Showing papers on "Sliding mode control published in 1984"

Admissible sets and feedback control for discrete-time linear dynamical systems with bounded controls and states

Abstract: For linear discrete time dynamical systems, necessary and sufficient conditions are given for a control sequence, belonging to a polyhedral constraint set, to stabilize the system under the condition that the state is restricted to a polyhedral state constraint set. A variable structure linear state feedback controller, given in terms of the controls at the vertices of the polyhedral state constraint set, is presented.

Discrete time adaptive control of linear dynamic systems with a two-segment piecewise-linear asymmetric nonlinearity

Abstract: In this note a method is presented for doing discrete adaptive control of a nonlinear system which is given by a cascade connection of a "two-segment piecewise-linear asymmetric nonlinearity" followed by a linear system. A switching gain sequence is introduced to make the parameter identification time invariant. The algorithm will ensure that the closed-loop system is globally convergent and stable for both the deterministic and stochastic cases.

Robustness of Luenberger Observers: Linear Systems Stabilized via Nonlinear Control

Abstract: Given a dynamical system whose state equations include time-varying uncertain parameters, it is often desirable to design a state feedback controller leading to uniform asymptotic stability of a given equilibrium point If, however, the controller operates on some estimate of the state, instead of the true state itself, it is of interest to know whether the desired stability will be preserved; eg, suppose that the measured output is processed by a Luenberger observer This paper concentrates on the scenario above and in addition, our analysis permits the controller to be nonlinear As a first step, inequalities are developed which have implications on the system's robustness; that is, when the uncertain parameters satisfy these inequalities, it becomes possible to separately design controller and observer This amounts to an extension of the classical separation theorem to the case when the controller is nonlinear It is also of interest to note that the approach given here enables us to guarantee stability for some nonzero range of admissible parameter variations This is achieved by introducing a certain "tuning parameter" into the Lyapunov function which is used to assure the stability of the cambined plant-observer-controller system

Asymptotic Reproducibility in Nonlinear Systems and Attitude Control of Gyrostat

Abstract: A control law is presented for asymptotic function reproducibility in a class of nonlinear-systems such that the output of the system asympotically tends to a given function. The controller consists of a prefilter and a servocompensator. Based on this result, a nonlinear feedback control law for the attitude control of a satellite containing symmetric rotors, in a circular orbit, is derived. In the closed-loop system, given trajectories of pitch, yaw, and roll angles are asymptotically followed, and set point control of attitude is accomplished. Digital simulation results are presented to show the capability of the nonlinear controller.

Sliding mode control system

Abstract: PURPOSE: To approximate the control input to the equivalent control input for suppression of the current chattering and at the same time to perform positioning while restricting a real locus on a gain switch line by reducing the absolute value of the switch gain by a minute amount each time the state of the real locus on a phase plane is changed to a plus from a minus at positioning control. CONSTITUTION: In case a gain switch line is added to a positioning control system applying a sliding mode control method, the absolute value of the switch gain is reduced by a minute amount each time the state of a real locus on a phase plane changes to a plus to a minus at positioning control in consideration of the dead time. Thus it is possible to approximate the control input to the equivalent control input for suppression of the current chattering and also to perform the positioning while restricting the real locus on a gain switch line. COPYRIGHT: (C)1990,JPO&Japio

Nonlinear Trajectory Control of Autonomous Underwater Vehicles Using the Sliding Methodology

Abstract: A new variation on sliding control is shown to be very effective for the control of underwater vehicles. The method deals with nonlinearities directly, is highly robust to imprecise models, and is intuitively appealing. The method is demonstrated using a nonlinear vehicle simulation.

Analysis of variable structure systems with sliding modes

Abstract: Single variable control systems of variable structure are analysed. The conditions for the control law and for a hyperplane are determined so that a stable sliding mode is obtained. No restrictions are placed on the linear state variable representation and it is not necessary to switch all of the states. An approximation is presented which simplifies the determination of an admissible sliding hyperplane.

Control Effort Considerations in the Stabilization of Uncertain Dynamical Systems

Abstract: This paper investigates the problem of designing a state feedback control to stabilize an uncertain nonlinear system. We focus attention on the amplitude (norm) of the controller which is used to achieve this end. The uncertain system is described by a state equation which contains uncertain parameters which are unknown but bounded. A Lyapunov function is used to establish the stability of the closed loop system. The paper gives necessary and sufficient conditions for the uncertain system to be stabilizable with a given Lyapunov function. Furthermore, a procedure is indicated for the construction of the desired feedback control law. The control scheme presented is referred to as the minimum effort control. This terminology refers to the fact that at each state and time, the resulting control vector is the smallest allowable control vector which will ensure the desired degree of negativity of the Lyapunov derivative. Implementation of this control scheme requires the repeated solution of a mathematical program.

Variable structure postition control

Abstract: This paper describes the application of the variable structure control (VSC) concept for dc motor position control. The control scheme is derived, implemented, and tested in the laboratory where both digital and analog controllers have been used to control a representative servo system. The control-system schematics are given and sample results are shown for illustration. The VSC experiment should be of interest to educators and design engineers who wish to demonstrate and investigate sophisticated position-control methods and their applications. This experiment may also serve as a basis for further applications of VSC.

