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2009 | Buch

Sliding Mode Control Using Novel Sliding Surfaces

verfasst von: Bijnan Bandyopadhyay, Fulwani Deepak, Kyung-Soo Kim

Verlag: Springer Berlin Heidelberg

Buchreihe : Lecture Notes in Control and Information Science

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Über dieses Buch

AfterasurveypaperbyUtkininthelate1970s,slidingmodecontrolmeth- ologies emerged as an e?ective tool to tackle uncertainty and disturbances which are inevitable in most of the practical systems. Sliding mode control is a particular class of variable structure control which was introduced by Emel’yanov and his colleagues. The design paradigms of sliding mode c- trol has now become a mature design technique for the design of robust c- troller of uncertain system. In sliding mode technique, the state trajectory of the system is constrained on a chosen manifold (or within some neighb- hood thereof) by an appropriatecontrolaction. This manifold is also called a switching surface or a sliding surface. During sliding mode, system dynamics is governed by the chosen manifold which results in a well celebrated inva- ance property towards certain classes of disturbance and model mismatches. The purpose of this monograph is to give a di?erent dimension to sl- ing surface design to achieve high performance of the system. Design of the switching surface is vital because the closed loop dynamics is governed by the parameters of the sliding surface. Therefore sliding surface should be - signed to meet the closed loop speci?cations. Many systems demand high performance with robustness. To address this issue of achieving high perf- mance with robustness, we propose nonlinear surfaces for di?erent classes of systems. The nonlinear surface is designed such that it changes the system’s closed-loop damping ratio from its initial low value to a ?nal high value.

