Showing papers on "Sliding mode control published in 2000"

A game theoretic approach to controller design for hybrid systems

Abstract: We present a method to design controllers for safety specifications in hybrid systems. The hybrid system combines discrete event dynamics with nonlinear continuous dynamics: the discrete event dynamics model linguistic and qualitative information and naturally accommodate mode switching logic, and the continuous dynamics model the physical processes themselves, such as the continuous response of an aircraft to the forces of aileron and throttle. Input variables model both continuous and discrete control and disturbance parameters. We translate safety specifications into restrictions on the system's reachable sets of states. Then, using analysis based on optimal control and game theory for automata and continuous dynamical systems, we derive Hamilton-Jacobi equations whose solutions describe the boundaries of reachable sets. These equations are the heart of our general controller synthesis technique for hybrid systems, in which we calculate feedback control laws for the continuous and discrete variables, which guarantee that the hybrid system remains in the "safe subset" of the reachable set. We discuss issues related to computing solutions to Hamilton-Jacobi equations. Throughout, we demonstrate out techniques on examples of hybrid automata modeling aircraft conflict resolution, autopilot flight mode switching, and vehicle collision avoidance.

Output feedback control of nonlinear systems using RBF neural networks

Abstract: An adaptive output feedback control scheme for the output tracking of a class of continuous-time nonlinear plants is presented. An RBF neural network is used to adaptively compensate for the plant nonlinearities. The network weights are adapted using a Lyapunov-based design. The method uses parameter projection, control saturation, and a high-gain observer to achieve semi-global uniform ultimate boundedness. The effectiveness of the proposed method is demonstrated through simulations. The simulations also show that by using adaptive control in conjunction with robust control, it is possible to tolerate larger approximation errors resulting from the use of lower order networks.

Energy based control of the Pendubot

Abstract: This paper presents the control of an underactuated two-link robot called the Pendubot. We propose a controller for swinging the linkage and raise it to its uppermost unstable equilibrium position. The balancing control is based on an energy approach and the passivity properties of the system.

On multi-input chattering-free second-order sliding mode control

Abstract: A solution to the problem of eliminating the chattering effect, which is always associated with practical implementations of variable structure control, is presented with reference to a class of uncertain multi-input nonlinear systems. The solution procedure relies on the application of an original control approach capable of enforcing a second-order sliding mode (i.e., a sliding regime on a surface s[x(t)]=0 in the system state space, with s/spl dot/[x(t)] identically equal to zero, a regime enforced by a control signal depending on s[x(t)], but directly acting only on s/spl uml/[x(t)]). Such an approach, in its original formulation, only applies to single-input nonlinear systems with particular types of uncertainties. In the present paper, its validity is extended to multi-input nonlinear systems characterized by uncertainties of more general nature, covering a wide class of real processes.

Sensorless sliding-mode control of induction motors

Abstract: This paper develops the ideas of speed- and flux-sensorless sliding-mode control for an induction motor illustrated in previous work by one of the authors. A sliding-mode observer/controller is proposed in this paper. The convergence of the nonlinear time-varying observer along with the asymptotic stability of the controller is analyzed. Pulsewidth modulation implementation using sliding-mode concepts is also discussed. Major attention is paid to torque control, and then the developed approach is utilized for speed control. Computer simulations and experiments have been carried out to test the proposed estimation and control algorithm. The experimental results demonstrated high efficiency of the proposed estimation and control method.

An O(T/sup 2/) boundary layer in sliding mode for sampled-data systems

Abstract: The use of a discontinuous control law (typically, sign functions) in a sampled-data system will bring about chattering phenomenon in the vicinity of the sliding manifold, leading to a boundary layer with thickness O(T), where T is the sampling period. However, by proper consideration of the sampling phenomenon in the discrete-time sliding mode control design, the thickness of the boundary layer can be reduced to O(T/sup 2/). In contrast to discontinuous control for continuous-time VSS, the discrete-time sliding mode control need not be of switching type.

Robust nonlinear speed control of PM synchronous motor using boundary layer integral sliding mode control technique

Abstract: A digital signal processor (DSP)-based robust nonlinear speed control of a permanent magnet synchronous motor (PMSM) is presented. A quasi-linearized and decoupled model including the influence of parameter variations and speed measurement error on the input-output feedback linearization of a PMSM is derived. Based on this model, a boundary layer integral sliding mode controller is designed and compared to a feedback linearization-based controller that uses proportional plus derivative (PD) controller in the outer loop. To show the validity of the proposed control scheme, DSP-based experimental works are carried out and compared with the conventional control scheme.

