Khalid Abidi

On the Discrete-Time Integral Sliding-Mode Control

A new discrete-time integral sliding-mode control (DISMC) scheme is proposed for sampled-data systems. The new control scheme is characterized by a discrete-time integral sliding manifold which inherits the desired properties of the continuous-time integral sliding manifold, such as full order sliding manifold with pole assignment, and elimination of the reaching phase. In particular, comparing with existing discrete-time sliding-mode control, the new scheme is able to achieve more precise tracking performance. It will be shown in this work that, the new control scheme achieves O(T2) steady-state error for state regulation with the widely adopted delay-based disturbance estimation. Another desirable feature is, the proposed DISMC prevents the generation of overlarge control actions due to deadbeat response, which is usually inevitable due to the existence of poles at the origin for a reduced order sliding manifold designed for sampled-data systems. Both the theoretical analysis and illustrative example demonstrate the validity of the proposed scheme

Sliding-Mode Control for High-Precision Motion of a Piezostage

In this paper, control of piezostage using sliding-mode control (SMC) method is presented. Due to the fast dynamics of the piezostage and since high accuracy is required the special attention is paid to avoid chattering. The presence of hysteresis characteristics represents main nonlinearity in the system. Structure of proposed SMC controller is proven to offer chattering-free motion and rejection of the disturbances represented by hysteresis and the time variation of the piezostack parameters. In order to enhance the accuracy of the closed loop system, a combination of disturbance rejection method and the SMC controller is explored and its effectiveness is experimentally demonstrated. The disturbance observer is constructed using a second-order lumped parameter model of the piezostage and is based on SMC framework. Closed-loop experiments are presented using a proportional-integral-derivative controller and sliding-mode controller with disturbance compensation for the purpose of comparison

Sliding-Mode Neuro-Controller for Uncertain Systems

In this paper, a method that allows for the merger of the good features of sliding-mode control and neural network (NN) design is presented. Design is performed by applying an NN to minimize the cost function that is selected to depend on the distance from the sliding-mode manifold, thus providing that the NN controller enforces sliding-mode motion in a closed-loop system. It has been proven that the selected cost function has no local minima in controller parameter space, so under certain conditions, selection of the NN weights guarantees that the global minimum is reached, and then the sliding-mode conditions are satisfied; thus, closed-loop motion is robust against parameter changes and disturbances. For controller design, the system states and the nominal value of the control input matrix are used. The design for both multiple-input-multiple-output and single-input-single-output systems is discussed. Due to the structure of the (M)ADALINE network used in control calculation, the proposed algorithm can also be interpreted as a sliding-mode-based control parameter adaptation scheme. The controller performance is verified by experimental results

Discrete-Time Output Integral Sliding-Mode Control for a Piezomotor-Driven Linear Motion Stage

In this paper, a discrete-time output integral sliding-mode control (DOISMC) is developed for the precision control of a piezomotor-driven linear motion stage. A new integral-type sliding surface is first designed for arbitrary output reference tracking control. To estimate the unknown state and disturbance, two observers based on the integral-type sliding surface are designed. It is shown in this paper, through both theoretical analysis and experiments, that the discrete-time output integral sliding mode controller, together with the state and disturbance estimation, achieves an O(T2) tracking precision w.r.t. the sampling period T. The superior performance of DOISMC achieved in the control of piezomotor-driven linear stage indicates that it is a suitable control method for precision control or servo applications.

Iterative Learning Control for Sampled-Data Systems: From Theory to Practice

This paper aims to present a framework for the design and performance analysis of iterative learning control (ILC) for sampled-data systems. The analysis is presented in both time and frequency domains. Monotonic convergence criteria are derived in both time and frequency domains and coined in ILC designs. In particular, the causes or conditions that lead to the poor transient responses in the time domain are explored and disclosed. Four ILC designs associated with different learning functions and filters are considered, namely, the P-type, D-type, D2-type, and general filters. The criteria for the selection of each type are presented. In addition, a relationship is shown between sampling-time selection and ILC convergence. Theoretical work concludes with a guideline for the ILC designs. Simulation results are shown to support the theoretical analysis in the time and frequency domains. Furthermore, based on the frequency-domain design tools, a successful experimental implementation on an electric piezomotor is demonstrated.

