mpcmove
Compute optimal control action and update controller states
Syntax
Description
Use this command to simulate an MPC controller in closed-loop with a plant model.
Call mpcmove
repeatedly in a for loop to calculate the manipulated
variable and update the controller states at each time step.
returns the optimal move mv
= mpcmove(MPCobj
,xc
,ym
,r
,v
)mv
and updates the states
xc of the controller MPCobj
.
The manipulated variable mv
at the current time is calculated given:
the controller object,
MPCobj
,a pointer to the current estimated extended state,
xc
,the measured plant outputs,
ym
,the output references,
r
,and the measured disturbance input,
v
.
If ym
, r
or v
is
specified as []
, or if it is missing as a last input argument,
mpcmove
uses the appropriate MPCobj.Model.Nominal
value instead.
When using default state estimation, mpcmove
also updates the
controller state referenced by the handle object xc
. Therefore, when
using default state estimation, xc
always points to the updated
controller state. When using custom state estimation, you should update
xc
prior to each mpcmove
call.
[___] = mpcmove(___,
overrides default constraints and weights in options
)MPCobj
with the values
specified in Options
, an mpcmoveopt
object. Use Options
to provide run-time
adjustment of constraints and weights during the closed-loop simulation.
Examples
Simulate Closed-Loop Response Using mpcMove
Perform closed-loop simulation of a plant with one MV and one measured OV.
Define a plant model and create a model predictive controller with MV constraints.
ts = 2; Plant = ss(0.8,0.5,0.25,0,ts); mpcobj = mpc(Plant);
-->The "PredictionHorizon" property is empty. Assuming default 10. -->The "ControlHorizon" property is empty. Assuming default 2. -->The "Weights.ManipulatedVariables" property is empty. Assuming default 0.00000. -->The "Weights.ManipulatedVariablesRate" property is empty. Assuming default 0.10000. -->The "Weights.OutputVariables" property is empty. Assuming default 1.00000.
mpcobj.MV(1).Min = -2; mpcobj.MV(1).Max = 2;
Obtain an handle object pointing to the controller state.
xc = mpcstate(mpcobj)
-->Assuming output disturbance added to measured output channel #1 is integrated white noise. -->The "Model.Noise" property is empty. Assuming white noise on each measured output. MPCSTATE object with fields Plant: 0 Disturbance: 0 Noise: [1x0 double] LastMove: 0 Covariance: [2x2 double]
The controller has one state for the internal plant model, one for the disturbance model, and one to hold the last value of the manipulated variable. All these three states are initialized to zero.
Set the reference signal. There is no measured disturbance.
r = 1;
Simulate the closed-loop response by calling mpcmove
iteratively. In the simulation, assume that the simulated plant is identical to the predictive model. Therefore the plant state x
in this case is identical to xc.Plan
t and the plant output is y = C*x
+ D*u
= 0.25*x
= 0.25*xc.Plan
t. Here, mpcmove
updates the controller state referenced by xc
(therefore including xc.Plant
), and returns the manipulated variable in u(i)
, which is used just for plotting.
t = 0:ts:40; N = length(t); y = zeros(N,1); u = zeros(N,1); for i = 1:N y(i) = 0.25*xc.Plant; u(i) = mpcmove(mpcobj,xc,y(i),r); end
Analyze the result.
[ts,us] = stairs(t,u); plot(ts,us,'r-',t,y,'b--') legend('MV','OV')
Modify the MV upper bound as the simulation proceeds using an mpcmoveopt
object. Since the options argument overrides selected mpcobj
properties, specify MV constraints again.
MPCopt = mpcmoveopt; MPCopt.MVMin = -2; MPCopt.MVMax = 2;
Simulate the closed-loop response and introduce the real-time upper limit change at eight seconds (the fifth iteration step).
xc = mpcstate(mpcobj); y = zeros(N,1); u = zeros(N,1); for i = 1:N y(i) = 0.25*xc.Plant; if i == 5 MPCopt.MVMax = 1; end u(i) = mpcmove(mpcobj,xc,y(i),r,[],MPCopt); end
Analyze the results.
[ts,us] = stairs(t,u); plot(ts,us,'r-',t,y,'b--') legend('MV','OV')
Evaluate Scenario at Specific Time Instant
Define a plant model.
ts = 2; Plant = ss(0.8,0.5,0.25,0,ts);
Create a model predictive controller with constraints on both the manipulated variable and the rate of change of the manipulated variable. The prediction horizon is 10
intervals, and the control horizon is blocked.
MPCobj = mpc(Plant,ts,10,[2 3 5]);
-->The "Weights.ManipulatedVariables" property is empty. Assuming default 0.00000. -->The "Weights.ManipulatedVariablesRate" property is empty. Assuming default 0.10000. -->The "Weights.OutputVariables" property is empty. Assuming default 1.00000.
