Discrete-Time Sliding Mode Control Using Output Feedback and Nonlinear Surface
01 Jan 2011-pp 381-405
TL;DR: In this chapter, a nonlinear sliding surface is discussed to improve the transient response for general discrete-time multiple input multiple output linear systems with matched perturbations.
Abstract: In this chapter, a nonlinear sliding surface is discussed to improve the transient response for general discrete-time multiple input multiple output linear systems with matched perturbations. The nonlinear surface modulates the closed loop damping ratio from an initial low to final high value to achieve better transient performance. The control law is based on the discrete-time sliding mode equivalent control and thus eliminates chattering. The control law is proposed based on two approaches: (1) reaching law based approach which needs only disturbance bounds and (2) disturbance observer based approach. Multirate output feedback is used to relax the need of the entire state vector for implementation of the control law. A possible extension of the nonlinear surface to input-delay systems is also presented.
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TL;DR: It is shown that this design problem of an output bounded control may be converted into the corresponding attractive ellipsoid “minimization” under some constraints of BMI's (bilinear matrix inequalities) type.
Abstract: This paper deals with designing of robust tracking controllers for a class of nonlinear uncertain discrete-time stochastic systems which are affine with respect to a control action on a bounded energy level. The considered nonlinear dynamics is admitted to be a priori unknown but belonging to the class of the so-called quasi-Lipschitz vector-field. The current states may be unavailable on-line, but the corresponding output vector is assumed to be measured during the process. Both the state dynamics and the output measurements are disturbed by external additive noises which are also supposed to be immeasurable. In this situation any suitable controller can only provide the boundedness of the tracking-error trajectories within a bounded zone with probability one. In this paper we suggest designing of both the control and observer “optimal” gain-matrices minimizing the “size” of the attractive ellipsoid containing all tracking-error trajectories in the vicinity of the origin. It is shown that this design problem of an output bounded control may be converted into the corresponding attractive ellipsoid “minimization” under some constraints of BMI's (bilinear matrix inequalities) type. The application of an adequate coordinate changing transforms these BMI's into a set of LMI's (linear matrix inequalities) that permits to use directly the standard MATLAB-toolbox. Two illustrative examples are considered: the first one concerns a two state—single output stochastic model, and the second one deals with a discrete-time model of electric-magnetic-tape-drive containing the four states-positions and two measured outputs.
7 citations
TL;DR: The suggested approach is illustrated by designing of a robust tracking controller for a benchmark example in the presence of stochastic noises both in the state dynamics and in the output observations.
Abstract: We study the behaviour of stochastic discrete-time models controlled by an output linear feedback during a tracking process. The controlled system is assumed to be nonlinear satisfying the global ‘quasi-Lipschitz’ condition and subjected to stochastic input and output disturbances. Two gain matrices in a feedback and in an observer define an ‘averaged’ ellipsoid in the tracking-error space where all system's trajectories arrive ‘with probability one’. The selection of the ‘best’ gain matrices is realised numerically by application of the robust attractive ellipsoid method with the linear matrix inequality technique application. The suggested approach is illustrated by designing of a robust tracking controller for a benchmark example in the presence of stochastic noises both in the state dynamics and in the output observations.
1 citations
Cites background from "Discrete-Time Sliding Mode Control ..."
...The nominal trajectory which this system have to follow is x n ¼ ½ 0:526 1:4733 0 0 |: ð45Þ The authors in Bijnam and Fulwani (2010) have applied the following ‘sliding-mode equivalent controller’ uðkÞ ¼ ðc|Tr Þ 1 c|ðkþ 1ÞTr LyYk þ c|ðkþ 1ÞTr Luuðkþ 1Þ ~xdðkþ 1Þ : ð46Þ The results of the…...
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...…0 0 0:0007 223:1366 2 6664 3 7775, K ¼ 0:3385 0:0458 , L ¼ 0:001 0:2306 : Example 2: Now let us consider the problem of magnetic tape position tracking as described in Bijnam and Fulwani (2010) and Franklin, Powell, and Workman (1997) dealing with a nonlinear version of the mathematical model....
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References
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TL;DR: Design and analysis forVariable structure systems are surveyed in this paper and it is shown that advantageous properties result from changing structures according to this switching logic.
Abstract: Variable structure systems consist of a set of continuous subsystems together with suitable switching logic. Advantageous properties result from changing structures according to this switching logic. Design and analysis for this class of systems are surveyed in this paper.
5,076 citations
Book•
01 Jan 1980
TL;DR: This well-respected, market-leading text discusses the use of digital computers in the real-time control of dynamic systems and thoroughly integrates MATLAB statements and problems to offer readers a complete design picture.
Abstract: From the Publisher:
This well-respected, market-leading text discusses the use of digital computers in the real-time control of dynamic systems The emphasis is on the design of digital controls that achieve good dynamic response and small errors while using signals that are sampled in time and quantized in amplitude Both classical and modern control methods are described and applied to illustrative examples The strengths and limitations of each method are explored to help the reader develop solid designs with the least effort Two new chapters have been added to the third edition offering a review of feedback control systems and an overview of digital control systems Updated to be fully compatible with MATLAB versions 4 and 5, the text thoroughly integrates MATLAB statements and problems to offer readers a complete design picture The new edition contains up-to-date material on state-space design and twice as many end-of-chapter problems to give students more opportunities to practice the material
3,756 citations
Book•
01 Jan 1999
TL;DR: Sliding mode control (SMC) is gaining increasing importance as a universal design tool for the robust control of linear and nonlinear systems as mentioned in this paper, and is particularly useful for electro-mechanical systems because of its discontinuous structure.
Abstract: Sliding Mode Control (SMC) is gaining increasing importance as a universal design tool for the robust control of linear and nonlinear systems. The strengths of sliding mode controllers result from the ease and flexibility of the methodology for their design and implementation. They provide inherent order reduction, direct incorporation of robustness against system uncertainties and disturbances, and an implicit stability proof. They also allow for the design of high performance control systems at low costs. SMC is particularly useful for electro-mechanical systems because of its discontinuous structure. In fact, since the hardware of many electro-mechanical systems (such as electric motors) prescribes discontinuous inputs, SMC has become the natural choice for direct implementation. The book is intended primarily for engineers and establishes an interdisciplinary bridge between control science, electrical and mechanical engineering.
2,593 citations
TL;DR: An accurate assessment of the so-called chattering phenomenon is offered, which catalogs implementable sliding mode control design solutions, and provides a frame of reference for future sliding Mode control research.
Abstract: Presents a guide to sliding mode control for practicing control engineers. It offers an accurate assessment of the so-called chattering phenomenon, catalogs implementable sliding mode control design solutions, and provides a frame of reference for future sliding mode control research.
2,082 citations
TL;DR: This paper presents a treatment of discrete variable structure control systems, and a recently introduced "reaching law approach" is conveniently used to develop the control law for robust control.
Abstract: This paper presents a treatment of discrete variable structure control systems. The purpose is to lay a foundation upon which design of such type of systems can be made properly. Phenomena of switching, reaching, and quasi-sliding mode are investigated thoroughly. Terms pertaining to discrete variable structure control are defined. A method of quasi-sliding mode design is given. The inherently existing quasi-sliding mode band is analyzed. A recently introduced "reaching law approach" is conveniently used to develop the control law for robust control. Comments are given regarding chattering. The design technique is illustrated by a simulated system. >
1,428 citations