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Tune control system parameters in Simulink using `slTuner`

interface

`systune`

tunes fixed-structure control systems subject to both
soft and hard design goals. `systune`

can tune multiple fixed-order,
fixed-structure control elements distributed over one or more feedback loops. For an overview
of the tuning workflow, see Automated Tuning Workflow.

This command tunes control systems modeled in Simulink^{®}. For tuning control systems represented in MATLAB^{®}, use `systune`

for `genss`

models.

`[`

tunes
the free parameters of the control system in Simulink. The Simulink model, tuned blocks, and analysis points of
interest are specified by the `st`

,`fSoft`

]
= systune(`st0`

,`SoftGoals`

)`slTuner`

interface, `st0`

. `systune`

tunes
the control system parameters to best meet the performance goals, `SoftGoals`

.
The command returns a tuned version of `st0`

as `st`

.
The best achieved soft constraint values are returned as `fSoft`

.

If the `st0`

contains real parameter uncertainty, `systune`

automatically
performs robust tuning to optimize the constraint values for worst-case
parameter values. `systune`

also performs robust
tuning against a set of plant models obtained at different operating
points or parameter values. See Input Arguments.

Tuning is performed at the sample time specified by the `Ts`

property
of `st0`

.

*x* is the vector of tunable parameters in
the control system to tune. `systune`

converts each
soft and hard tuning requirement `SoftReqs(i)`

and `HardReqs(j)`

into
normalized values *f _{i}*(

`systune`

then solves the constrained
minimization problem:Minimize $$\underset{i}{\mathrm{max}}{f}_{i}\left(x\right)$$ subject to $$\underset{j}{\mathrm{max}}{g}_{j}\left(x\right)<1$$, for $${x}_{\mathrm{min}}<x<{x}_{\mathrm{max}}$$.

*x _{min}* and

When you use both soft and hard tuning goals, the software approaches this optimization problem by solving a sequence of unconstrained subproblems of the form:

$$\underset{x}{\mathrm{min}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{max}\left(\alpha f\left(x\right),g\left(x\right)\right).$$

The software adjusts the multiplier *α* so
that the solution of the subproblems converges to the solution of
the original constrained optimization problem.

`systune`

returns the `slTuner`

interface with parameters tuned
to the values that best solve the minimization problem. `systune`

also
returns the best achieved values of *f _{i}*(

`fSoft`

and `gHard`

respectively.For information about the functions *f _{i}*(

`TuningGoal`

requirement
object.`systune`

uses the nonsmooth optimization algorithms
described in [1],[2],[3],[4]

`systune`

computes the *H _{∞}*
norm using the algorithm of [5] and structure-preserving eigensolvers from the SLICOT library. For information about the
SLICOT library, see http://slicot.org.

Tune interactively using **Control
System Tuner**.

[1] P. Apkarian and D. Noll, "Nonsmooth H-infinity
Synthesis," *IEEE Transactions on Automatic Control*,
Vol. 51, Number 1, 2006, pp. 71–86.

[2] Apkarian, P. and D. Noll, "Nonsmooth Optimization
for Multiband Frequency-Domain Control Design," *Automatica*,
43 (2007), pp. 724–731.

[3] Apkarian, P., P. Gahinet, and C. Buhr,
"Multi-model, multi-objective tuning of fixed-structure controllers," *Proceedings
ECC* (2014), pp. 856–861.

[4] Apkarian, P., M.-N. Dao, and D. Noll,
"Parametric Robust Structured Control Design," *IEEE Transactions
on Automatic Control*, 2015.

[5] Bruinsma, N.A., and M. Steinbuch. "A Fast Algorithm to Compute the
H_{∞} Norm of a Transfer Function Matrix." *Systems
& Control Letters*, 14, no.4 (April 1990): 287–93.

```
systune (for
genss)
```

| `systuneOptions`

| `slTuner`

| `addPoint`

| `getIOTransfer`

| `getLoopTransfer`

| `writeBlockValue`

| `looptune`

| `hinfstruct`

(Robust Control Toolbox)