Scilab Home page | Wiki | Bug tracker | Forge | Mailing list archives | ATOMS | File exchange
Please login or create an account
Change language to: English - Português - Русский - 日本語

Please note that the recommended version of Scilab is 6.0.0. This page might be outdated.
See the recommended documentation of this function

Aide de Scilab >> CACSD (Computer Aided Control Systems Design) > lqg

lqg

LQG compensator

Calling Sequence

[K]=lqg(P,r)

Arguments

P

syslin list (augmented plant) in state-space form

r

1x2 row vector = (number of measurements, number of inputs) (dimension of the 2,2 part of P)

K

syslin list (controller)

Description

lqg computes the linear optimal LQG (H2) controller for the "augmented" plant P=syslin('c',A,B,C,D) (continuous time) or P=syslin('d',A,B,C,D) (discrete time).

The function lqg2stan returns P and r given the nominal plant, weighting terms and variances of noises.

K is given by the following ABCD matrices: [A+B*Kc+Kf*C+Kf*D*Kc,-Kf,Kc,0] where Kc=lqr(P12) is the controller gain and Kf=lqe(P21) is the filter gain. See example in lqg2stan.

Examples

s=poly(0,'s');
Plant=syslin('c',[1/(s+1)*s/(s-1)^2]);     //Nominal Plant
P22=tf2ss(Plant);    //...in state-space form
[ny,nu,nx]=size(P22);
rand('seed',0);rand('normal');
bigQ=rand(nx+nu,nx+nu);
bigQ=bigQ*bigQ';
bigR=rand(nx+ny,nx+ny);
bigR=bigR*bigR';  //random weighting matrices
[Plqg,r]=lqg2stan(P22,bigQ,bigR);     //LQG pb as a standard problem
Klqg=lqg(Plqg,r);          //Controller
spec(h_cl(Plqg,r,Klqg))    //Check internal stability
[Slqg,Rlqg,Tlqg]=sensi(P22,Klqg);  //Sensitivity functions
frq=logspace(-3,3);     //10^-3  to 10^3
y=svplot(Slqg);       //Computes singular values;
gainplot(frq,y)   //Plot sing. values

See Also

  • lqg2stan — LQG to standard problem
  • lqr — LQ compensator (full state)
  • lqe — linear quadratic estimator (Kalman Filter)
  • h_inf — Continuous time H-infinity (central) controller
  • obscont — observer based controller
Scilab Enterprises
Copyright (c) 2011-2017 (Scilab Enterprises)
Copyright (c) 1989-2012 (INRIA)
Copyright (c) 1989-2007 (ENPC)
with contributors
Last updated:
Thu Oct 02 13:54:31 CEST 2014