Showing papers on "Sliding mode control published in 1977"
TL;DR: In this article, a singular perturbation approach is used to unify a class of classical and recent results on high-gain systems and to show their relationships with multivariable transmission zero analysis, cheap control problems, and sliding mode in variable structure systems.
Abstract: In this paper a singular perturbation approach is used to unify a class of classical and recent results on high-gain systems and to show their relationships with multivariable transmission zero analysis, cheap control problems, and sliding mode in variable structure systems. A new pole placement method and a decomposition of near optimal high-gain regulator problems are presented.
366 citations
TL;DR: In this article, the application of the theory of variable structure systems (VSS) in the design of controllers for single input-single output model reference systems is considered, and it is shown that the resulting controller has similar structure as those obtained using the second method of Lyapunov except that the states of the model are also used.
Abstract: The application of theory of variable structure systems (VSS) in the design of controllers for single input-single output model reference systems is considered. It is shown that the resulting controller has similar structure as those obtained using the second method of Lyapunov except that the states of the model are also used. The error trajectories move towards the switching surface for all values of the error and continues on it as sliding motions. The present approach clarifies the relationship between stability and nonminimum phase zeros of the plant.
67 citations
TL;DR: A generalized theory of noninteracting (decoupling) control by state feedback is presented so that decoupling of linear and nonlinear systems can be studied within the same framework.
Abstract: A generalized theory of noninteracting (decoupling) control by state feedback is presented so that decoupling of linear and nonlinear systems can be studied within the same framework.
44 citations
TL;DR: In this article, a procedure for designing stable nonlinear control laws for linear plants is presented, based on an inverse optimal control problem with the closed form controller being directly given by the solution of a set of linear algebraic equations.
Abstract: A procedure for designing stable nonlinear control laws for linear plants is presented. The design is based on an inverse optimal control problem with the closed form controller being directly given by the solution of a set of linear algebraic equations. The nonlinear controllers can be used to produce saturation effects on particular states, and an example is included to illustrate the results.
38 citations
TL;DR: In this article, the problem of designing an observer for use in a linear quadratic optimal feedback control scheme so as to minimize the effects of small departures in the plant parameters from their nominal values is considered.
Abstract: This paper considers the problem of designing an observer for use in a linear quadratic optimal feedback control scheme so as to minimize the effects of small departures in the plant parameters from their nominal values.
20 citations
TL;DR: An iterative sequential observer is presented which enables us to estimate the transient state of power system with high accuracy and an observer gain is introduced which is easily and sequentially evaluated in a similar way as Kalman filter.
Abstract: This paper presents an iterative sequential observer which enables us to estimate the transient state of power system with high accuracy. This observer attempts to reduce the effect of both the dynamic non-linearity and the measurement nonlinearity. The latter is reduced by modifying the estimates iteratively and the former by discretizing the dynamic equation at every short interval of time. Furthermore an observer gain is introduced which is easily and sequentially evaluated in a similar way as Kalman filter. Simulation results, in which the observer is applied to the system of one machine infinite bus, indicate that the state is estimated successfully even in the cases of less available measurements and there is a capability of a real-time estimation using an on-line computer.
8 citations
5 citations
TL;DR: In this article, the optimal feedback control law for a nonlinear stochastic third-order system in which the nonlinear element is not completely specified is investigated, and it is shown that, due to the structure of the system, the optimal control law is not unique.
Abstract: This paper deals with the computation of optimal feedback control laws for a nonlinear stochastic third-order system in which the nonlinear element is not completely specified It is shown that, due to the structure of the system, the optimal feedback control law, whenever it exists, is not unique Also, it is shown that, in order to implement an optimal feedback control law, a nonlinear partial differential equation has to be solved A finite-difference algorithm for the solution of this equation is suggested, and its efficiency and applicability are demonstrated with examples
5 citations
01 Dec 1977
TL;DR: It is shown that a variable structure modelFollowing control system (VSMFC) possesses an adaption mechanism similar to that in adaptive model following control systems that can be achieved systematically using this design.