Sliding mode control: an approach to regulate nonlinear chemical processes

Abstract: A new approach for the design of sliding mode controllers based on a first-order-plus-deadtime model of the process, is developed. This approach results in a fixed structure controller with a set of tuning equations as a function of the characteristic parameters of the model. The controller performance is judged by simulations on two nonlinear chemical processes

A High Performance Pneumatic Force Actuator System: Part II—Nonlinear Controller Design

Abstract: In this article we present two nonlinear force controllers based on the sliding mode control theory. For this purpose we use the detailed mathematical model of the pneumatic system developed in the first part of the paper. The first controller is based on the complete model, and exhibits superior performance both in the numerical simulation and experiments, but requires complex online computations for the control law. The second controller neglects the valve dynamics and the time delay due to connecting tubes. The performance of this controller exhibits slight degradation for configurations with relatively short tubes, and at frequencies up to 20 Hz. At higher frequencies or when long connecting tubes are used, however, the performance exhibits significant degradation compared to the one provided by the full order controller.@S0022-0434~00!00703-6#

Design of a nonlinear disturbance observer

Abstract: This paper presents a new disturbance observer based on the variable structure system theory for minimum-phase (with respect to the relationship between the disturbance and output) dynamical systems with arbitrary relative degrees. The model uncertainties and the nonlinear parts of the system are merged into the disturbance term and are regarded as a part of the disturbances. The upper and lower bounds of the disturbance are assumed to be known as a priori information. Simulation results are presented to show the robustness and effectiveness of the new disturbance observer. Experimental results show the practicality of the new observer.

Reach Set Computation Using Optimal Control

Abstract: Reach set computation is a basic component of many verification and control synthesis procedures. Effective computation schemes are available for discrete Systems described by finite state machines and continuous-variable Systems described by linear differential inequalities. This paper suggests an approach based on the Pontryagin maximum principle of optimal control theory. The approach is elaborated for linear systems, and it may prove useful for more general continuous-variable systems

Disturbance Observer Based Tracking Control

Abstract: A disturbance observer based tracking control algorithm is presented in this paper. The key idea of the proposed method is that the plant nonlinearities and parameter variations can be lumped into a disturbance term. The lumped disturbance signal is estimated based on a plant dynamic observer. A state observer then corrects the disturbance estimation in a two-step design. First, a Lyapunov-based feedback estimation law is used. The estimation is then improved by using a feedforward correction term. The control of a telescopic robot arm is used as an example system for the proposed algorithm. Simulation results comparing the proposed algorithm against a standard adaptive control scheme and a sliding mode control algorithm show that the proposed scheme achieves superior performance, especially when large external disturbances are present. @S0022-0434~00!00802-9# Tracking control for uncertain nonlinear systems with unknown disturbances is a challenging problem. To achieve good tracking under uncertainties, one usually needs to combine several or all of the following three mechanisms in the control design: adaptation, feedforward ~plant-inversion!, and high-gain, this paper is no exception. The tracking control of nonlinear systems under plant uncertainties and exogenous disturbances is studied in this paper. However, we will focus on the robotic examples for both literature review and numerical simulations. Many adaptive control schemes for robotic manipulators assume that the structure of the manipulator dynamics is known and/or the unknown parameters influence the system dynamics in an affine manner @1‐5#. There are several inherent difficulties associated with these approaches. First of all, the plant dynamic structure may not be known exactly. Second, it was demonstrated @6,7# that some of these designs may lack robustness against uncertainties. Recently, adaptive control algorithms requiring less model information were proposed @8‐11#. These algorithms adjust the control gains based on the system performance and thus are commonly referred to as performance-based adaptive control. These algorithms require little knowledge of system structures and parameter values. However, the control signal might become quite large. Plant-inversion based methods ~e.g., I/O linearization, backstepping!, roughly speaking, focus on the canceling of unwanted nonlinear dynamics. High-gain approaches such as sliding model controls could guarantee stability but, again, sometimes require very large control signals. While in some cases this may be a viable approach, in many other applications it may not be the best solution. In this paper, a disturbance-estimation based tracking control method is presented. Disturbance observer based control algorithms first appeared in the late 1980s @12#. Since then, they have been applied to many applications @13‐15#. Recently, the H‘ technique has been applied for the design of an optimal disturbance observer @16#. In this paper, we focus on the design for nonlinear systems. The magnitude of the disturbance is estimated based on the state estimation error in a two-step design. The estimated disturbance can then be used to improve the performance of literally any control algorithms. In this paper, a simple computed torque method is selected. The performance of the disturbanceobserver-enhanced method is then compared against those of a simple adaptive control and a simple robust control algorithm.

