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.

Two-Time-Scale Feedback Design of Nonlinear Singularly Perturbed Systems

Abstract: For nonlinear singularly perturbed systems a stabilizing feedback control law is designed using two separate lower order subsystems. The two-time-scale property greatly simplifies the stability analysis and the nonlinear controller design.

Design and analysis of a sliding mode controller for systems with hysteresis

Abstract: A sliding mode controller is proposed for a class of systems comprising a hysteresis operator preceding an kth-order linear plant without zero dynamics. The hysteresis operator is modeled with piecewise linear characteristics with uncertainties, and a nominal inverse operator is included to mitigate the hysteresis effect. A bound on the inversion error is used in the design of the sliding mode controller. The stability of the closed-loop system is established, and singular perturbation is exploited to analyze the system behavior within the boundary layer. In particular, analytical insight is gained on the frequency-scaling behavior of the tracking error under a periodic reference. Simulation and experimental results on a piezoelectric actuator-based nanopositioner are presented to illustrate the design and analysis, where the hysteresis nonlinearity is represented by a Prandtal-Ishlinskii operator.

Inversion-free stabilization and regulation of systems with hysteresis using integral action

Abstract: In this paper, we present analysis on the stabilization and regulation of the tracking error for an n-dimensional dynamic system with zero dynamics, which is preceded by a Prandtl-Ishlinskii hysteresis operator. A general controller structure is considered; however, we assume that an integral action is present. We treat this problem from the perspective of switched systems, where the state of the hysteresis operator defines the switching surfaces. The common Lyapunov function theorem is utilized together with an LMI condition to show that, under suitable conditions, the tracking error of the system goes to zero exponentially fast when a constant reference is considered. A key feature of this LMI condition is that it does not require the hysteresis effect to be small, meaning that hysteresis inversion is not required. We use this condition together with a periodicity assumption to prove that a servocompensator-based controller can stabilize a system with hysteresis without using hysteresis inversion. Finally, we conduct experiments using a servocompensator-based controller, where we verify the stability of the system and achieve a mean tracking error of 0.5% at 200 Hz using a sinusoidal reference.

Self-excited limit cycles in an integral-controlled system with backlash

Abstract: The stability of systems with hysteresis, driven by developments in smart material applications, has been an important topic of research over the past two decades. Most results provide sufficient conditions for boundedness of the system states, but do not further investigate the steady state solutions. In this paper, we present an example of a system with hysteresis that possesses self-excited limit cycles. In particular, we consider an integral-controlled system with backlash (also known as play operator). A Newton-Raphson algorithm is formulated to calculate the limit cycles in the system. We then prove that the amplitude and period of these limit cycles have linear relationships to parameters within the system. These results are then confirmed in simulation, where we demonstrate our ability to predict and modify the properties of the limit cycles.

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...