Abstract: A design procedure for model following control systems is developed by utilizing sliding mode in variable structure systems. It is shown that a variable structure model following control system (VSMFC) possesses an adaption mechanism similar to that in adaptive model following control systems. For some classes of plant parameter variations, shaping of the error transients can be achieved systematically using this design. Two control problems which have been approached via adaptive model following technique are considered and performance comparison with the present design is made.
4 citations
TL;DR: It is shown that an efficient structure analysis of periodically controlled nonlinear systems is possible by use of the computer simulation technique coupled with the stroboscopic approach and seems to be the only way for finding out periodic states of the saddle mode.
Abstract: It is shown that an efficient structure analysis of periodically controlled nonlinear systems is possible by use of the computer simulation technique coupled with the stroboscopic approach. The existence and stability of every periodic state can be determined together with the dynamic behavior in the neighborhood of these periodic states. Especially, the proposed technique seems to be the only way for finding out periodic states of the saddle mode.
3 citations
TL;DR: In this paper, a high-speed vehicle suspension is synthesized using advanced dynamics, deterministic and stochastic optimal control theory, and applied mathematics to the problem of synthesizing a high speed vehicle suspension.
Abstract: This two-part paper is concerned with the problem of synthesizing a high-speed vehicle suspension system. In part I [13] a new suspension structure was developed which features three independent parts. All three parts are calculated for a vehicle which travels along a rigid guideway with arbitrary vertical and lateral curves and grades. In this part in developing the system control the use of instantaneous state feedback and the presence of inaccessible states demand the use of Ito-calculus and the Athans matrix minimum principle in order to solve the problems of vibration control synthesis. It is concluded that the application of the principles and methods of advanced dynamics, deterministic and stochastic optimal control theory, and applied mathematics to the problem of synthesizing a high-speed vehicle suspension is successful and results in the identification of a new suspension structure which is proposed as a starting point in the development and design of a high-speed vehicle suspension system. Augmented by a thorough system simulation and hardward tests for verification of all assumptions made and by implementation of the sensor-and actuator-dynamics, the described synthesis procedure will lead to an effective suspension system.
TL;DR: In this article, a procedure for the design of optimal nonlinear controllers for linear plants is presented, based on the minimization of a performance index which is nonquadratic in the system states.
TL;DR: In this paper, it is shown that the optimal control becomes totally bang-bang or totally singular for systems which are linear in control but nonlinear in state, provided that the controlled system is controllable and observable.
Abstract: This paper is concerned with the problem of optimal control for systems which are linear in control but nonlinear in state. It is shown that there is a large class of control systems in which optimal singular trajectories are allowed to lie only on a certain hypersurface when a condition similar to the normality condition for linear time-optimal control systems is fulfilled. It follows from this result that the optimal control becomes totally bang-bang or totally singular. Furthermore, for a special class of position control systems including a nonlinear element and a controller, it is proved that the optimal control becomes totally bang-bang, provided that the controlled system is controllable and observable. Finally some practical examples are given to see whether the proposed criterion is applicable or not to characterizing the type of optimal control.
TL;DR: The results presented in this paper indicate that the time-optimal control of a multi-variable, time-invariant linear system with inaccessible state variables is made possible by the introduction of a continuous-time observer system.
Abstract: The results presented in this paper indicate that the time-optimal control of a multi-variable, time-invariant linear system with inaccessible state variables is made possible by the introduction of a continuous-time observer system. The basic system and the observer system were simulated on a parallel-logic analogue computer for a third-order system and the associated three-dimensional switch surface for the time-optimal control sequence was simulated on a small digital computer: the communications between the analogue and the digital computers were accomplished by a simple interface system
TL;DR: The problem of control of a linear stochastic system observed by both linear and hard-limited measurements is considered and it is shown that the feedback nature of the control induces a natural probing which activates the filter.