Inhaltsverzeichnis

Frontmatter
Introduction
Sliding Mode Control
Control System (VSCS). Recently many successful practical applications of sliding mode control (SMC) have established the importance of sliding mode theory which has mainly been developed in the last three decades. This fact is also witnessed by many special issues of learned journals focusing on sliding mode control [13, 15]. The research in this field was initiated by Emel’yanov and his colleagues [38, 39], and the design paradigm now forms a mature and an established approach for robust control and estimation. The idea of sliding mode control (SMC) was not known to the control community at large until an article published by Utkin [96] and a book by Itkis [52].
Bijnan Bandyopadhyay, Fulwani Deepak, Kyung-Soo Kim
High Performance Robust Controller Design Using Nonlinear Surface
Introduction
Many practical systems call for an improvement in transient performance along with the steady state accuracy. For example, many electro-mechanical, robotics and power converter systems require a quick response without any overshoot. It is a well understood fact that a low overshoot can be achieved at the cost of high settling time. However, a low settling time is also necessary for a quick response. Thus, most of the design schemes make a tradeoff between these two transient performance indices and the damping ratio is chosen as a fixed number. As explained in the first chapter, a variable damping ratio improves the system performance significantly. This chapter presents a method to design a nonlinear sliding surface for a linear uncertain system; and the method is also extended for a class of nonlinear system. A nonlinear sliding surface is designed by using the principle of composite nonlinear control [70, 94, 21]. Using a nonlinear sliding surface, the damping ratio of a system can be changed from its initial low value to final high value. The initial low value of damping ratio results in a quick response and the later high damping avoids overshoot. Thus the proposed surface ascertains the reduction in settling time without any overshoot. Furthermore, systems’s damping ratio changes continuously as per the chosen function. Both regulator and tracking cases are considered in this chapter. The proposed approach inherits the robustness of SMC and delivers high performance due to change of damping ratio through the nonlinear sliding surface. During sliding mode, because of the order reduction, system response is unaffected by m poles. For a systems of order higher than 2, the damping ratio is specified by considering the contribution of dominant poles. However, non-dominant poles always affect the system response to some extent depending on their relative locations with respect to the dominant poles. Due to the order reduction property of SMC, m non-dominant poles will not contribute in the system response and thus, the performance specifications can be achieved more closely. The proposed nonlinear sliding surface achieves high performance and robustness unlike a sliding surface designed by assigning eigenvalues or by minimizing a quadratic index, which normally lead to a linear sliding surface. This chapter contains some results from [2] and several additional results.
Bijnan Bandyopadhyay, Fulwani Deepak, Kyung-Soo Kim
High Performance Tracking Controller for Discrete Plant Using Nonlinear Surface
Introduction
In this chapter, a nonlinear surface is proposed to improve the performance of discrete-time system. Recall that, in the previous chapter a regulator design for continuous time system is considered. Due to the flexibility of implementation, most of the controllers are implemented through digital signal processor or high end microcontrollers. Due to this reason study and research on discrete sliding mode has received a considerable amount of attention (e.g., see [12, 10, 44, 8] and [54], among many). In this chapter, a step tracking control for general discrete-timemultivariable system is considered based on DSMC with nonlinear sliding surface. To relax the need of measuring the entire state vector, the multi-rate output feedback (MROF) is used. Discrete-time system represented in delta operator is also analysed in this chapter to understand the effect of change in sampling time explicitly. This chapter reconstructs the research results proposed in [1, 3] as well as some additional results are included.
The brief outline of this chapter is as follows. Section 2 contains a brief review of themultirate output feedback strategy. The structure of nonlinear sliding surface and the proof of its stability is given in Section 3. Section 4 discusses two approaches to design control law, first is based on reaching law approach and the second is based on disturbance observer. Analysis of system represented with delta operator is presented in Section 3.5. Application and simulation results are presented in Section 6 followed by the conclusion in Section 7.
Bijnan Bandyopadhyay, Fulwani Deepak, Kyung-Soo Kim
An Improvement in Performance of Input-Delay System Using Nonlinear Sliding Surface
Introduction
It is well recognized that the existence of a time delay may affect the performance or result in loss of stability as shown in [65]. Recently many methods have been published in [106, 104, 57, 83, 103] on the design of control laws for time-delay systems; see the references therein. In [77], it has been shown that all the proposed methods for time delay systems use prediction of state either explicitly or implicitly. Control algorithms based on state prediction were first proposed in [72]. Furukawa and Shimemura [43] proposed a predictor-observer based scheme to control plants with time-delay. Using the predictor, the original input-delay system can be converted into a delay-free system and the problem reduces to finite dimensions. The predictor is used when the delay is known which restricts its scope. However, Lozano et al. [71] consider uncertainty in the knowledge of delay with a state predictor based scheme. Recently, in [104], sliding mode control is proposed based on a discrete predictor for a regulator case. In [71], a state predictor based state feedback control law is proposed; and the authors also propose a predictor in the discretetime framework. The performance of a system is adversely affected by a delay in the input as shown in [65, 83], which necessitates compensation. In this chapter, it has