Digital stochastic control of distributed-parameter systems

Abstract: This paper presents a method for discrete-time control and estimation of flexible structures in the presence of actuator and sensor noise. The approach consists of complete decoupling of the modal equations and estimator dynamics based on the independent modal-space control technique and modal spatial filtering of the system output. The solution for the Kalman filter gains reduces to that of independent second-order modal estimators, thus permitting real-time digital control of distributed-parameter systems in a noisy environment. The method can be used to control and estimate any number of modes without computational restraints and is theoretically free of observation spillover. Two examples, the first using nonlinear, quantized control and the second using linear, state feedback control are presented.

Partial realization of a nonlinear discrete-time system from an equilibrium point

Abstract: It is shown that the truncated Volterra series of a nonlinear analytic discrete-time system initialized at an equilibrium point can be realized by a polynomial affine system: i.e. a system which is polinomial in the input and affine in the state.

Non linear control of variable structure systems

Abstract: Sliding modes in the control of systems described by ordinary differential equations have been investigated both from a theoretical point of view and from practical considerations, when the control variables enter linearly in the system. In this paper we extend the sliding mode control technique to fully non linear systems. We introduce a definition of equi valent control and show, under suitable conditions, the equivalence between the relevant Filippov solutions and the solutions obtained by using the equivalent control law. We discuss the physical meaning of such an equivalent control taking into account the behaviour of the corrisponding trajectories as far as approximability properties (physically relevant) are considered. We introduce a definition of approximability for nonlinear control systems with sliding surfaces, which shows the inherent limitations of the concept of equivalent control for general nonlinear dynamics. This validates some conjectures of [1] and extends basic results thereof to certain classes of fully nonlinear control systems. We show that the equivalent control may be defined and the approximability property holds for control systems of the following form: $$z^{(n)} = g(t,z,z',...z^{(n - 1)} ,u);$$ (A)) $$\dot x = A(t,x) + B(t,x)h(u)$$ (B)) , under suitable explicit conditions about g, A, B, h and the sliding manifold.

Control in power electronics and electrical drives : proceedings of the Third IFAC Symposium, Lausanne, Switzerland, 12-14 September 1983

Abstract: (partial) Modelling and Control Laws: Closed mathematical description of line commutated converter-drives, K Hofer. Non-linear and linearized models for control systems including static converters, J P Louis. Identification and Observation: A novel approach on parameter self-tuning method in AC servo system, T Irisa et al. A microcomputer system for estimating the parameters of an induction motor model, A Gallo et al. New Methods of Control: Non-linear controller allowing for an upper bound on the system internal variables, G Celentano & P Marino. Speed control of an AC motor by state variables feedback with decoupling, P Feller. Adaptive and Sliding Mode Control: Microprocessor-based adaptive control for electrical drives, A Brickwedde. Adaptive control design in servosystems, A Balestrino et al. Current Converters and Inverters: Effect of source reactance on the controllable three-phase bridge rectifier operation with series R-L loads, S I El-Kassas et al. The family of commutation modes of converters, F Kehtari.

Two-stage PFM control

Abstract: Pulse frequency modulated (PFM) control, thus far primarily used in step motors and attitude control systems of space vehicles, is gaining more and more significance as a natural, failsafe link between the "intelligent" and the "dynamic" part of general process computer control systems. However, no analytical design methods of practical relevance have been available so far. This paper describes a method for the analytical design of PFM control systems. This method is based on a new mathematical model of the PFM controller introduced by Frank in 1979 [6]. A "two-stage" configuration for the implementation of the PFM controller is proposed.

Adaptive dual control of discrete-time distributed-parameter stochastic systems

Abstract: The problem of adaptive dual control of discrete-time distributed-parameter stochastic systems is examined. It is shown that there exists an important difference between feedback and closed-loop policies of control for this type of system as for the lumped parameter case. This difference is based on the adaptivity feature of the control. Namely, when the control policy affects both the state and its uncertainty (dual effect) it possesses the so-called feature of active adaptivity and can only be a characteristic of a closed-loop policy, whereas a feedback policy can only be passively adaptive. These results can be used to develop a control algorithm for non-linear problems for which the realization of optimal control laws involves control strategies with both learning and control features.

Robust Decentralized Control for Nonlinear Interconnected Systems using Optimal Control

Abstract: A decentralized control law for a class of nonlinear interconnected system is proposed. This control law is derived by solving a local optimal control problem for each isolated subsystem with an appropriate performance index. It is also shown that the proposed decentralized control is the solution of an optimal control problem for the global system with an appropriate performance index.

On Nonlinear Perturbations of Nonlinear Dynamical Systems and Applications to Control

Abstract: The nonlinear variation of constants formula is generalised to infinite dimensional systems and applied to the stability problem and to obtain bounds on the states of a nonlinear control system when the controls are bounded. The theory is illustrated by a simple model from nuclear reactor dynamics

Microprocessor-based force control for manipulator using variable structure with sliding mode

Abstract: The design principles of sliding mode control are studied and then are applied to force control of a manipulator hand powered by a PWM transistor converter-fed dc servomotor. Each step in the formulation of the control algorithm is clearly defined and explained. The feasibility of this control scheme is experimentally verified. The control strategy is implemented by using a Motorola 6809 Microprocessor. The proposed controller is robust in both dynamic and steady state performances and provides extremely smooth force control independent of system parameter variations, nonlinearities and external disturbances. In addition to this, the design procedure of the controller is very simple, since it does not require accurate modeling, but it is sufficient to know only the bounds of the model parameters and disturbances. The designer can easily determine a desired time constant by choosing a sliding curve.