Adaptive sliding-mode control for induction servomotor drive

Abstract: An adaptive sliding-mode control system is proposed to control the position of an induction servomotor drive. First, a newly designed total sliding-mode control system, which is insensitive to uncertainties including parameter variations and external disturbance in the whole control process, is introduced. The total sliding-mode control comprises the baseline model design and the curbing controller design. In the baseline model design a computed torque controller is designed to cancel the nonlinearity of the nominal plant. In the curbing controller design an additional controller is designed using a new sliding surface to ensure the sliding motion through the entire state trajectory. Therefore, in the total sliding-mode control system the controlled system has a total sliding motion without a reaching phase. Then, to relax the requirement for the bound of uncertainties, an adaptive sliding-mode control system is investigated to control the induction servomotor. In the adaptive sliding-mode control system a simple adaptive algorithm is utilised to estimate the bound of uncertainties. Simulated and experimental results due to periodic sinusoidal command show that the dynamic behaviours of the proposed control systems are robust with regard to uncertainties.

Universal integral controllers for minimum-phase nonlinear systems

Abstract: We consider a single-input-single-output (SISO) nonlinear system that has a well-defined normal form with asymptotically stable zero dynamics. Using only knowledge of the relative degree and the sign of the high-frequency gain, we design an output feedback integral controller that asymptotically regulates the output to a bounded time-varying reference signal with a constant limit. We give regional as well as semi-global results. We also show that, for relative degree one and two systems, the proposed integral controller reduces to the classical PI and PID controllers, respectively.

Aircraft Pitch Control via Second-Order Sliding Technique

Abstract: Control of high-performa nce low-cost unmanned air vehicles involves the problems of incomplete measurements, external disturbances and modeling uncertainties Sliding mode control combines high precision with robustness to the aforementioned factors The idea behind this approach is the choice of a particular constraint which, when maintained, will provide the process with the required features and remove, therefore, the plant's uncertainty However, standard sliding modes are characterized by a high-frequency switching of control, which causes problems in practical applications (so-called chattering effect) A second order sliding controller implemented in the present paper features bounded continuously time-dependent control and provides higher accuracy than the standard sliding mode, while preserving precise constraint fulfillment within a finite time It possesses, also, significant adaptive properties The general approach is demonstrated by solving a real-life pitch control problem Results of a computer simulation and flight tests are presented I Introduction Aircraft and missile systems are equipped with control systems whose tasks are to provide stability, disturbance attenuation and reference signal tracking, while their aerodynamic coefficients vary over a wide dynamic range due to large Mach-altitude fluctuations and due to aerodynamic coefficient uncertainties resulting from inaccurate wind tunnel measurements It is common practice, when designing a control system for an unmanned air vehicle (UAV), to represent the flight envelope by a grid of Mach-altitude operating

Nonlinear adaptive control using neural networks and multiple models

Abstract: The principal contribution described here is concerned with combining linear and nonlinear models to improve the performance of essentially nonlinear dynamical systems even while assuring their stability. The system under consideration is defined, and some preliminaries about neural networks and growth rates of signals are given, which is central to the proof of stability. Following this, the well-known results in robust linear adaptive control are reproduced for easy reference. The key result of stability analysis when multiple models are used is presented. This is a very general result, and the special case when some of the models are actually neural networks is included.

Sensorless PMSM drive with a sliding mode control based an adaptive speed and a rotor resistance estimator

Abstract: This paper presents a new speed and position sensorless control method of permanent magnet synchronous motors based on the sliding mode observer. The sliding mode observer structure and its design method are described. Also, Lyapunov functions are chosen for determining the adaptive law for the speed and the stator resistance estimator. The effectiveness of the proposed observer is confirmed by experimental results.

