Lahcen Saydy

Stabilisation and control synthesis of switching systems subject to actuator saturation

This article presents sufficient conditions for the stabilisation of switching discrete-time linear systems subject to actuator saturations. These conditions are obtained by using successively state and output feedback control laws. The obtained results are formulated in terms of linear matrix inequalities (LMIs). The saturating and non-saturating controllers are synthesised for both cases in this work. Three sets of LMIs are presented for output feedback case. Numerical examples are used to illustrate these techniques by using a linear optimisation problem subject to LMI constraints.

Gain scheduling with guardian maps for longitudinal flight control

A new approach to gain scheduling of linear controllers is proposed and applied to a longitudinal flight control pro-blem. Traditionally, gain scheduling is done a posteriori by the interpolation of controller gains designed for several operating points or conditions. The method proposed here is based on guardian maps and does not require as many linear controller syntheses as there are design points. Rather, it extends the performance of an initial single controller carried out on an arbitrary operating point to the entire domain while ensuring generalized stability all along the process. The method, which uses a given fixed architecture controller, is successfully applied on the longitudinal flight control of a business jet aircraft.

Nonlinear Control of an Electrostatic Micromirror Beyond Pull-In With Experimental Validation

This paper is aimed at demonstrating the potential benefits of applying nonlinear control techniques to a type of microelectromechanical system, namely, electrostatic micromirrors, in order to extend their stable operation range, enhance the systems performance, and allow controller tuning and system operation to be performed in a systematic manner. A nonlinear tracking control based on feedback linearization and trajectory planning has been developed. Aspects essential to the implementation, such as the prevention of devices from destruction due to contact, modeling and sensing schemes, the influence of the dynamics of the driving circuit on performance, and the device characterization, have been thoroughly addressed, and practical solutions have been proposed. The experimentation is performed on a setup built with low-cost commercial off-the-shelf instruments and components in a laboratory environment. The experimental results show that the developed control system can achieve stable operation beyond the pull-in position for both set-point and scanning controls.

Modeling and Control of Electrostatically Actuated MEMS in the Presence of Parasitics and Parametric Uncertainties

Due to the compact layout, manufacturing tolerance, modeling errors, and environmental changes, microelectromechanical systems (MEMSs) are subjected to parasitics and parameter variations. In order to better guarantee their stability and a certain level of performance, one must take into account these factors in the design of MEMS control systems. This work presents two robust control laws for a parallel-plate electrostatic microactuator in the presence of uncertainties. The dynamical model of the system, including parallel and serial parasitics, is firstly established and two control schemes, both based on input-to-state stabilization and robust backstepping, are proposed. The stability and the performance ofthe system using these control schemes are demonstrated through both stability analysis and numerical simulation.

Robust control of an electrostatically actuated MEMS in the presence of parasitics and parametric uncertainties

Due to the compact layout, manufacturing tolerance, modeling errors, and environmental changes, micro-electromechanical systems (MEMS) are subjected to parasitics and parameter variations. In order to better guarantee their stability and a certain level of performance, one must take into account these factors in the design of MEMS control systems. This work presents two robust control laws for a parallel-plate electrostatic micro-actuator in the presence of uncertainties. The dynamical model of the system is firstly established and two control schemes, both based on input-to-state stabilization (ISS) and robust backstepping, are proposed. The stability and performance of the system using these control schemes are demonstrated through both stability analysis and numerical simulation

Stabilization of Switched Systems Subject to Actuator Saturation by Output Feedback

This paper presents sufficient conditions for asymptotic stabilizability of switched discrete-time linear systems subject to actuator saturations using output feedback. The results are obtained by using a composite Lyapunov function and are given in the form of LMI conditions. It is shown that the union of all the associated level sets is a set of asymptotic stability of the switched system. A numerical example is used to illustrate the technique

Longitudinal flight control design with handling quality requirements

This work presents a method for selecting the gain parameters of a C* control law for an aircraft’s longitudinal motion. The design incorporates various handling quality requirements involving modal, time- and frequency-domain criteria that were fixed by the aircraft manufacturer. After necessary model order- reductions, the design proceeds in essentially two-step s: Stability Augmentation System (SAS) loop design and Control Augmentation System (CAS) loop design. The approach partly relies on the use of guardian maps to characterize, in each case, the set of gain parameters for which desired handling quality requirements are satisfied. The approach is applied throughout the full flight envelope of a business jet aircraft and yields satisfactory results.

New stability/performance results for singularly perturbed systems

The guardian map theory of generalized stability of parametrized linear time-invariant systems is used to prove new results on stability/performance of linear time-invariant singularly perturbed systems with an exogenous parameter, i.e. systems that contain, in addition to a singular parameter ϵ, another uncertain parameter μ. The results give necessary and sufficient conditions for generalized stability for all sufficiently small values of ϵ and all values of μ in a given interval [μ1, μ2]. In addition, explicit expressions for the largest upper bound ϵ∗ on ϵ for guaranteed stability and performance are given and the cases leading to finite or infinite ϵ∗ are clearly delineated. Thus the results represent a significant addition to the classical Klimushev-Krasovskii theorem, while at the same time providing closed-form expressions for the maximum parameter range for stability and performance.

A Robustness Approach for Handling Modeling Errors in Parallel-Plate Electrostatic MEMS Control

This paper addresses the control of electrostatic parallel-plate microactuators in the presence of such modeling errors as unmodeled fringing field effect and deformations. In general, accurate descriptions of these phenomena often lead to very complicated mathematical models, while ignoring them may result in significant performance degradation. In this paper, it is shown by finite-element-method-based simulations that the capacitance due to fringing field effect and deformations can be compensated by introducing a variable serial capacitor. When a suitable robust controller is used, the full knowledge of the introduced serial capacitor is not required, but merely its boundaries of variation. Based on this model, a robust control scheme is derived using the theory of input-to-state stability combined with backstepping state feedback design. Since the full state measurement may not be available under practical operational conditions, an output feedback control scheme is developed. The stability and performance of the system using the proposed control schemes are demonstrated through both stability analysis and numerical simulation. The present approach allows the loosening of the stringent requirements on modeling accuracy without compromising the performance of control systems.

Gain scheduling control design for a pitch-axis missile autopilot

A new approach to gain-scheduling of linear controllers is proposed. Traditionally, gain scheduling is done a posteriori by interpolation of gains computed for several operating points within the parameter space. The method proposed here which is based on guardian maps does not require the design of linear controllers for several points. Rather, it attempts to extend the performance of an initial design obtained for a single arbitrary point to the whole linearized domain while ensuring generalized stability all along the process. The method is successfully applied on a missile autopilot benchmark problem.