sim

Simulate an MPC controller in closed loop with a linear plant

Syntax

sim(mpcobj,Ns,r)

sim(mpcobj,Ns,r,v)

sim(___,SimOptions)

[y,t,u,xp,xc,SimOptions] = sim(___)

Description

Use the Model Predictive Control Toolbox™ sim function to simulate the closed-loop or open-loop response of an MPC controller with constraints and weights that do not change at run time. The MPC controller can be implicit or explicit, the controlled plant must be linear and time-invariant, and you must specify the reference and disturbance signals in advance. By default, the plant used in the simulation is the one in MPCobj.Model.Plant, but you can use a different plant model to assess the controller robustness to model mismatch.

To run simulink models programmatically instead, see sim (Simulink).

sim(mpcobj,Ns,r) simulates the closed-loop system formed by the plant model specified in mpcobj.Model.Plant and by the MPC controller mpcobj, in response to the specified reference signal, r. The MPC controller can be either a traditional MPC controller (mpc) or explicit MPC controller (explicitMPC). The simulation runs for the specified number of simulation steps, Ns. sim plots the simulation results.

sim(mpcobj,Ns,r,v) also specifies the measured disturbance signal v.

sim(___,SimOptions) specifies additional simulation options. This syntax allows you to alter the default simulation options, such as initial states, input/output noise, and unmeasured disturbances, plant mismatch, etc. It also allows you to simulate the plant in open loop. You can use SimOptions with any of the previous input combinations.

[y,t,u,xp,xc,SimOptions] = sim(___) suppresses plotting and instead returns:

• the sequence of plant outputs y,

• the time sequence t (equally spaced by mpcobj.Ts),

• the manipulated variables u generated by the MPC controller,

• the sequence xp of states of the model of the plant used for simulation,

• the sequence xmpc of states of the MPC controller (provided by the state observer),

• and the simulation options object, SimOptions.

Examples

Simulate MPC Control of MISO Plant

Simulate the MPC control of a MISO system. The system has one manipulated variable, one measured disturbance, one unmeasured disturbance, and one output.

Create the continuous-time plant model. This plant will be used as the prediction model for the MPC controller.

sys = ss(tf({1,1,1},{[1 .5 1],[1 1],[.7 .5 1]}));

Discretize the plant model using a sampling time of 0.2 units.

Ts = 0.2;
sysd = c2d(sys,Ts);

Specify the MPC signal type for the plant input signals.

sysd = setmpcsignals(sysd,'MV',1,'MD',2,'UD',3);

Create an MPC controller for the sysd plant model. Use default values for the weights and horizons.

MPCobj = mpc(sysd);

-->The "PredictionHorizon" property of "mpc" object is empty. Trying PredictionHorizon = 10.
-->The "ControlHorizon" property of the "mpc" object is empty. Assuming 2.
-->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.

Constrain the manipulated variable to the [0 1] range.

MPCobj.MV = struct('Min',0,'Max',1);

Specify the simulation stop time.

Tstop = 30;

Define the reference signal and the measured disturbance signal.

num_sim_steps = round(Tstop/Ts);
r = ones(num_sim_steps,1);
v = [zeros(num_sim_steps/3,1); ones(2*num_sim_steps/3,1)];

The reference signal, r, is a unit step. The measured disturbance signal, v, is a unit step, with a 10 unit delay.

Simulate the controller.

sim(MPCobj,num_sim_steps,r,v)

-->The "Model.Disturbance" property of "mpc" object is empty:
   Assuming unmeasured input disturbance #3 is integrated white noise.
   Assuming no disturbance added to measured output channel #1.
-->The "Model.Noise" property of the "mpc" object is empty. Assuming white noise on each measured output channel.

Input Arguments

mpcobj — Model predictive controller

mpc object | explicitMPC object

Model predictive controller, specified as one of the following:

• mpc object — Implicit MPC controller

• explicitMPC object — Explicit MPC controller created using generateExplicitMPC.

Ns — Number of simulation steps

positive integer

Number of simulation steps, specified as a positive integer.

If you omit Ns, the default value is the number of rows of whichever of the following arrays has the largest number of rows:

• The input argument r

• The input argument v

• The UnmeasuredDisturbance property of SimOptions, if specified

• The OutputNoise property of SimOptions, if specified

Example: 100

r — Reference signal

MPCobj.Model.Nominal.Y (default) | double array

Reference signal, specified as an array. This array has ny columns, where ny is the number of plant outputs. r can have anywhere from 1 to Ns rows. If the number of rows is less than Ns, the missing rows are set equal to the last row.

Example: ones(100,1)

v — Measured input disturbance signal

MPCobj.Model.Nominal.U (default) | double array

Measured disturbance signal, specified as an array. This array has nv columns, where nv is the number of measured input disturbances. v can have anywhere from 1 to Ns rows. If the number of rows is less than Ns, the missing rows are set equal to the last row.

Example: [zeros(50,1);ones(50,1)]

SimOptions — Simulation options

[] (default) | mpcsimopt object

Simulation options, used to specify additional simulation options as well as noise and disturbance signals that feed into the plant but are unknown to the controller. You can also use this object to simulate the plant in open loop, or to specify a plant model to be used in simulation that is different from the one in MPCobj.Model.Plant, which allows you to assess the robustness of the control loop response to model mismatch.

For more information, see mpcsimopt.

Output Arguments

y — Sequence of plant outputs values

double array

Sequence of plant outputs values, returned as a Ns-by-Ny array, where Ns is the number of simulation steps and Ny is the number of plant outputs. The values in y include neither additive output disturbances nor additive measurement noise (if any).

t — Time sequence

double column vector

Time sequence, returned as a Ns-by-1 array, where Ns is the number of simulation steps. The values in t are equally spaced by MPCobj.Ts.

u — Sequence of manipulated variables

double array

Sequence of manipulated variables values generated by the MPC controller, returned as a Ns-by-Nu array, where Ns is the number of simulation steps and Nu is the number of manipulated variables.

xp — Sequence of plant model states values

struct array

Sequence of plant model states values, returned as an Ns-by-Nxp array, where Ns is the number of simulation steps and Nxp is the number of states in the plant model. The plant model is either MPCobj.Model or SimOptions.Model, if the latter is specified.

xc — Controller states

struct array

Sequence of MPC controller states, returned as an Ns-by-1 structure array. Each entry in the structure array has the same fields as an mpcstate object. At each time step, the MPC controller obtains the manipulated variable by multiplying an estimate of the plant state by a gain matrix (computed by solving a constrained quadratic optimization problem). By default, the controller uses a linear Kalman filter to estimate the state of the discrete time plant, augmented by the disturbance and noise models. Therefore, the states of the controller are the states of this Kalman filter, which are in turn the estimates of the plant, disturbance, and noise model states at each time step.

SimOptions — Simulation options object

mpcsimopt object

Simulation options objects used for the simulation. This object can specify noise and disturbance signals that feed into the plant but are unknown to the controller. It can also specify if the simulated system is open loop or if the plant model used in the simulation is different from the one in MPCobj.Model.Plant.

For more information, see mpcsimopt.