W.E. Schmitendorf

Effects of using observers on stabilization of uncertain linear systems

The effects of observers on robust linear feedback controllers are studied. Sufficient conditions are obtained that guarantee full recovery of the allowable uncertainty bounds attainable by full state feedback. The effects of the resulting high gain observers on the disturbance rejection bounds are also studied. It is shown that full recovery of the uncertainty bound leads to possible large degradation in disturbance rejection. However, if there is only additive plant disturbance and no measurement disturbance, this degradation can be prevented. >

A noniterative method for the design of linear robust controllers

A procedure for determining a linear control law which guarantees asymptotic stability for an uncertain system is derived. Using an elementary matrix identity, an alternative proof of the existence of stabilizing control law for the matched case is provided. Bounds for the rates of decay are established, and by using these bounds it is shown that every trajectory of the closed-loop system can be made to decay at a prespecified exponential rate. The technique is simpler to use than existing techniques since it does not require a numerical procedure, but allows the control law to be obtained from some simple formulas. >

Robust linear controllers using observers

The possibility of determining a linear robust control law when the full state cannot be measured and observers are implemented to estimate the state is considered. The focus is on systems where the uncertainty satisfies the matching condition. The control law and the observer are designed using two Riccati equations. The first result establishes that if certain scalar parameters are chosen so that a matrix inequality is satisfied, the closed-loop system is stable for the uncertainty levels of interest. It is then shown that if there are at least as many sensors as there are actuators and the transfer function of the nominal system (or a squared-down form of it) does not have zeros in the closed right-half plane, the closed-loop system can be stabilized by the technique, regardless of the size of the uncertainty bounding set. >

Simultaneous stabilization via linear state feedback control

The problem of simultaneously stabilizing a finite collection of plants via a single compensator utilizing full state information is considered. The authors assume that the complete state can be measured and seek a (static) linear state feedback control law. Sufficient conditions for such full state gains to exist are given and they show via several examples how stabilizing compensators can be designed. >

Use of a Genetic Algorithm to Analyze Robust Stability Problems

This note resents a genetic algorithm technique for testing the stability of a characteristic polynomial whose coefficients are functions of unknown but bounded parameters. This technique is fast and can handle a large number of parametric uncertainties. We also use this method to determine robust stability margins for uncertain polynomials. Several benchmark examples are included to illustrate the two uses of the algorithm. 27 refs., 4 figs.

Designing tuned mass dampers via static output feedback: a numerical approach

The paper presents a numerical approach to the problem of determining the design parameters of a vibration absorber to minimize the effect of disturbing forces. The approach is also applicable to multi-input systems such as civil engineering structures. The resulting devices are appealing since they can be implemented passively and are more economic and reliable than active control devices.

Observers for stabilization and disturbance attenuation in uncertain systems

Examines the ability to recover the robust disturbance attenuation properties of full state controllers when observers are used to estimate the state. The main emphasis is placed on identifying structural properties of the nominal system or the uncertainty, that guarantee full recovery. Such information can be used for control law design - by separating the controller and observer design - or for improving the system performance by identifying the appropriate number and location of the sensors. The results presented extend the results of (Jabbari and Schmitendorf, 1993, and Peterson and Hollot, 1988). The uncertainty structure here allows time variations in the uncertain parameters and cross terms in the controlled output vector. These terms arise naturally in many practical problems, such as structural control in earthquake applications. The effects of sensor noise are also included. In particular, the authors develop sufficient conditions under which full recovery is possible in the presence of sensor noise. All results have elementary proofs, based on the bounded real lemma and standard Lyapunov stability theory. The relationship to control design with linear matrix inequalities is also discussed.<<ETX>>

Improving stability margins via dynamic-state feedback for systems with constant uncertainty

It is well known that if a linear system with time-varying uncertainty in the system matrix and/or the input connection matrix is quadratically stabilizable by linear dynamic state feedback, then it is also quadratically stabilizable by linear static state feedback. In this paper, we provide an example of a system with unknown constant real uncertainty which is stabilizable by a linear, dynamic-state feedback controller but not by a static-state feedback controller.

Feedforward tracking for uncertain systems

The tracking problem for uncertain systems with time-invariant uncertainty is considered. A feedforward tracking approach to both full state feedback and measurement feedback problems is proposed. The design is reduced to a standard H/sub infinity / problem.<<ETX>>

A Non-Iterative Riccati Approach to Robust Control Design

In this paper we present a non-iterative procedure for designing a linear control law that guarantees practical stability of a system with matched additive disturbances and matched uncertainties in the system matrix and the input connection matrix. The solution of an algebraic Riccati equation is used to generate the feedback gains for a linear controller that guarantees asymptotic stability of the uncertain system without the additive disturbances. Then a multiplier which is a function of the magnitude of the additive disturbances is applied, and the resulting control guarantees practical stability. Unlike other Riccati approaches which require a search procedure, our approach leads directly to a control without requiring any iteration. Application of the results to tracking problems is discussed since formulation of the tracking problem for an uncertain system requires stabilization of a new system with additive disturbances.