Matei Kelemen

One-point feedback approach to distributed linear systems

Abstract The disturbance attenuation problem is studied for linear (distributed) plants described by partial differential operators and by using one lumped- (i.e. acting at a single point) feedback loop. A result emphasizing the trade-off between stability and disturbance attenuation is proven. Also, the effect of the feedback loop location on disturbance attenuation is pointed out. Finally, a synthesis procedure is derived, valid also for plants having bounded uncertainty in the gain. The procedure is illustrated by two significant examples in a one-dimensional, bounded domain.

Arbitrarily fast and robust tracking by feedback

The output of a singe-input-single-output linear feedback system with more than one pole in excess over the zeros in the loop transmission cannot track arbitrarily fast its input (by the root locus). In this work we extend the linear feedback so that some of the open loop poles may depend on the open loop gain; we call this new class quasi-linear feedback systems. We then derive time domain, pole-zero, and frequency domain conditions which ensure arbitrarily fast and robust tracking by quasi-linear feedback, for an arbitrary number of poles in excess over the zeros. We prove that in a particular case these conditions are equivalent, and that the boundedness in frequency of the closed loop transfer function is no longer necessary for achieving arbitrarily fast tracking. The robustness is to external disturbances and initial conditions, and the open loop has to be minimum phase. Some examples are presented which illustrate these results. They also show that this good performance can be obtained with a reduced control effort, and that quasi-linear feedback can alleviate the limitation on performance of non-minimum phase open loops.

On the design, robustness, implementation and use of quasi-linear feedback compensators

A quasi-linear feedback compensator is one in which its poles depend in an appropriate way on its gain. The reason for introducing this new concept was the desire to remove the limitation to performance imposed by a plant with more than one pole in excess of its zeros. In this article it is shown that this objective is realized for plants with zeros in the left half of the complex plane. The consequences are surprising. In time domain it is possible to track arbitrarily fast a class of reference inputs despite a large class of disturbances and uncertainty in plant parameters. The response is non-oscillatory for high enough compensator gains, which is explained by the automatic adaptation of the closed loop poles to stability and stability margins for such gains. And in frequency domain the phase margin tends to 90° while the gain margin and crossover frequency become unlimited. Technically the design procedure of quasi-linear compensators presented here is based on our theoretical result concerning the asymptotic behaviour of the roots of certain polynomials in a complex variable which depend also on a large positive parameter. We also show how to implement such quasi-linear compensators in practical feedback control schemes, and their use at lower gains which is the case of most industrial applications.

Arbitrarily low sensitivity (ALS) in linear distributed systems using pointwise linear feedback

The sensitivity problem is defined for feedback systems with plants described by linear partial differential operators having constant coefficients, in a bounded one-dimensional domain. there are also finitely many observation points and finitely many lumped feedback loops, and a finite number of disturbance inputs. The sensitivity problem is studied in detail for the heat equation, and comments are made about the linearized damped beam equation and the damped wave equation. It is shown that it is possible to reduce arbitrarily the sensitivity over any temporal frequency interval uniformly in the space domain (except for the undamped wave equation, where a limitation in the frequency interval is induced by the plant). This reduction may require a high-gain feedback around the points where the disturbances appear. >

Linear robust control of a synchronous motor, experimental comparison with non-linear control

We present a linear robust design method (of quantitative feedback theory type) to control a permanent magnet synchronous motor to achieve demanding time domain quantitative specifications despite large parametric and load uncertainties which affect it. The linear control is compared with a non-linear design (of adaptive feedback linearization type) for the same motor. The experimental results show that: the linear control compares favourably to the non-linear one on robustness of performance and stability, and simplicity of implementation; both the linear and non-linear control have good sensor noise response. The non-linear method did prove the non-local stability of the design while the linear method did not.

Spatial discretization and approximation of distributed feedback loops and inputs

The problem of approximating distributed feedback loops and inputs by ones that are discrete (in space) is studied in some detail. The main result, based on integral equations, gives sufficient conditions on the plant, input and compensator enabling such an approximation. The result is illustrated by three plants.

Application of Quasi-Linear Feedback to the Control of a Hard Disk Drive Servo System

This study illustrates the capability of quasi-linear systems to achieve arbitrarily high performance both in the time domain and the frequency domain of a linear plant, in this case a hard disk drive servo system

Towards a systematic procedure to design robust power system stabilizers

A linear robust method to design power system stabilizers for multimachine power systems is presented. The method is of quantitative feedback theory type. The robustness of the system is tested both for short circuit disturbances and for abrupt and permanent changes in the load parameter of the multimachine power network. The results are compared in simulation with a standard design from the literature.

Experimental comparison on a synchronous motor of linear robust and nonlinear controls

The authors present a linear robust design method (of quantitative feedback theory type) to control a permanent magnet synchronous motor to achieve demanding time domain quantitative specifications despite large parametric and load uncertainties which affect it. The linear control is compared with a nonlinear design (of adaptive feedback linearization type) for the same motor. The experimental results show that the linear control compares favorably to the nonlinear one on robustness of performance and stability, and simplicity of implementation. The nonlinear method did prove the nonlocal stability of the design while the linear method did not.

A dynamic model of production

In this article we establish a model of economic growth. The model is a dynamic one, its dynamics being generated by an objective to be reached. We take into account physical as well as human factors. In a particular case, we have obtained mathematically some conclusions concerning realistic ways of choosing objectives and necessary relations between the growing rates of the industries involved.