Sliding mode based piezoelectric actuator control

In this paper a control of method for a piezoelectric stack actuator control is proposed. In addition briefly the usage of the same methods for estimation of external force acting to the actuator in contact with environment is discussed. The method uses sliding mode framework to design both the observer and the controller based on an electromechanical lumped model of the piezoelectric actuator. Furthermore, using a nonlinear differential equation the internal hysteresis disturbance is removed from the total disturbance in an attempt to estimate the external force acting on the actuator. It is then possible to use this external force estimate as a means of force control of the actuator. Simulation and experiments are compared for validating the disturbance and external force estimation technique. Some experiments that incorporate disturbance compensation in a closed-loop SMC control algorithm are also presented to prove the effectiveness of this method in producing high precision motion

Sliding mode control based piezoelectric actuator control

In this paper a method for piezoelectric stack actuator control is proposed. In addition a brief discussion about the usage of the same methods for estimation of external force acting to the actuator in contact with environment is made. The method uses sliding mode framework to design both the observer and the controller based on an electromechanical lumped model of the piezoelectric actuator. Furthermore, using a nonlinear differential equation the internal hysteresis disturbance is removed from the total disturbance in an attempt to estimate the external force acting on the actuator. It is then possible to use this external force estimate as a means of force control of the actuator. Simulation and experiments are compared for validating the disturbance and external force estimation technique. Some experiments that incorporate disturbance compensation in a closed-loop SMC control algorithm are also presented to prove the effectiveness of this method in producing high precision motion

A study on high accuracy discrete-time sliding mode control

In this paper a Discrete-Time Sliding-Mode based controller design for high accuracy motion control systems is presented. The controller is designed for a general SISO system with nonlinearity and external disturbance. Closed-Loop behavior of the general system with the proposed control and Lyapunov stability is shown and the error of the closed loop system is proven to be within an o(T2). The proposed controller is applied to a stage driven by a piezo drive that is known to suffer from hysteresis nonlinearity in the control gain. Proposed SMC controller is proven to offer chattering-free motion and rejection of the disturbances represented by hysteresis and the time variation of the piezo drive parameters. As a separate idea to enhance the accuracy of the closed loop system a combination of disturbance rejection method and the SMC controller is explored and its effectiveness is experimentally demonstrated. Closed-loop experiments are presented using PID controller with and without disturbance compensation and Sliding-Mode Controller with and without disturbance compensation for the purpose of comparison

Continuous time controller based on SMC and disturbance observer for piezoelectric actuators

Abstract – In this work, analog application for the Sliding Mode Control (SMC) to piezoelectric actuators (PEA) is presented. DSP application of the algorithm suffers from ADC and DAC conversions and mainly faces limitations in sampling time interval. Moreover piezoelectric actuators are known to have very large bandwidth close to the DSP operation frequency. Therefore, with the direct analog application, improvement of the performance and high frequency operation are expected. Design of an appropriate SMC together with a disturbance observer is suggested to have continuous control output and related experimental results for position tracking are presented with comparison of DSP and analog control application

Modeling and Control of Piezoelectric Actuators

Piezoelectric actuators (PEAs) utilize the inverse piezoelectric effect to generate fine displacement with a resolution down to sub-nanometers and as such, they have been widely used in various micro- and nanopositioning applications. However, the modeling and control of PEAs have proven to be challenging tasks. The main difficulties lie in the existence of various nonlinear or difficult-to-model effects in PEAs, such as hysteresis, creep, and distributive vibration dynamics. Such effects can seriously degrade the PEA tracking control performances or even lead to instability. This raises a great need to model and control PEAs for improved performance. This research is aimed at developing novel models for PEAs and on this basis, developing model-based control schemes for the PEA tracking control taking into account the aforementioned nonlinear effects. In the first part of this research, a model of a PEA for the effects of hysteresis, creep, and vibration dynamics was developed. Notably, the widely-used Preisach hysteresis model cannot represent the one-sided hysteresis of PEAs. To overcome this shortcoming, a rate-independent hysteresis model based on a novel hysteresis operator modified from the Preisach hysteresis operator was developed, which was then integrated with the models of creep and vibration dynamics to form a comprehensive model for PEAs. For its validation, experiments were carried out on a commercially-available PEA and the results obtained agreed with those from model simulations. By taking into account the linear dynamics and hysteretic behavior of the PEA as well as the presliding friction between the moveable platform and the end-effector, a model of the piezoelectric-driven stick-slip (PDSS) actuator was also developed in the first part of the research. The effectiveness of the developed model was illustrated by the experiments on the PDSS actuator prototyped in the author's lab. In the second part of the research, control schemes were developed based on the aforementioned PEA models for tracking control of PEAs. Firstly, a novel PID-based sliding mode (PIDSM) controller was developed. The rational behind the use of a sliding mode (SM) control is that the SM control can effectively suppress the effects of matched uncertainties, while the PEA hysteresis, creep, and external load can be represented by a lumped matched uncertainty based on the developed model. To solve the chattering and steady-state problems, associated with the ideal SM control and the SM control with boundary layer (SMCBL), the novel PIDSM control developed in the present study replaces the switching control term in the ideal SM control schemes with a PID regulator. Experiments were carried out on a commercially-available PEA and the results obtained illustrate the effectiveness of the PIDSM controller, and its superiorities over other schemes of PID control, ideal SM control, and the SMCBL in terms of steady state error elimination, chattering suppression, and tracking error suppression. Secondly, a PIDSM observer was also developed based on the model of PEAs to provide the PIDSM controller with state estimates of the PEA. And the PIDSM controller and the PIDSM observer were combined to form an integrated control scheme (PIDSM observer-controller or PIDSMOC) for PEAs. The effectiveness of the PIDSM observer and the PIDSMOC were also validated experimentally. The superiority of the PIDSMOC over the PIDSM controller with σ-β filter control scheme was also analyzed and demonstrated experimentally. The significance of this research lies in the development of novel models for PEAs and PDSS actuators, which can be of great help in the design and control of such actuators. Also, the development of the PIDSM controller, the PIDSM observer, and their integrated form, i.e., PIDSMOC, enables the improved performance of tracking control of PEAs with the presence of various nonlinear or difficult-to-model effects