MPCobj.MV(1).Min = -2; MPCobj.MV(1).Max = 2; MPCobj.MV(1).RateMin = -1; MPCobj.MV(1).RateMax = 1;
Initialize (and return an handle to) the controller internal state for simulation.
xc = mpcstate(MPCobj);
-->Assuming output disturbance added to measured output channel #1 is integrated white noise. -->The "Model.Noise" property is empty. Assuming white noise on each measured output.
xc.Plant = 2.8; xc.LastMove = 0.85;
Compute the optimal control move at the current time.
y = 0.25*xc.Plant; r = 1; [u,Info] = mpcmove(MPCobj,xc,y,r);
Analyze the predicted optimal sequences.
[ts,us] = stairs(Info.Topt,Info.Uopt); plot(ts,us,'r-',Info.Topt,Info.Yopt,'b--') legend('MV','OV')
plot
ignores Info.Uopt(end)
as it is NaN
.
Examine the optimal cost.
Info.Cost
ans = 0.0793
Input Arguments
MPCobj
— Model predictive controller
MPC controller object
Model predictive controller, specified as an MPC controller
object. To create an MPC controller, use mpc
.
xc
— Current controller state handle
mpcstate
object
Current controller state handle, specified as an mpcstate
object.
Before you begin a simulation with mpcmove
, initialize the
controller, and return an handle to its state using xc =
mpcstate(MPCobj)
. Then, modify the default properties of
xc
as appropriate. mpcmove
modifies the
controller state. The handle object xc
always reflect the current
(updated) state of the controller.
If you are using default state estimation, mpcmove
expects
xc
to represent xc[n|n-1]
. The
mpcmove
command updates the state values in the previous control
interval with that information. Therefore, you should not programmatically update
xc
at all. The default state estimator employs a steady-state
Kalman filter.
If you are using custom state estimation, mpcmove
expects
xc
to represent xc[n|n]
. Therefore, prior to
each mpcmove
command, you must set xc.Plant
,
xc.Disturbance
, and xc.Noise
to the best
estimates of these states (using the latest measurements) at the current control
interval.
ym
— Current measured output values
column vector of length Nym
Current measured output values at time k, specified as a column vector of length Nym, where Nym is the number of measured outputs.
If you are using custom state estimation, set ym = []
.
r
— Plant output reference values
p-by-Ny array
Plant output reference values, specified as a
p-by-Ny array, where
p is the prediction horizon of MPCobj
and
Ny is the number of outputs. Row
r(i,:)
defines the reference values at step i of
the prediction horizon.
r
must contain at least one row. If r
contains fewer than p rows, mpcmove
duplicates
the last row to fill the
p-by-Ny array. If you
supply exactly one row, therefore, a constant reference applies for the entire
prediction horizon.
To implement reference previewing, which can improve tracking when a reference
varies in a predictable manner, r
must contain the anticipated
variations, ideally for p steps.
v
— Current and anticipated measured disturbances
(p+1)-by-Nmd
array
Current and anticipated measured disturbances, specified as a
(p+1)-by-Nmd array,
where p is the prediction horizon of MPCobj
and
Nmd is the number of measured
disturbances. The first row of v
specifies the current measured
disturbance values. Row v(i+1,:)
defines the anticipated disturbance
values at step i of the prediction horizon.
Modeling of measured disturbances provides feedforward control action. If your plant
model does not include measured disturbances, use v
=
[]
.
If your model includes measured disturbances, v
must contain at
least one row. If v
contains fewer than p+1
rows, mpcmove
duplicates the last row to fill the
(p+1)-by-Nmd array. If
you supply exactly one row, a constant measured disturbance applies for the entire
prediction horizon.
To implement disturbance previewing, which can improve tracking when a disturbance
varies in a predictable manner, v
must contain the anticipated
variations, ideally for p steps.
options
— Run-time options
mpcmoveopt
object
Run-time options, specified as an mpcmoveopt
object. Use options
to override selected
properties of MPCobj
during simulation. These options apply to the
current mpcmove
time instant only. Using
options
yields the same result as redefining or modifying
MPCobj
before each call to mpcmove
, but
involves considerably less overhead. Using options
is equivalent to
using an MPC Controller
Simulink® block in combination with optional input signals that modify controller
settings, such as MV and OV constraints.
Output Arguments
mv
— Optimal manipulated variable moves
column vector
Optimal manipulated variable moves, returned as a column vector of length Nmv, where Nmv is the number of manipulated variables.
If the controller detects an infeasible optimization problem or encounters numerical
difficulties in solving an ill-conditioned optimization problem, mv
remains at its most recent successful solution, xc.LastMove
.
Otherwise, if the optimization problem is feasible and the solver reaches the
specified maximum number of iterations without finding an optimal solution,
mv
:
Remains at its most recent successful solution if the
Optimizer.UseSuboptimalSolution
property of the controller isfalse
.Is the suboptimal solution reached after the final iteration if the
Optimizer.UseSuboptimalSolution
property of the controller istrue
. For more information, see Suboptimal QP Solution.
info
— Solution details
structure
Solution details, returned as a structure with the following fields.
