Variable Structure Systems Theory Research Articles

Variable Structure Control Method for Fuel-Injected Systems

A nonlinear control method for automotive fuel-injection systems is developed using the theory of variable structure systems. This fuel-injection control method is formulated to be compatible with production sensors and actuators, and its feasibility and potential benefits are demonstrated using a research automobile. The motivation for this research stems from the fact that fuel-injection control is a difficult control problem due to the nonlinear and complex nature of engine dynamics and due to the limitations imposed by a switching-type feedback sensor.

Robust Sliding Mode Control of Semi-Active and Active Suspension for Private Cars

In this paper, we show the interest to consider variable structure system theory, for the design of semi-active and active suspension based on quarter car model and full car model, in order to take into account, easily, some technological constraints on the actuator which has, often, for adaptive suspension, two laws of damping : soft or hard.

Decentralized variable-structure adaptive controller synthesis of large-scale systems subjected to bounded disturbances

Abstract The regulation control problem is considered for a large-scale system in the presence of interconnected terms, system parameter variations and external disturbances. Based on the technique of parameter estimations and the theory of variable-structure systems, this paper presents a new and feasible design algorithm for the synthesis of a decentralized variable-structure adaptive controller which can easily tackle the control problem of large-scale systems subjected to interconnected terms, system parameter variations and bounded disturbances. In contrast to previous results, the restrictive condition that the exact value of the parameter describing the input gain must be known can be relaxed. A series of computer simulations are also included to illustrate the proposed design algorithm.

Discrete-time sliding mode control in the presence of system uncertainty

A discrete-time sliding-mode controller is presented in this paper, based on the theory of variable structure systems. It is assumed that the parameters of the system are uncertain and external disturbances are present. A measure of these effects is obtained through the deviations from the desired sliding surface, and this information is incorporated in the control law. A predictive corrective scheme is utilized in the calculation of the control inputs and, as a result, no a priori knowledge of the uncertainty bounds is required. This approach leads to a non-switching type of control, thereby eliminating the fundamental cause of chatter. The convergence and disturbance rejection properties of the approach are verified, and its performance is tested for the tracking control of an industrial robot.

Finite-dimensional model reference adaptive control of a class of nonlinear distributed systems with quasi-sliding mode

Abstract We propose a new design method for a finite-dimensional model reference adaptive control of a class of non-linear distributed systems with input and output disturbances, when only input and output measurements are available. We consider the case where the relative degree of the dominant part of the plant is arbitrary, and introduce the idea of quasi-sliding mode in variable structure systems theory which can avoid the chattering problem. The proposed method assures that any accuracy of the output error is obtained in any finite time, independently of the presence of bounded disturbances, non-linearity and unmodelled dynamics and that all signals in the closed-loop system are uniformly bounded. Finally, we show the effectiveness of the proposed method by a simple numerical example.

Sliding Mode Method in Inverse Motion Control Problems

A new design concept for multivariable control systems capable of command tracking and disturbances decoupling is developed using the theory of inverse systems. variable structure systems and sliding modes. The both feedback and feedforward control algorithms are elaborated based on state-space realization of plant’s inverse models. The properties of the closed-loop control system are established and it is shown, that the control error is invariant with respect to the command signals and unmeasurable disturbances. The properties of realizable invariant systems with real differentiators are also investigated using motion decoupling method. The method of inverse systems synthesis basec on variable structure systems theory is proposed.

Force/motion control of constrained robots using sliding mode

A sliding mode control algorithm is presented for trajectory tracking of an end-effector on a constrained surface with specified constraint forces by using the theory of variable structure systems. The development of the algorithm is based on a new formulation of the dynamic model and the expansion of sliding surfaces to include the constraint force error. The proposed sliding controller is explicit, which ensures the occurrence of the sliding mode on the intersection of the surfaces. A detailed numerical example is presented to illustrate the method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Neuromorphic Control of Robotic Manipulators Using Sliding Mode

A neuromorphic controller is presented for trajectory control of a robot manipulator with unknown dynamics using the theory of variable structure systems. It consists of two neural networks with PD feedback and full dynamics feedforward compensation. The learning scheme only makes use of a priori knowledge of the general structure of robot dynamics, and is computationally very fast and amenable to parallel processing implementation. The global stability of the closed-loop dynamics can also be guaranteed. Simulation of a two-link manipulator verifies the proposed learning algorithm.