A Discrete-Time Periodic Adaptive Control Approach for Time-Varying Parameters With Known Periodicity

A periodic adaptive control approach is proposed for a class of nonlinear discrete-time systems with time-varying parametric uncertainties which are periodic, and the only prior knowledge is the periodicity. The new adaptive controller updates the parameters and the control signal periodically in a pointwise manner over one entire period, in the sequel achieves the asymptotic tracking convergence. The result is further extended to a scenario with mixed time-varying and time-invariant parameters, and a hybrid classical and periodic adaptation law is proposed to handle the scenario more appropriately

Intelligent Control System for Microgrids Using Multiagent System

This paper presents an intelligent control of a microgrid in both grid-connected and islanded modes using the multiagent system (MAS) technique. This intelligent control consists of three levels. The first level is based on local droop control, the second level compensates power balance between the supply and the demand optimally, and the third level is at the system level based on electricity market. An intelligent MAS was developed and implemented based on foundation for intelligent physical agents standards by representing each major autonomous component in the microgrid as an intelligent software agent. The agents interact with each other for making their own decisions locally and optimally. The coordination among the agents ensures power quality, voltage, and frequency of the microgrid by determining the set points that optimize the overall operation of the microgrid. The proposed control architecture and strategies for the real-time control of microgrids were analyzed in detail, and tested under various load conditions and different network configurations. The outcomes of the studies demonstrate the feasibility of the proposed control and strategies, as well as the capability of the MAS technique for the operation of microgrids.

On the Discrete-Time Integral Sliding Mode Control

A new discrete-time integral sliding mode control (DISMC) scheme is proposed for sampled-data systems. The new control scheme is characterized by a discrete-time integral switching surface which inherits the desired properties of the continuous-time integral switching surface, such as full order sliding manifold with eigenvalue assignment, and elimination of the reaching phase. In particular, comparing with existing discrete-time sliding mode control, the new scheme is able to achieve more precise tracking performance. It is shown in this work that, the new control scheme achieves O(T2) steadystate error for state regulation with the widely adopted delay-based disturbance estimation. Another desirable feature is, the proposed DISMC prevents the generation of overlarge control actions, which are usually inevitable due to the deadbeat poles of a reduced order sliding manifold designed for sampled-data systems. Both the theoretical analysis and illustrative example demonstrate the validity of the proposed scheme

Sliding mode control based disturbance compensation and external force estimation for a piezoelectric actuator

In this paper a sliding mode algorithm for total disturbance estimation and control of piezoelectric stack actuator is proposed. The disturbance observer is based on the lumped parameters model of mechanical motion so it allows the summary action of nonlinear hysteresis disturbance, external forces acting on the system as well as parameters variation to be estimated. Furthermore, using a nonlinear differential equation the internal hysteresis disturbance is removed from the total disturbance in an attempt to estimate the external force acting on the actuator. It is then possible to use this external force estimate as a means of observer based force control of the actuator. Simulation and experiments are compared for validating the disturbance and external force estimation technique. Experiments that incorporate disturbance compensation in a closed-loop SMC control algorithm are also presented to prove the effectiveness of this method in producing high precision motion.

Sliding-mode based force control of a piezoelectric actuator

In this paper force control of a piezoelectric actuator is presented. Force control based on a force observer is emphasized; however, results with a force sensor are also presented for comparison purposes. With the help of the proposed force observer, sensorless force control and estimation of environmental forces are realized. The force observer is first compared with the force sensor for different step motions to verify the capability of the force estimation. The observer output is then used for feedback of the force information in the closed-loop system. Experiments are made to validate the method.