Ruiyue Ouyang

Stability of systems with the Duhem hysteresis operator

In this paper, we discuss the dissipativity property of the counterclockwise Duhem operator. Sufficient conditions on the functions which define the Duhem operator are given such that the Duhem operator has counterclockwise input-output dynamics. In particular, an explicit construction of the storage functions satisfying the counterclockwise dissipation inequality is given. The constructed storage function is also related to the underlying anhysteresis function which is commonly used to describe hysteresis in magnetic materials. The results can thus facilitate analysis of systems with the counterclockwise Duhem operator via the dissipativity approach.

On the characterization of the Duhem hysteresis operator with clockwise input–output dynamics

Abstract In this paper we investigate the dissipativity property of a certain class of Duhem hysteresis operator, which has clockwise (CW) input–output (I/O) behavior. In particular, we provide sufficient conditions on the Duhem operator such that it is CW and propose an explicit construction of the corresponding function satisfying dissipation inequality of CW systems. The result is used to analyze the stability of a second order system with hysteretic friction which is described by a Dahl model.

Absolute stability analysis of linear systems with Duhem hysteresis operator

In this paper, we investigate the stability of positive and negative feedback interconnections of a linear system and a Duhem hysteresis operator. We provide sufficient conditions on the linear plant and on the Duhem operator which are based on the counterclockwise (CCW) or clockwise (CW) input-output property of the plant and hysteresis operator. We show the application of our main result in the design of a linear controller to stabilize a simple mechanical system driven by a hysteretic actuator, such as, piezo-actuator or smart material-based actuator.

Dissipativity of general Duhem hysteresis models

In this paper, we discuss the dissipativity property of Duhem hysteresis models. Under some sufficient conditions on the functions which defines the Duhem model, an explicit construction of the storage functions is given which takes into account the data on the anhysteresis function. We present an example on the semi-linear Duhem model.

PD control of a second-order system with hysteretic actuator

In this paper, we design a proportional and derivative (PD) controller for a mass-damper-spring system interconnected with a hysteretic actuator, such as, the piezo-actuated stage. The hysteretic actuator is assumed to have a counterclockwise (CCW) input-output (I/O) dynamics (e.g. piezo-actuator) and is modeled by a Duhem operator. Based on the CCW of the hysteretic actuator, we provide sufficient conditions on the controller gains that depend on known intervals where the plant and hysteresis parameters lie such that the velocity of the linear plant converges to the origin. Robustness analysis and experimental results for tracking a constant reference velocity are also presented.

On the robustness of hysteretic second-order systems with PID: iISS approach

In this paper, we study the robustness property of a second-order linear plant controlled by a proportional, integral and derivative (PID) controller with a hysteretic actuator. The hysteretic actuator is modeled by a Duhem model that exhibits clockwise (CW) input-output (I/O) dynamics (such as the Dahl model, LuGre model and Maxwell-Slip model, which describe hysteresis phenomena in mechanical friction). Based on our main result, we provide sufficient conditions on the controller gains that depend on the plant parameters such that the origin of the plant and the state of the hysteresis is globally attractive. The robustness of the closed-loop system with respect to the measurement noise is also given, using the integral input-to-state stability (iISS) concept. The applicability of the robustness analysis in the design of state observer for such systems is shown in the simulation.

Stability analysis and controller design for a linear system with Duhem hysteresis nonlinearity

In this paper, we investigate the stability of feedback interconnections between a linear system and a Duhem hysteresis operator, where the linear system satisfies either counter-clockwise (CCW) or clockwise (CW) input-output dynamics [1], [13]. More precisely, depending on the input-output dynamics of each system, we present sufficient conditions on the linear system that guarantee the stability of the closed-loop systems. Based on these results we introduce a control design methodology for stabilizing a linear plant with a counterclockwise Duhem hysteresis operator.

Controller Design for Automatic Micro-assembly Systems Under the Influence of Surface Forces, Hysteresis and Quantizer

Abstract In this paper, we design nonlinear controllers for micro-magnetic levitation systems. The controller takes into account the influence of the surface forces and hysteresis/quantizer. We show the exponential convergence of the error signal and its time derivative to a compact set, which is determined by the uncertainty in the hysteresis and in the quantizer.