Hassan K. Khalil

Bio: Hassan K. Khalil is an academic researcher from Michigan State University. The author has contributed to research in topics: Nonlinear system & Nonlinear control. The author has an hindex of 57, co-authored 284 publications receiving 15992 citations. Previous affiliations of Hassan K. Khalil include Ford Motor Company & National Chiao Tung University.

On the steady-state error of a nonlinear regulator

Abstract: SUMMARY This paper proves a new property of the nonlinear regulators that proposed in two previous papers by the second author with co-workers. In both papers, the steady-state control is immersed into a linear internal model. In general, the model produces the sinusoidal signals generated by an exosystem, as well as a number of their harmonics, which are induced by the system's nonlinearities. When the internal model does not account for all harmonics or when the model's characteristic frequencies are not exactly those of the exosystem, there will be an error between the steady-state control needed to achieve zero steady-state regulation error and the steady-state control produced by the internal model. If the norm of this error is bounded by a constant δ, it has been shown that the steady-state regulation error will be of the order O(δ). In this paper, we prove a shaper result where the steady-state regulation error is shown to be of the order O(μδ), where μ is a design parameter of a continuously implemented sliding mode controller. Therefore, the regulation error can be reduced by decreasing μ. This result allows us to trade off the accuracy of the internal model versus the value of μ as means of reducing the regulation error.Copyright © 2012 John Wiley & Sons, Ltd.

On the robustness of output feedback control methods to modeling errors.

Abstract: Singular perturbation analysis is employed to study the robustness of output feedback control schemes for linear time-invariant systems. The effect of designing the control strategy using a model that neglects unknown parasitic elements is considered. It is shown that such a strategy may, in general, be destabilizing even when the neglected modes are asymptotically stable. Special structures that will not permit this situation and will guarantee asymptotic stability are illustrated.

Adaptive Stabilization of SISO Systems with Unknown High-Frequency Gains

Abstract: This paper presents an algorithm for adaptively stabilizing a single-input single output system admitting any minimum phase plant of relative degree q. A priori knowledge of the sign of the plant's high frequency gain and an upper bound on the plant order is not needed.

Closed-loop analysis for systems with fast linear dynamics preceded by hysteresis

Abstract: Piezoelectric actuators are commonly modelled by a hysteresis operator preceding fast, stable linear dynamics. This motivates our work to analyze systems with these characteristics when a popular control architecture involving both hysteresis inversion and feedback is adopted. In particular, we are interested in the frequency-scaling behavior of the tracking error for such systems, which is of practical interest but has received little attention in the literature. The hysteresis nonlinearity in our analysis is represented by piecewise linear segments, which is applicable to many hysteresis operators. To fix ideas, we consider a proportional integral controller for the feedback component, as well as the case where a constant-gain feedforward component is added to the feedback term. This work is a continuation of our previous work where we only examined the system behavior for a given hysteresis segment. Here we use singular perturbation techniques to separate the slow variables of the controller from the fast variables of the plant dynamics, and derive the solution of the closed-loop system and the tracking error at the steady state under a sinusoidal reference. The analysis incorporates the effect of uncertainty in the hysteresis model, and offers insight into how the tracking error scales with the reference frequency. The analysis is confirmed with experimental and simulation results for the control of a piezo-actuated nanopositioner.

I and i

Abstract: There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality. Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

Linear Matrix Inequalities in System and Control Theory

Abstract: Preface 1. Introduction Overview A Brief History of LMIs in Control Theory Notes on the Style of the Book Origin of the Book 2. Some Standard Problems Involving LMIs. Linear Matrix Inequalities Some Standard Problems Ellipsoid Algorithm Interior-Point Methods Strict and Nonstrict LMIs Miscellaneous Results on Matrix Inequalities Some LMI Problems with Analytic Solutions 3. Some Matrix Problems. Minimizing Condition Number by Scaling Minimizing Condition Number of a Positive-Definite Matrix Minimizing Norm by Scaling Rescaling a Matrix Positive-Definite Matrix Completion Problems Quadratic Approximation of a Polytopic Norm Ellipsoidal Approximation 4. Linear Differential Inclusions. Differential Inclusions Some Specific LDIs Nonlinear System Analysis via LDIs 5. Analysis of LDIs: State Properties. Quadratic Stability Invariant Ellipsoids 6. Analysis of LDIs: Input/Output Properties. Input-to-State Properties State-to-Output Properties Input-to-Output Properties 7. State-Feedback Synthesis for LDIs. Static State-Feedback Controllers State Properties Input-to-State Properties State-to-Output Properties Input-to-Output Properties Observer-Based Controllers for Nonlinear Systems 8. Lure and Multiplier Methods. Analysis of Lure Systems Integral Quadratic Constraints Multipliers for Systems with Unknown Parameters 9. Systems with Multiplicative Noise. Analysis of Systems with Multiplicative Noise State-Feedback Synthesis 10. Miscellaneous Problems. Optimization over an Affine Family of Linear Systems Analysis of Systems with LTI Perturbations Positive Orthant Stabilizability Linear Systems with Delays Interpolation Problems The Inverse Problem of Optimal Control System Realization Problems Multi-Criterion LQG Nonconvex Multi-Criterion Quadratic Problems Notation List of Acronyms Bibliography Index.

Higher-order sliding modes, differentiation and output-feedback control

Abstract: Being a motion on a discontinuity set of a dynamic system, sliding mode is used to keep accurately a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes provide for finite-time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Yet the relative degree of the constraint has to be 1 and a dangerous chattering effect is possible. Higher-order sliding modes preserve or generalize the main properties of the standard sliding mode and remove the above restrictions. r-Sliding mode realization provides for up to the rth order of sliding precision with respect to the sampling interval compared with the first order of the standard sliding mode. Such controllers require higher-order real-time derivatives of the outputs to be available. The lacking information is achieved by means of proposed arbitrary-order robust exact differentiators with finite-time convergence. These differentiators feature optimal asymptot...