Operator-Based Robust Nonlinear Free Vibration Control of a Flexible Plate With Unknown Input Nonlinearity

In this paper,a robust nonlinear free vibration control design using an operator based robust right coprime factorization approach is considered for a flexible plate with unknown input nonlinearity.With considering the effect of unknown input nonlinearity from the piezoelectric actuator,operator based controllers are designed to guarantee the robust stability of the nonlinear free vibration control system.Simultaneously,for ensuring the desired tracking performance and reducing the effect of unknown input nonlinearity,operator based tracking compensator and estimation structure are given,respectively.Finally,both simulation and experimental results are shown to verify the effectiveness of the proposed control scheme.

Passive robust control for uncertain Hamiltonian systems by using operator theory

In this study,the passivity-based robust control and tracking for Hamiltonian systems with unknown perturbations by using the operator-based robust right coprime factorisation method is concerned.For the system with unknown perturbations,a design scheme is proposed to guarantee the uncertain non-linear systems to be robustly stable while the equivalent non-linear systems is passive,meanwhile the asymptotic tracking property of the plant output is discussed.Moreover,the design scheme can be also used into the general Hamiltonian systems while the simulation is used to further demonstrate the effectiveness of the proposed method.

Robust Stability of Nonlinear Plants with a Non-symmetric Prandtl-Ishlinskii Hysteresis Model

In this paper, robust stability of nonlinear plants represented by non-symmetric Prandtl-Ishlinskii （PI） hysteresis model is studied. In general, PI hysteresis model is the weighted superposition of play or stop hysteresis operators, and the slopes of the operators are considered to be the same. In order to make a hysteresis model, a modified form of non-symmetric play hysteresis operator with unknown slopes is given. The hysteresis model is described by a generalized Lipschitz operator term and a bounded parasitic term. Since the generalized Lipschitz operator is unknown, a new condition using robust right coprime factorization is proposed to guarantee robust stability of the controlled plant with the hysteresis nonlinearity. As a result, based on the proposed robust condition, a stabilized plant is obtained. A numerical example is presented to validate the effectiveness of the proposed method.

THE DISCUSSION ON ALGEBRAIC PROPERTIESOF POLYNOMIAL MATRICES

By using the results about polynomial matrix in the system and control theory. this paper gives some discussions about the algebraic properties of polynomial,matrices. The obtained main results include that the,ring of rr x n polynomial matrices is a principal ideal and principal one-sided ideal ring.

Fully Actuated System Approach for Linear Systems Control:A Frequency-Domain Solution

This note studies fully actuated linear systems in the frequency domain in terms of polynomial matrix description(PMD).For a controllable first-order linear state-space system model,by using the right coprime factorization of its transfer function matrix,under the condition that the denominator matrix in the right coprime factorization is column reduced,it is equivalently transformed into a fully actuated PMD model,whose time-domain expression is just a high-order fully actuated(HOFA)system model.This method is a supplement to the previous one in the time-domain,and reveals a connection between the controllability of the first-order linear state-space system model and the fullactuation of its PMD model.Both continuous-time and discrete-time linear systems are considered.Some numerical examples are worked out to illustrate the effectiveness of the proposed approaches.

An Operator-based Nonlinear Vibration Control System Using a Flexible Arm with Shape Memory Alloy

In the past,arms used in the fields of industry and robotics have been designed not to vibrate by increasing their mass and stiffness.The weight of arms has tended to be reduced to improve speed of operation,and decrease the cost of their production.Since the weight saving makes the arms lose their stiffness and therefore vibrate more easily,the vibration suppression control is needed for realizing the above purpose.Incidentally,the use of various smart materials in actuators has grown.In particular,a shape memory alloy(SMA)is applied widely and has several advantages:light weight,large displacement by temperature change,and large force to mass ratio.However,the SMA actuators possess hysteresis nonlinearity between their own temperature and displacement obtained by the temperature.The hysteretic behavior of the SMA actuators affects their control performance.In previous research,an operator-based control system including a hysteresis compensator has been proposed.The vibration of a flexible arm is dealt with as the controlled object;one end of the arm is clamped and the other end is free.The effectiveness of the hysteresis compensator has been confirmed by simulations and experiments.Nevertheless,the feedback signal of the previous designed system has increased exponentially.It is difficult to use the system in the long-term because of the phenomenon.Additionally,the SMA actuator generates and radiates heat because electric current passing through the SMA actuator provides heat,and strain on the SMA actuator is generated.With long-time use of the SMA actuator,the environmental temperature around the SMA actuator varies through radiation of the heat.There exists a risk that the ambient temperature change dealt with as disturbance affects the temperature and strain of the SMA actuator.In this research,a design method of the operator-based control system is proposed considering the long-term use of the system.In the method,the hysteresis characteristics of the SMA actuator and the temperature change around the actuator are considered.The effectiveness of the proposed method is verified by simulations and experiments.