Mixed H2/H∞ synthesis with regional pole placement constraints - MATLAB h2hinfsyn - 金宝app,下载188bet金宝搏,金宝搏官方网站

Syntax

[K,CL,normz,info] = h2hinfsyn(P,Nmeas,Ncon,Nz2,Wz,Name,Value)

Description

[K,CL,normz,info] = h2hinfsyn(P,Nmeas,Ncon,Nz2,Wz,Name,Value)employs LMI techniques to compute an output-feedback control lawu=K(s)yfor the control problem of the following illustration.

The LTI plantPhas partitioned state-space form given by

$\begin{matrix} \dot{x} = A x + B_{1} w + B_{2} u, \\ z_{\infty} = C_{1} x + D_{11} w + D_{12} u, \\ z_{2} = C_{2} x + D_{21} w + D_{22} u, \\ y = C_{y} x + D_{y 1} w + D_{y 2} u . \end{matrix}$

The resulting controllerK:

Keeps theH_∞normGof the transfer function fromwtoz_∞below the value you specify using theName,Valueargument“HINFMAX”.
Keeps theH₂normHof the transfer function fromwtoz₂below the value you specify using theName,Valueargument'H2MAX'.
Minimizes a trade-off criterion of the form

$W_{1} G^{2} + W_{2} H^{2},$

whereW₁andW₂are the first and second entries in the vectorWz.
Places the closed-loop poles in the LMI region that you specify using theName,Valueargument'REGION'.

Use the input argumentsNmeas,Ncon, andNz2to specify the number of signals iny,u, andz₂, respectively. You can use additionalName,Valuepairs to specify additional options for the computation.

Input Arguments

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`P`— Plant
LTI model

Plant, specified as an LTI model such as atforssmodel.Pmust be a continuous-time model.

`Nmeas`— Number of measurement signals
positive integer

Number of measurement signals, specified as a positive integer. This value is the number of signals iny.

`Ncon`— Number of control signals
positive integer

Number of control signals, specified as a positive integer. This value is the number of signals inu.

`Nz2`— Number of signals subject toH2constraint
positive integers

Number of signals subject to the constraint on theH₂norm, specified as a positive integer. This value is the number of signals inz₂. If the total number of outputs ofPisNout, then the firstNout - Nz2 - Nmeasoutputs ofPare subject to the constraint on theH_∞norm.

`Wz`— Weights forH_∞andH₂performance
1-by-2 vector

Weights forH_∞andH₂performance, specified as a 1-by-2 vector of the form[Winf,W2].

Name-Value Pair Arguments

Specify optional comma-separated pairs ofName,Valuearguments.Nameis the argument name andValueis the corresponding value.Namemust appear inside single quotes (' '). You can specify several name and value pair arguments in any order asName1,Value1,...,NameN,ValueN.

例子:'REGION',reg,'H2MAX',1,'HINFMAX',1,'DISPLAY','on'

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`'REGION'`— Pole placement region
`[]`(default) | matrix

Pole placement region, specified as a comma-separated pair consisting of'REGION'and a matrix of the form[L,M]. This matrix specifies the pole placement region as:

${z : L + z M + \bar{z} M^{T} < 0} .$

Generate the matrix usinglmireg. The default LMI region for pole placement, specified by the empty matrix[], is the open left-half plane, enforcing closed-loop stability only.

`'H2MAX'`— Upper bound onH₂norm
`Inf`(default) | positive scalar

Upper bound on theH₂norm of the transfer function fromwtoz₂, specified as a comma-separated pair consisting of'H2MAX'and a positive scalar value orInf. The default valueInfis equivalent to setting the limit to zero, and causesh2hinfsynto minimize theH₂norm subject to the trade-off criterion.

例子:'H2MAX',1

`“HINFMAX”`— Upper bound onH_∞norm
`Inf`(default) | positive scalar

Upper bound on theH_∞norm of the transfer function fromwtoz_∞, specified as a comma-separated pair consisting of“HINFMAX”and a positive scalar value orInf. The default valueInfis equivalent to setting the limit to zero, and causesh2hinfsynto minimize theH_∞norm subject to the trade-off criterion.

例子:“HINFMAX”,1

`'DKMAX'`— Bound on controller feedthrough
100 (default) | nonnegative scalar

Bound on the norm on the feedthrough matrixD_Kof the controller, specified as a comma-separated pair consisting of'DKMAX'and a nonnegative scalar value. To make the controllerKstrictly proper, set'DKMAX'to 0.

例子:'DKMAX',0

`'TOL'`— Relative accuracy of trade-off criterion
0.01 (default) | positive scalar

Desired relative accuracy on the optimal value of the trade-off criterion, specified as a comma-separated pair consisting of'TOL'and a positive scalar value.

`'DISPLAY'`— Toggle for screen display
`“关闭”`(default) |`'on'`

Toggle for screen display of synthesis information, specified as a comma-separated pair consisting of'DISPLAY'and either'on'or“关闭”.

Output Arguments

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`K`— Optimal output-feedback controller
state-space model

Optimal output-feedback controller, returned as a state-space (ss) model withNmeasinputs andNconoutputs.

`CL`— Closed-loop system
state-space model

Closed-loop system with synthesized controller, returned as a state-space (ss) model. The closed-loop system isCL = lft(P,K).

`normz`— Closed-loop norms
1-by-2 vector

Closed-loop norms, returned as a 1-by-2 vector. The entries in this vector, respectively, are:

TheH_∞norm of the closed-loop transfer function fromwtoz_∞.
TheH₂norm of the closed-loop transfer function fromwtoz₂.

`info`— Solutions of LMI solvability conditions
structure

Solutions of LMI solvability conditions, returned as a structure containing the following fields:

R— SolutionRof LMI solvability condition
S— SolutionSof LMI solvability condition

References

[1] Chilali, M., and P. Gahinet, "H_∞Design with Pole Placement Constraints: An LMI Approach,"IEEE Trans. Aut. Contr., 41 (1995), pp. 358–367.

[2] Scherer, C., "Mixed H2/H-infinity Control,"Trends in Control: A European Perspective斯普林格出版社(1995), pp.173–216.

Documentation

h2hinfsyn

Syntax

Description