
```

To run this example, Simulink® is required.

```if ~mpcchecktoolboxinstalled('simulink')
disp('Simulink(R) is required to run this example.')
return
end
% Define reference signal.
Tstop = 10;
ref = [1 0 3 1];
r = struct('time',(0:Ts:Tstop)');
N = numel(r.time);
r.signals.values=ones(N,1)*ref;
```

Define measured disturbance.

```v = 0.5;
```

OV weights are linearly increasing with time, except for output #2 that is not weighted.

```ywt.time = r.time;
ywt.signals.values = (1:N)'*[.1 0 .1 .1];
```

MVRate weights are decreasing linearly with time.

```duwt.time = r.time;
duwt.signals.values = (1-(1:N)/2/N)'*[.1 .1 .1];
```

ECR weight increases exponentially with time.

```ECRwt.time = r.time;
ECRwt.signals.values = 10.^(2+(1:N)'/N);
```

Start simulation.

```mdl = 'mpc_onlinetuning';
sim(mdl);                           % Start Simulation
```
```-->Integrated white noise added on measured output channel #1.
-->Integrated white noise added on measured output channel #2.
-->Integrated white noise added on measured output channel #3.
-->The "Model.Noise" property of the "mpc" object is empty. Assuming white noise on each measured output channel.
```

Simulate Using MPCMOVE Command

Define real plant and MPC state object.

```[A,B,C,D] = ssdata(plant);
x = zeros(size(plant.B,1),1);   % Initial state of the plant
xmpc = mpcstate(mpcobj);        % Initial state of the MPC controller
```

Store the closed-loop MPC trajectories in arrays YY,UU,XX.

```YY = [];
UU = [];
XX = [];
```

Use MPCMOVEOPT object to provide weights at run-time.

```options = mpcmoveopt;
```

Start simulation.

```for t = 0:N-1,
% Store states
XX = [XX,x]; %#ok<*AGROW>
% Compute plant output (no feedthrough from MV to Y)
y = C*x+D(:,4)*v;
YY = [YY;y'];
% Obtain reference signal
ref = r.signals.values(t+1,:)';
% Update MPCMOVEOPT object with run-time weights
options.MVRateWeight = duwt.signals.values(t+1,:);
options.OutputWeight = ywt.signals.values(t+1,:);
options.ECRWeight = ECRwt.signals.values(t+1,:);
% Compute control action
u = mpcmove(mpcobj,xmpc,y(1:3),ref,v,options);
UU = [UU;u'];
% Update plant states
x = A*x + B(:,1:3)*u + B(:,4)*v;
end
```

Plot and Compare Simulation Results

```figure(1);
clf;
subplot(121)
plot(0:Ts:Tstop,[YY ysim])
grid
title('output')
subplot(122)
plot(0:Ts:Tstop,[UU usim])
grid
title('input')
```

Simulation results are the same.

```fprintf('\n\nDifference between MPC Simulink block and MPCMOVE simulations: %g',norm(UU-usim)+norm(YY-ysim));
```
```
Difference between MPC Simulink block and MPCMOVE simulations: 6.19412e-11```
```bdclose(mdl);
```