sim

Simulate closed-loop/open-loop response to arbitrary reference and disturbance signals for implicit or explicit MPC

Syntax

sim(MPCobj,T,r)
sim(MPCobj,T,r,v)
sim(___,SimOptions)
[y,t,u,xp,xmpc,SimOptions] = sim(___)


Description

Use sim to simulate the implicit (traditional) or explicit MPC controller in closed loop with a linear time-invariant model, which, by default, is the plant model contained in MPCobj.Model.Plant. As an alternative, sim can simulate the open-loop behavior of the model of the plant, or the closed-loop behavior in the presence of a model mismatch, when the controller’s prediction model differs from the actual plant model.

sim(MPCobj,T,r) simulates the closed-loop system formed by the plant model specified in MPCobj.Model.Plant and by the MPC controller specified 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, T. sim plots the simulation results.

sim(MPCobj,T,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. You can use SimOptions with any of the previous input combinations.

[y,t,u,xp,xmpc,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, SimOptions. You can use this syntax with any of the allowed input argument combinations.

Input Arguments

MPCobj	MPC controller containing the parameters of the Model Predictive Control law to simulate, specified as either an implicit MPC controller (mpc) or an explicit MPC controller (explicitMPC).
T	Number of simulation steps, specified as a positive integer. If you omit T, the default value is the row size of whichever of the following arrays has the largest row size: The input argument r The input argument v The UnmeasuredDisturbance property of SimOptions, if specified The OutputNoise property of SimOptions, if specified Default: The largest row size of r, v, UnmeasuredDisturbance, and OutputNoise
r	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 T rows. If the number of rows is less than T, the missing rows are set equal to the last row. Default: MPCobj.Model.Nominal.Y
v	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 T rows. If the number of rows is less than T, the missing rows are set equal to the last row. Default: Corresponding entries from MPCobj.Model.Nominal.U
SimOptions	Simulation options, specified as an mpcsimopt object. Default: []

Output Arguments

y	Sequence of controlled plant outputs, returned as a T-by-Ny array, where T 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, returned as a T-by-1 array, where T is the number of simulation steps. The values in t are equally spaced by MPCobj.Ts.
u	Sequence of manipulated variables generated by the MPC controller, returned as a T-by-Nu array, where T is the number of simulation steps and Nu is the number of manipulated variables.
xp	Sequence of plant model states, T-by-Nxp array, where T 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.
xmpc	Sequence of MPC controller state estimates, returned as a T-by-1 structure array. Each entry in the structure array has the same fields as an mpcstate object. The state estimates include plant, disturbance, and noise model states at each time step.
SimOptions	Simulation options used, returned as an mpcsimopt object.

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.