precision control of smart actuators such as piezoelectric actuators is a challenging problem. The major part of research work reported has been concentrated on ...
A robust adaptive control for micropositioning of piezoelectric actuators with environment force estimation HGhafarirad, SM Rezaei, M Zareinejad and M Hamdi Piezoelectric actuators are widely used for fine positioning because of their specific properties such as high resolution, natural frequency and frequency response (Putra, 2008), but precision control of smart actuators such as piezoelectric actuators is a challenging problem. The major part of research work reported has been concentrated on the hysteresis nonlinearity effect. There are different approaches considered for position control in free and constrained motions. Preisach (Hughes and Wen, 1997), Krasnosel’skii– Pokrovskii (Krasnoselskii and Pokrovskii, 1989), Prandtl– Ishlinskii (Brokate and Sprekels, 1996), Duhem (Visintin, 1994) and Bouc–Wen (Ang et al., 2007) models have been proposed for identification of hysteresis effects. Applying the inverse hysteresis models as a feedforward compensator, position control of such actuators is carried out (GarciaValdovinos et al., 2007). Several methods have also been suggested for free motion micro-positioning control. Impedance control (Garcia-Valdovinos et al., 2007), sliding mode control (Bashash and Jalili, 2007) and robust control coupled with adaptive approaches (Bashash and Jalili, 2009; Li and Xu, 2009) have been derived in such a case. The main restriction is the assumption that full states of the actuator such as position and velocity are available, but in fact, the only measurable state is position. A challenging control problem appears when contact with the environment occurs and an external force is presented. The induced environmental forces could disarrange the positioning and the control structure, but in piezoelectric actuators, these forces have an extra undesired effect too. The external forces could generate a reverse induced voltage that has also a hysteretic behaviour. This voltage could interfere with the actuator activation voltage. Therefore, a backward hysteresis effect (BHE) has a role of an extra perturbation in the system.
Small forces in micromanipulation pose a challenge on the design and construction of sensors that can provide measurements with high resolution and accuracy (Zhe, 2008). Instead of expensive force sensors, estimation algorithms for contact forces have been widely developed. Different approaches have been reported for the disturbance estimation. Considering the error in the actuator position estimation with a linear observer, Alcocera et al. (2003) presented an external force estimation approach based on the estimation error. Also, Abidi et al. (2004) proposed an observer based on a similarity in dynamics of the system and observer. A new force estimation method by eliminating the system uncertainties effect has been introduced by Bhattacharjee et al. (Bhattacharjee et al., 2008; Son et al., 2010). However, the mentioned approaches have not taken into account any dynamic error for the proposed observers. This means that the stability of the observer and controller should be proved separately. As a result, stability of the overall system and controller structure in the presence of estimated forces could not be analytically proved. Daly et al. (Daly and Wang, 2009a; Daly, 2010) proposed a sliding-based disturbance observer with the consideration of the error dynamic. The major problem is that all the external forces and perturbations are observed together. In this paper, a generalized Prandtl–Ishlinskii model and its inverse is utilized for identification and online feedforward compensation of hysteresis. This leads to the actuator dynamic model being transformed to the second-order linear dynamic model. Considering the BHE, parametric uncertainties, PI estimation error and probably unmodelled dynamics, a variable structure controller is proposed for trajectory tracking. A sliding-based observer would estimate full states from the only measurable position trajectory. An adaptive perturbation estimation approach is proposed to estimate pure external forces separately. The stability of the controller in the presence of estimated states and the environment force is demonstrated with the Lyapunov criterion. Finally, experimental results demonstrate that the proposed controller achieves precise trajectory tracking and good external force estimation.
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