Feedback control methodologies for nonlinear systems

Abstract: A number of computational methods have been proposed in the literature to design and synthesize feedback controls when the plant is modeled by nonlinear dynamics. However, it is not immediately clear which is the best method for a given problem; this may depend on the nature of the nonlinearities, size of the system, whether the amount of control used or time needed for the method is a concern, and other factors. In this paper, a comprehensive comparison study of five methods for the synthesis of nonlinear control systems is carried out. The performance of the methods on several test problems are studied, and some recommendations are made as to which feedback control method is best to use under various conditions.

Reusable Launch Vehicle Control in Multiple Time Scale Sliding Modes

Abstract: A reusable launch vehicle control problem during ascent is addressed via multiple-time scaled continuous sliding mode control. The proposed sliding mode controller utilizes a two-loop structure and provides robust, de-coupled tracking of both orientation angle command profiles and angular rate command profiles in the presence of bounded external disturbances and plant uncertainties. Sliding mode control causes the angular rate and orientation angle tracking error dynamics to be constrained to linear, de-coupled, homogeneous, and vector valued differential equations with desired eigenvalues placement. Overall stability of a two-loop control system is addressed. An optimal control allocation algorithm is designed that allocates torque commands into end-effector deflection commands, which are executed by the actuators. The dual-time scale sliding mode controller was designed for the X-33 technology demonstration sub-orbital launch vehicle in the launch mode. Simulation results show that the designed controller provides robust, accurate, de-coupled tracking of the orientation angle command profiles in presence of external disturbances and vehicle inertia uncertainties. This is a significant advancement in performance over that achieved with linear, gain scheduled control systems currently being used for launch vehicles.

A Sliding Mode Control of a Full-Car Electrorheological Suspension System Via Hardware in-the-Loop Simulation

Abstract: This paper presents a feedback control performance of a full-car suspension system featuring electrorheological (ER) dampers for a passenger vehicle. A cylindrical ER damper is designed and manufactured by incorporating a Bingham model of an ER fluid which is commercially available. After evaluating field-dependent damping characteristics of the ER damper, a full-car suspension system installed with four independent ER dampers is then constructed and its governing equation of motion, which includes vertical, pitch, and roll motions, is derived. A sliding mode controller, which has inherent robustness against system uncertainties, is then formulated by treating the sprung mass as uncertain parameter. For the demonstration of a practical feasibility, control characteristics for vibration suppression of the proposed ER suspension system are evaluated under various road conditions through the hardware-in-the-loop simulation (HILS).

Sliding-mode control of interleaved boost converters

Abstract: Boost topologies in interleaved operation under sliding-mode control are analyzed in this paper. First, the interleaving connection of two identical boost converters results in a new step-up structure whose closed-loop dynamics are asymptotically stable with good start-up and excellent load regulation when a self-oscillating sliding-mode control is applied to the converter. For a duty cycle of 50%, the new regulator acts as a small-ripple voltage doubler. Later, an extension of the voltage doubler yields a voltage quadrupler with similar dynamic characteristics. Simulated and experimental results verify the theoretical predictions.

Dynamical sliding mode power control of wind driven induction generators

Abstract: This paper concerns power regulation of variable-speed wind energy conversion systems. These systems have two regions of operation, depending on the tip speed ratio of the wind turbines. They are distinguished by a minimum phase behavior in one of these regions and a nonminimum phase one in the other. A sliding mode control strategy is proposed that assures stability in both regions of operation and imposes the ideally designed feedback control solution in spite of model uncertainties. Moreover, power regulation by the proposed sliding control in the minimum phase region is completely robust to wind disturbances and parameter uncertainties.

Discontinuous unit feedback control of uncertain infinite-dimensional systems

Abstract: Control systems, driven by a discontinuous unit feedback in a Hilbert space, are studied. The equation which describes a system motion, taking place in the discontinuity manifold and further referred to as a sliding mode, is derived by means of a special regularization technique. Based on the sliding mode equation, the procedure of synthesis of a discontinuous unit control signal is developed. Restricted to a class of infinite-dimensional systems with finite-dimensional unstable part, this procedure generates the control law which ensures desired dynamic properties as well as robustness of the closed-loop system with respect to matched disturbances. As an illustration of the capabilities of the procedure proposed, a scalar unit controller of an uncertain exponentially minimum phase dynamic system is constructed and applied to heat processes and distributed mechanical oscillators.