Design of sinusoidal oscillators using the theory of variable structure systems

Abstract This paper presents a new simple scheme to design sinusoidal oscillators by using the theory of variable structure systems. The desired oscillation frequency and amplitude can be independently determined. Significantly, the total system of the sinusoidal oscillator is easily completed by choosing two linear second-order subsystems with some appropriate switching conditions and the required circuit components for the developed system are all commercially available.

Robust Control of Magnetic Gear Transmitting System.

A new magnetic gear transmitting system with an actuator made of an electromagnet is proposed in this paper. The vibration due to the system parameter variations or external disturbance is absorbed by means of changing magnetic fluxes of the electromagnet and the controller is designed by variable structure system (VSS) theory. The theoretical expressions of the transmitting torque, magnetic spring constant and control force versus electric current in the electromagnet were derived. Both the simulations and experiments of this magnetic gear system were carried out by means of the sliding mode regulator and were compared with the PID linear control method. The experimental results confirmed the theoretical analyses.

A new controller design for a flexible one-link manipulator

A novel controller design for noncollocated flexible one-link manipulator arm tip position control based on variable structure sliding mode control is presented. Using the assumed-mode method, the plant model is derived. The discontinuous control law based on the variable structure system theory for the noncollocated manipulator tip position control is then designed. The position state variables are obtained directly from the inversion of the output submatrix multiplied by the sensor measurements. The velocity state variables are estimated through decoupled estimators-a separate first-order observer for each of the system's modes under consideration. Different sampling periods are used for the estimator and the controller. The performance of the controller is evaluated through a series of simulations, followed by an analysis of the designed control system. >

Sliding Mode Control and Elastic Mode Stabilization of a Robotic Arm With Flexible Links

This paper treats the question of control of an elastic robotic arm of two links based on variable structure system (VSS) theory and pole assignment technique for stabilization. A discontinuous joint angle control law, based on VSS theory, is designed which accomplishes asymptotic decoupled joint angle trajectory tracking. In the closed-loop system, the trajectories are attracted toward a chosen hypersurface in the state space and then slide along it. Although, joint angles are controlled using variable structure control (VSC) law, the flexible modes of the links are excited. Using center manifold theory, it is shown that the closed-loop system, including the sliding mode controller, is stable. Based on a linearized model about the terminal state, a stabilizer is designed using pole assignment technique to control the elastic oscillations of the links. A control logic is included which switches the stabilizer at the instant when the joint angle trajectory enters a specified neighborhood of the terminal state. Simulation results are presented to show that in the closed-loop system, accurate joint angle trajectory tracking, and elastic mode stabilization are accomplished in the presence of payload uncertainty.

Path tracking control of robot manipulators via the VSS approach

The path tracking control problem is considered for a robot manipulator subject to parameter uncertainty and external disturbance. By using the theory of variable structure systems (VSS) and taking advantage of the important property of the robot dynamics, a new control strategy is proposed in which both parameter uncertainty and external disturbance can easily be taken into account. It is shown that with this control strategy, accurate path tracking is guaranteed. Moreover, on-line parameter estimation is not required, which makes the strategy easy to implement.

Relay control for a vibration isolator using the theory of variable structure systems.

Relay control for a vibration isolator using the theory of variable structure systems.

Sliding mode control of flexible arm.

