Nonlinear average passivity and stabilizing controllers in discrete time (original) (raw)
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The feedback passivity problem in nonlinear discrete-time systems is examined in this paper. The characteristics of the relative degree and zero dynamics of the nonpassive system are related to its feedback passivity property. The main contribution is the study of the relative degree properties of single-input single-output (SISO) passive systems in general form, and the use of them in the proposal of sufficient conditions to render this class of systems passive by means of a static state feedback control law. Some notes, based on previous results, referring the feedback passivity problem of multipleinput multiple-output (MIMO) nonlinear systems which are affine in the input are also given.
Feedback passivity of nonlinear discrete-time systems with direct input-output link
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This paper is devoted to the study of the feedback passivity property in nonlinear discrete-time systems. The relative degree and zero dynamics of the non-passive system are related to the feedback passivity of the system. Two main results are presented. First, some relative degreerelated properties of passive systems in general form are stated. Second, sufficient conditions in order to render a multiple-input multiple-output (MIMO) system passive by means of a static state feedback control law are obtained.
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Recent publications have shown that under some conditions continuous linear time-invariant systems become strictly positive real with constant feedback. This paper expands the applicability of this result to discrete linear systems. The paper shows the sufficient conditions that allow a discrete system to become stable and strictly passive via static (constant or nonstationary) output feedback.
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From passivity under sampling to a new discrete-time passivity concept
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IET Control Theory & Applications, 2010
The stability and control of systems possessing passivity violations is considered. The authors seek to exploit the finite gain characteristics of a plant over a range in which a passive mapping no longer exists while implementing a similar hybrid passive and finite gain controller. Using the dissipative systems framework the authors define a hybrid system: one which possesses a passive map, and finite gain characteristics when the passive map is destroyed. The definition of a hybrid system utilises a switching parameter to break the system into passive and finite gain regions. It is shown that this switching parameter is equivalent to an ideal lowpass filter and can be approximated by a Butterworth filter. The stability of two hybrid systems within a negative feedback interconnection is also considered. A hybrid passivity and finite gain stability theorem is developed using both Lyapunov and input -output techniques, which yield equivalent results. Sufficient conditions for the closed-loop system to be stable are presented, which resemble an amalgamation of the traditional passivity and small-gain theorems.
A remark on passivity-based and discontinuous control of uncertain nonlinear systems
Automatica, 2001
We address the problem of robust stabilisation of nonlinear systems a!ected by time-varying uniformly bounded (in time) a$ne perturbations. Our approach relies on the combination of sliding mode techniques and passivity-based control. Roughly speaking we show that under suitable conditions the sliding mode variable can be chosen as the passive output of the perturbed system. Then we show how to construct a controller which guarantees the global uniform convergence of the plant's outputs towards a time-varying desired reference, even in the presence of permanently exciting time-varying disturbances. We illustrate our result on the tracking control of the van der Pol oscillator.
Stability Guaranteed Control: Time Domain Passivity Approach
IEEE Transactions on Control Systems Technology, 2004
A general framework for expanding the time-domain passivity control approach [12], [24] to large classes of control systems is proposed. We show that large classes of control systems can be described from a network point of view. Based on the network presentation, the large classes of control systems are analyzed in a unified framework. In this unified network model, we define "virtual input energy," which is a virtual source of energy for control, and "real output energy" that is physically transferred to a plant to allow the concept of passivity to be used to study the stability of large classes of control systems. For guaranteeing the stability condition, the time-domain passivity controller for two-port [24] is applied. Design procedure is demonstrated for a motion control system. The developed method is tested with numerical simulation in the regulation of a single link flexible manipulator. Totally stable control is achieved under wide variety of operating condition and uncertainties without any model information.