Uopt
— Optimal manipulated variable sequence
(p+1)-by-Nmv
array
Predicted optimal manipulated variable adjustments (moves), returned as a (p+1)-by-Nmv array, where p is the prediction horizon and Nmv is the number of manipulated variables.
Uopt(i,:)
contains the calculated optimal values at
time k+i-1
, for i = 1,...,p
, where
k
is the current time. The first row of
Info.Uopt
contains the same manipulated variable
values as output argument mv
. Since the controller does
not calculate optimal control moves at time k+p
,
Uopt(p+1,:)
is equal to
Uopt(p,:)
.
Yopt
— Optimal output variable sequence
(p+1)-by-Ny
array
Optimal output variable sequence, returned as a (p+1)-by-Ny array, where p is the prediction horizon and Ny is the number of outputs.
The first row of Info.Yopt
contains the calculated
outputs at time k
based on the estimated states and
measured disturbances; it is not the measured output at time
k
. Yopt(i,:)
contains the
predicted output values at time k+i-1
, for i =
1,...,p+1
.
Yopt(i,:)
contains the calculated output values at time
k+i-1
, for i = 2,...,p+1
, where
k
is the current time. Yopt(1,:)
is computed based on the estimated states and measured disturbances.
Xopt
— Optimal prediction model state sequence
(p+1)-by-Nx
array
Optimal prediction model state sequence, returned as a (p+1)-by-Nx array, where p is the prediction horizon and Nx is the number of states in the plant and unmeasured disturbance models (states from noise models are not included).
Xopt(i,:)
contains the calculated state values at time
k+i-1
, for i = 2,...,p+1
, where
k
is the current time. Xopt(1,:)
is the same as the current states state values.
Topt
— Time intervals
column vector of length p+1
Time intervals, returned as a column vector of length
p+1. Topt(1)
= 0, representing the
current time. Subsequent time steps Topt(i)
are given by
Ts*(i-1)
, where Ts = MPCobj.Ts
is
the controller sample time.
Use Topt
when plotting the Uopt
,
Xopt
, or Yopt
sequences.
Slack
— Slack variable
nonnegative scalar
Slack variable, ε, used in constraint softening, returned as
0
or a positive scalar value.
ε = 0 — All constraints were satisfied for the entire prediction horizon.
ε > 0 — At least one soft constraint is violated. When more than one constraint is violated, ε represents the worst-case soft constraint violation (scaled by your ECR values for each constraint).
See Optimization Problem for more information.
Iterations
— Number of solver iterations
positive integer | 0
| -1
| -2
Number of solver iterations, returned as one of the following:
Positive integer — Number of iterations needed to solve the optimization problem that determines the optimal sequences.
0
— Optimization problem could not be solved in the specified maximum number of iterations.–1
— Optimization problem was infeasible. An optimization problem is infeasible if no solution can satisfy all the hard constraints.–2
— Numerical error occurred when solving the optimization problem.
QPCode
— Optimization solution status
'feasible'
| 'infeasible'
| 'unrealiable'
Optimization solution status, returned as one of the following:
'feasible'
— Optimal solution was obtained (Iterations
> 0)'infeasible'
— Solver detected a problem with no feasible solution (Iterations
= –1) or a numerical error occurred (Iterations
= –2)'unreliable'
— Solver failed to converge (Iterations
= 0). In this case, ifMPCobj.Optimizer.UseSuboptimalSolution
isfalse
,u
freezes at the most recent successful solution. Otherwise, it uses the suboptimal solution found during the last solver iteration.
Cost
— Objective function cost
nonnegative scalar
Objective function cost, returned as a nonnegative scalar value. The cost quantifies the degree to which the controller has achieved its objectives. For more information, see Optimization Problem.
The cost value is only meaningful when QPCode =
'feasible'
, or when QPCode = 'feasible'
and
MPCobj.Optimizer.UseSuboptimalSolution
is
true
.
Tips
mpcmove
updatesxc
, even though it is an input argument.If
ym
,r
orv
is specified as[]
, or if it is missing as a last input argument,mpcmove
uses the appropriateMPCobj.Model.Nominal
value instead.To view the predicted optimal behavior for the entire prediction horizon, plot the appropriate sequences provided in
Info
.To determine the optimization status, check
Info.Iterations
andInfo.QPCode
.
Alternatives
Use
sim
for plant mismatch and noise simulation when not using run-time constraints or weight changes.Use the MPC Designer app to interactively design and simulate model predictive controllers.
Use the MPC Controller block in Simulink and for code generation.
Use
mpcmoveCodeGeneration
to simulate an MPC controller prior to code generation.
Version History
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