Define Plant Model

Define linear open-loop dynamic plant model.

num = [1 1];
den = [1 3 2 0.5];
sys = tf(num,den);

The plant is a stable single-input single-output system as seen in its step response.

step(sys)

Design MPC Controller

Create an MPC controller, specifying the:

Ts = 0.5;
p = 15;
m = 2;
mpcobj = mpc(sys,Ts,p,m);

-->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.

Define constraints on the manipulated variable.

mpcobj.MV=struct('Min',-1,'Max',1);

Specify the output tuning weight.

mpcobj.Weights.Output=0.01;

Open and Configure Simulink Model

Open the Simulink model.

mdl = 'mpc_bumpless';
open_system(mdl)

In this model, the MPC Controller block is already configured for bumpless transfer using the following controller parameter settings.

To achieve bumpless transfer, the initial states of your plant and controller must be the same, which is the case for the plant and controller in this example. However, if the initial conditions for your system do not match, you can set the initial states of the controller to the plant initial states. To do so, extract the mpcstate object from your controller and set the initial state of the plant.

stateobj = mpcstate(MPC1);
stateobj.Plant = x0;

where x0 is a vector of the initial plant states. Then, set the Initial Controller State parameter of the MPC Controller block to stateobj.

To simulate switching between manual and automatic operation, the Switching block sends either 1 or 0 to control a switch. When it sends 0, the system is in automatic mode, and the output from the MPC Controller block goes to the plant. Otherwise, the system is in manual mode, and the signal from the Operator Commands block goes to the plant.

In both cases, the actual plant input feeds back to the controller ext.mv inport, unless the plant input saturates at -1 or 1. The controller constantly monitors the plant output and updates its estimate of the plant state, even when in manual operation.

This model also shows the optimization switching option. When the system switches to manual operation, a nonzero signal enters the switch inport of the controller block. The signal turns off the optimization calculations of the controller, which reduces computational effort.

Simulate Controller in Simulink

Simulate closed-loop control of the linear plant model in Simulink.

sim(mdl)

-->Converting the "Model.Plant" property of "mpc" object to state-space.
-->Converting model to discrete time.
-->Assuming output disturbance added to measured output channel #1 is integrated white noise.
-->The "Model.Noise" property of the "mpc" object is empty. Assuming white noise on each measured output channel.

For the first 90 time units, the Switching Signal is 0, which makes the system operate in automatic mode. During this time, the controller smoothly drives the controlled plant output from its initial value, 0, to the desired reference value, -0.5.

The controller state estimator has zero initial conditions as a default, which is appropriate when this simulation begins. Thus, there is no bump at startup. In general, start the system running in manual mode long enough for the controller to acquire an accurate state estimate before switching to automatic mode.

At time 90, the Switching Signal changes to 1. This change switches the system to manual operation and sends the operator commands to the plant. Simultaneously, the nonzero signal entering the switch inport of the controller turns off the optimization calculations. While the optimization is turned off, the MPC Controller block passes the current ext.mv signal to the Controller Output.

Once in manual mode, the operator commands set the manipulated variable to -0.5 for 10 time units, and then to 0. The Plant Output plot shows the open-loop response between times 90 and 180 when the controller is deactivated.

At time 180, the system switches back to automatic mode. As a result, the plant output returns to the reference value smoothly, and a similar smooth adjustment occurs in the controller output.

Turn Off Manipulated Variable Feedback

To examine the controller behavior without manipulated variable feedback, modify the model as follows:

To perform these steps programmatically, use the following commands.

delete_line(mdl,'Switch/1','Unit Delay/1');
delete_line(mdl,'Unit Delay/1','MPC Controller/3');
delete_block([mdl '/Unit Delay']);
delete_line(mdl,'Switching/1','MPC Controller/4');
set_param([mdl '/MPC Controller'],'mv_inport','off');
set_param([mdl '/MPC Controller'],'switch_inport','off');

Adjust the limits of the response plots, and simulate the model.

set_param([mdl '/Yplots'],'Ymin','-1.1~-0.1')
set_param([mdl '/Yplots'],'Ymax','2~1.1')
set_param([mdl '/MVplots'],'Ymin','-0.6~-0.5')
set_param([mdl '/MVplots'],'Ymax','1.1~1.1')
sim(mdl)

The behavior of the system is identical to the original case for the first 90 time units.

When the system switches to manual mode at time 90, the plant behavior is the same as before. However, the controller tries to hold the plant at the setpoint. So, its output increases and eventually saturates, as seen in Controller Output. Since the controller assumes that this output is going to the plant, its state estimates become inaccurate. Therefore, when the system switches back to automatic mode at time 180, there is a large bump in the Plant Output.

Such a bump creates large actuator movements within the plant. By smoothly transferring from manual to automatic operation, a model predictive controller eliminates such unwanted movements.

bdclose(mdl)