Showing papers by "Hassan K. Khalil published in 2009"

High-gain observers in nonlinear feedback control

Abstract: The theory of high-gain observers has been developed for about twenty years. This talk is a brief introduction to high-gain observers in nonlinear feedback control, with emphasis on the peaking phenomenon and the role of control saturation in dealing with it. The talk surveys recent results on the nonlinear separation principle, extended high-gain observers, performance in the presence of measurement noise, sampled-data control, and experimental testbeds.

Multirate Sampled-Data Output Feedback Control With Application to Smart Material Actuated Systems

Abstract: We consider multirate sampled-data output feedback control of a class of nonlinear systems using high-gain observers where the measurement sampling rate is made faster than the control update rate. We show that, in the presence of bounded disturbances, given a sampled data state feedback controller that achieves stabilization with respect to a closed set, the multirate output feedback controller recovers stabilization of the same set provided the measurement sampling rate is sufficiently fast. As an application we consider the control of smart material actuated systems. This scheme combines a discrete-time high-gain observer with a hysteresis inversion controller where the hysteresis is modeled using a Preisach operator. Experimental results for the control of a shape memory alloy actuated rotary joint are provided.

Speed Observer and Reduced Nonlinear Model for Sensorless Control of Induction Motors

Abstract: We consider field-oriented speed control of induction motors without mechanical sensors. We augment the traditional approach with a flux observer and derive a sixth-order nonlinear model that takes into consideration the error in flux estimation. A high-gain speed observer is included to estimate the speed from field-oriented currents and voltages. The observer design is independent of the feedback controller design. By high-gain-observer theory, we define a virtual speed output for the sixth-order nonlinear model, which can now be used to design a feedback controller whose performance is recovered by the speed observer when the observer gain is chosen high enough. We then focus on the traditional field oriented control (FOC) approach where the flux is regulated to a constant reference and high-gain current controllers are used. By designing a flux regulator to maintain the flux at a constant reference, and a current regulator to regulate the q-axis current to its command, we derive a third-order nonlinear model that captures the essence of the speed regulation problem. The model has the speed and two flux estimation errors as the state variables, the q -axis current as the control input, and the virtual speed as the measured output. It enables us to perform rigorous analysis of the closed-loop system under different controllers, and under uncertainties in the rotor and stator resistances and the load torque. In this paper, we emphasize the design of feedback controllers that include integral action. The analysis reveals an important role played by the steady-state product of the flux frequency and the q-axis current in determining the control properties of the system. The conclusions arrived at by using the reduced-order model are collaborated by simulation and experimental results.

Two-time-scale averaging of systems involving operators and its application to adaptive control of hysteretic systems

Abstract: Motivated by the adaptive control problem for systems with hysteresis, a two-time-scale averaging framework is presented in this paper for systems involving operators, by extending the work of Teel and co-workers. The developed averaging theory is applied to the analysis of a model reference adaptive inverse control scheme for a system consisting of linear dynamics preceded by a Prandtl-Ishlinkskii (PI) hysteresis operator. The fast component of the closed-loop system involves the coupling of an ordinary differential equation and a hysteresis operator derived from the PI operator and its inverse, while the slow component is the parameter update rule. The stability of the boundary-layer system and that of the average system are established under suitable conditions, which implies practical regulation of the parameter error and tracking error under the adaptive scheme.

High-gain-observer tracking performance in the presence of measurement noise

Abstract: High-gain observers are commonly utilized to estimate the states used in constructing the output feedback control, when such states are derivatives of the output. In the presence of measurement noise, the estimation error can be noticeably compromised if the observer gain is chosen too large. However, the effect of measurement noise on the tracking error is less significant. This phenomenon is demonstrated with a nonlinear motivating example, and further explored in the context of linear systems from a transfer function perspective.

Full-order high-gain observers for minimum phase nonlinear systems

Abstract: This paper studies the design of a full-order, high-gain observer for a class of minimum-phase nonlinear systems. The dynamic state feedback design is modified to include the observer for the internal dynamics. It is shown that the performance of such a dynamic partial-state feedback control can be recovered by the output feedback control using a sufficiently fast high-gain observer, in the presence of model uncertainty.

Output regulation of non-minimum phase nonlinear systems using an extended high-gain observer

Abstract: In this paper, we present an output feedback regulator for nonlinear systems that could potentially include unstable zero dynamics. The regulation scheme adopted herein incorporates continuously-implemented sliding mode control and an extended high gain observer to estimate the derivatives of the output and one of the unknown functions. The result is illustrated using a simulation.

Shape and topology optimization of microwave components

Abstract: The design of advanced components for space and terrestrial telecommunications requires both sophisticated design methodologies and manufacturing technologies for improving current component performances. In particular, determining the optimal shape and size of a component is a problem of primary importance for microwave engineers. In order to improve the classical microwave filters, shape and topology optimization methods can be utilized together with numerical modeling methods. Topology gradient and level set methods are coupled here with the finite element method for optimizing the shape of dielectric resonators included in microwave filters.

Performance analysis of output regulation for a class of nonlinear systems

Abstract: In the paper [1], Serrani and Isidori design an output feedback controller that achieves semiglobal output regulation for a class of minimum phase nonlinear systems. The controller has three basic components: an internal model to ensure asymptotic regulation, a high-gain partial state feedback controller to stabilize the augmented system of the plant and the internal model, and a high-gain observer to implement the partial state feedback. In this paper we show a property of the transient performance of the controller of [1]. We consider an alternate controller that shares with the controller of [1] the structure of high-gain partial state feedback and high-gain observer, but without internal model. Such controller can only achieve practical regulation. We show that when the controller and observer gains are high enough, the trajectories under the two controllers will be close to each other. This property shows that the transient performance of the controller of [1] is not degraded by the inclusion of the internal model.