Low order sampled data H∞ control using the delta operator and LMIs

• A procedure for H∞ optimization of low order controllers for discrete-time and sampled-data systems is presented in this paper. Generally, low order H∞ controllers may be achieved by solving bilinear matrix inequalities (BMIs). In this paper an iterative alternation between two LMIs gives a suboptimal solution. To avoid local minima in this search the initial controller is obtained by a frequency weighted controller reduction scheme, where the closed loop properties of a full order controller is taken into account. A minimal number of parameters in the state space realization of the controller also reduces the complexity and improves numerical robustness. The complete presentation is based on delta operator models, which shows a close relationship between the continuous- and discrete-time solutions. The sensitivity of the ordinary discrete-time shift operator LMI formulation to small sampling periods is also analyzed.

Subject headings

TEKNIK OCH TEKNOLOGIER  -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)

Keyword

H∞control

H∞ optimisation

closed loop systems

discrete time systems

iterative methods

linear matrix inequalities

sampled data systems

H∞ optimization

closed loop properties

complexity

delta operator

discrete time shift operator

discrete-time systems

frequency weighted controller reduction scheme

full order controller

iterative alternation

low order controllers

low order sampled data H H∞ control

numerical robustness

state space

Automatic control

Control systems

Frequency

Robust control

Robustness

Sampling methods

Signal processing

State-space methods

Weight control

Produktions- och materialteknik

Manufacturing and materials engineering

Publication and Content Type

ref (subject category)

kon (subject category)