Re: question about robustness of LQR controllers

Dear Joris

For LQR (meaning optimal with full state feedback) continuous time
systems have infinite gain margin, at least a 50% gain reduction
margin, and at least a +/- 60 degrees phase margin in each control
input channel.

For LQR sampled data designs the margins approach those of the
continuous time case above as the sampling rate increases. See Mike
Safonov's book "Stability and Robustness of Multivariable Feedback
Systems".

Note the margins are not guaranteed in the LQG case.

Regards

Ian

> Reply-to: <joris.decuyper@lms.be>
> From: "Joris De Cuyper" <joris.decuyper@lms.be>
> To: <sigurd.skogestad@kjemi.unit.no>, <ixp@leicester.ac.uk>
> Cc: "Jan Swevers" <jan.swevers@mech.kuleuven.ac.be>,
> "Michel Verhaegen" <M.Verhaegen@tn.utwente.nl>,
> "Dominiek Coppens" <dominiek.coppens@lms.be>
> Subject: question about robustness of LQR controllers
> Date: Fri, 21 Apr 2000 18:01:58 +0200
> Importance: Normal

> Dear,
>
> I'm working as a research engineer at LMS in Leuven, Belgium (a sofware and
> engineering company with a focus on noise, vibrations, durability and
> mechanical simulation for the automotive industry) and I'm currently reading
> your book 'Multivariable Feedback Control. Analysis and Design' which is of
> great interest to my work.
>
> In this context, I have a question about section 9.2.2. where it is
> mentioned that LQR controllers exhibit certain (excellent) robustness
> properties. My question is if this is also true for a discrete controller
> design (so starting from a discrete-time state space model and using for
> example 'dlqr' in Matlab) ? It seems to me that this is NOT the case. Can
> you provide me with some more information on this ?
>
> Thanks in advance,
>
> Joris De Cuyper
>
> ++++++++++++++++++++++++++++++++++++++++++++++++
> Joris De Cuyper
> Research Engineer
> LMS International
> Interleuvenlaan 68
> B - 3001 Leuven
> tel. +32 16 384 233
> fax. +32 16 384 350
>
>
-------------------------------------------
Professor Ian Postlethwaite
Head of Department
Department of Engineering
University of Leicester
Leicester LE1 7RH
UK

Tel: +44 (0)116 252 2547
Fax: +44 (0)116 223 1369
Email: ixp@le.ac.uk
Received on Sat Apr 22 11:00:14 2000