been shown that how the performance of input-delay systems can be improved by using a nonlinear sliding surface unlike the use of a linear sliding surface (linear in the predicted states). A nonlinear sliding surface is designed in predicted state. Furthermore, it has been shown if performance of the system transformed in the predicted state is improved then it leads to the improvement of the performance of the original time-delay system. The general uncertain system is considered which contains both matched and unmatched perturbations. It is an established fact that for an uncertain system, discrete-time sliding mode is possible only in the vicinity of sliding surface s(k) = 0. To ensure ideal sliding motion s(k) = 0 for an uncertain system, the exact value of disturbance/uncertainty is needed. In general, the exact value of disturbance/uncertainty is not known. Therefore, in this chapter an ultimate boundedness of resulting motion is proved. This chapter extends the results of the previous chapter for a system with a delay and having both matched and unmatched uncertainties. This chapter is based on authors work in [7].
Bijnan Bandyopadhyay, Fulwani Deepak, Kyung-Soo Kim
Integral Sliding Mode Based Composite Nonlinear Feedback Control
Introduction
In this chapter we discuss the problem of improving performance yet preserving the invariance towards the matched disturbances from a different perspective. In the previous chapters, we proposed various schemes in which the nonlinear surfaces are designed for different types of systems for the improvement of performance. In this chapter we propose a nonlinear surface which considers actuator saturation and the elimination of the reaching phase with improvement in the performance. For any practical system, actuator output can not take any amplitude. Actuator capacity is always bounded, therefore it is necessary to consider the effect of saturation actuator a priori. In conventional sliding mode, the motion of the trajectory is constrained to lie in an (n − − m) dimensional manifold with a discontinuous control action. Here m is the number of inputs and n is the order of the system. The motion of the trajectory from the initial condition towards sliding surface until it hits the sliding surface is called the reaching phase. During the reaching phase, the system is not robust and even matched disturbances can affect the system performance. To solve this problem, in [100], an integral sliding mode (ISM) concept is proposed. An integral term is incorporated in the sliding manifold, this guarantees that the system trajectories will start in the manifold right from the beginning thus, the reaching phase is eliminated; and the system becomes invariant towards matching perturbation right from the beginning. The main idea behind the ISM controller is to define the control law as a sum of a nominal control and a discontinuous control. Nominal control takes care of the nominal plant dynamics and the discontinuous control rejects the disturbances. The nominal control can be of any form which is able to follow the reference trajectory within a given accuracy. In this work we have taken Composite Nonlinear Feedback (CNF) controller, which is based on variable damping ratio, as a nominal controller along with the ISM controller to reject disturbance.
Bijnan Bandyopadhyay, Fulwani Deepak, Kyung-Soo Kim
Multi-objective Sliding Mode Design Using Full-Order Lyapunov Matrix
Introduction
In this chapter, the sliding mode control (SMC) design for a class of continuous-time linear uncertain systems is considered based on the parametric approaches utilizing the Lyapunov (or Riccati-like) inequalities. SMC for the continuous-time linear systems is one of the well-known issues in control theory. However, this chapter addresses a new aspect of SMC for linear uncertain systems and establishes a systematic procedure to design a sliding hyperplane having multiple design objectives.
In the literature, much effort has been made to design sliding modes that satisfy the desired performance criteria. The well-known criteria include quadratic performance optimization [101], guaranteed H2 cost minimization [90], eigen-structure assignment including pole-clustering [25, 31, 37], robustness to parametric uncertainties [88, 64, 107], and so on. Note that all these approaches are concerned with satisfying a single design objective. Moreover, the design objectives have not been presented in a unified framework.
Bijnan Bandyopadhyay, Fulwani Deepak, Kyung-Soo Kim
Lyapunov-Based Sliding Mode Control with Multi-Rate Output Feedback
Introduction
In the preceding chapter a design method for sliding surface is presented for continuous time system using full order Lyapunov matrix. Also this method is extended for to continuous uncertain time system. It is also noted as elaborated in introduction chapter that discrete-time sliding mode control is gaining more necessity since the actual implementation of control is generally carried out with digital signal processors. Recently, efforts have been made to recover the robustness of DSMC such as the discrete approximation approach [102], the sliding sector [45], and the quasisliding modes [92, 12]. Here, it is pointed out that the research on the sliding hyperplane design itself has drawn little attention in the literature relative to the studies on reaching law design. As for the sliding hyperplane design, the eigenvalue assignment methods for the equivalent dynamics matrix have been considered as standard (e.g., see Tang & Misawa [92] and references therein). Apart from those eigenvalue approaches, the parametric approaches utilizing the Lyapunov equation or the Riccati equation have been investigated in some studies. Spurgeon [87] introduced the usage of the Lyapunovmatrix for calculating the sliding hyperplanes. In [45], a Riccati equation is used for the discrete-time sliding mode design for a class of single input systems. Recently, the LQ optimization approach was proposed by Janardhanan & Kariwala [55].
Bijnan Bandyopadhyay, Fulwani Deepak, Kyung-Soo Kim
Backmatter
Metadaten
Titel
Sliding Mode Control Using Novel Sliding Surfaces
verfasst von
Bijnan Bandyopadhyay
Fulwani Deepak
Kyung-Soo Kim
Copyright-Jahr
2009
Verlag
Springer Berlin Heidelberg
Electronic ISBN
978-3-642-03448-0
Print ISBN
978-3-642-03447-3
DOI
https://doi.org/10.1007/978-3-642-03448-0

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