A new control design of flexible arms using the theory of variable structure systems (VSS) is presented. The control is designed so that a new type of state space trajectories called sliding modes exists. While in the sliding mode, the performance of the system remains insensitive to parameter variation and disturbance. This property of VSS is very important in eliminating the effects due to load variation of the arm. Both simulation and experiment demonstrate the satisfactory performance of the slidding mode control system for the flexible arm.

Variable structure slewing control and vibration damping of flexible spacecraft

The question of attitude control and elastic mode stabilization of a spacecraft (orbiter) with “beam-tip mass” type payload is considered. It is assumed that bounded but unknown disturbance torques are acting on the spacecraft. Based on variable structure system theory, a discontinuous three-axis moment control law is derived to control the attitude of the spacecraft. Although, this control law accomplishes attitude trajectory tracking, it excites the elastic modes of the beam. A modal velocity feedback design is presented to damp the elastic oscillations using additional actuators at the tip of the beam. Simulation results are presented to show that rotational maneuvers and vibration stabilization can be accomplished in the closed-loop system in spite of disturbance torques and uncertainty in the system.

Robust trajectory following of robots using computed torque structure with VSS

A control approach is proposed for robust accurate trajectory tracking of manipulators based on the computed torque technique and variable-structure systems (VSS) theory. The computed torque structure of the control scheme, most importantly, provides greater insight to the control of manipulators and serves as a unifying framework for control law development. Looking at the control structure from a computed torque perspective also enables the extension of the technique from joint space to direct end-effector control of both non-redundant and redundant robots in task or operational space. The technique, perhaps, may be further augmented to incorporate force control to achieve hybrid force/position control. The use of sliding modes in the control scheme, in its idealized form, ensures accurate tracking while achieving insensitivity to parameter variations/uncertainties and bounded disturbances. In the development of the control laws, some useful properties of the robot dynamics, viz., positive definiteness of the inertia matrix, and its (dynamics structure) linear form with respect to its parameters, are exploited to make the control laws simple for real-time implementation and reflect the explicit inter-dependence of control non-linearity and structured dynamic model uncertainty. The control algorithms obtained by various researchers for manipulator control using VSS theory may be interpreted from the approach given, which thus to a certain extent unifies the VSS techniques suggested in the literature for robot control.

Performance improvement of output feedback control systems using the theory of variable structure systems

In order to improve the transient response of the existing output feedback control systems without changing the output feedback gain an output feedback controller, which uses both the theory of variable structure systems and the modified positive real lemma, is proposed. Simulation results shows that the proposed controller improves the transient response.

Robust tracking control of non-linear systems with uncertain dynamics Part 1

A robust tracking control algorithm based mainly on the theory of variable structure systems and Lyapunov's direct method is developed in this paper, to treat the tracking control problem of a class of non-linear time-varying systems with uncertain dynamics. A nominal model is used instead of an exact one. together with a description of the bounds of plant uncertainty. The objective is to design a control law such that all the plants lying within a specified band of uncertainly will be driven to reach the goal. The modelling error, time-varying system dynamics, system uncertainties, and disturbances are all treated as general disturbances to the nominal system. This algorithm greatly eases the difficulties present in requiring a precise model of the physical system for the control purpose and for handling the non-linear time-varying system. The non-linear time-varying system is first linearized to a linear time-varying system (with time-varying coefficients completely defined) via the method of variable s...

Sliding Modes in Signal Processing: An Observer of the Flux Induction Motors

The theory of variable structure systems is employed for implementing an observer which effects the estimation of the rotor flux components of an induction motor supplied by a PWM voltage source inverter. The observers’ algorithm is given directly in discrete form to take into account that the same is implemented on a digital computing device. The observer parameters are chosen so as to guarantee not only a satisfactory behaviour of the same as a follower, but also the robustness with respect to variations of the rotor resistance and the angular speed. Due to these characteristics the proposed strategy has shown to be very suited to allow a not negligible reduction of the computational effort when it is necessary to change in line the values of the observer parameters to compensate variations of the motor operating conditions.