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Improving Delay-Margin of Noncollocated Vibration Control of Piezo-Actuated Flexible Beams via a Fractional-Order Controller

DOI: 10.1155/2014/809173

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Abstract:

Noncollocated control of flexible structures results in nonminimum-phase systems because the separation between the actuator and the sensor creates an input-output delay. The delay can deteriorate stability of closed-loop systems. This paper presents a simple approach to improve the delay-margin of the noncollocated vibration control of piezo-actuated flexible beams using a fractional-order controller. Results of real life experiments illustrate efficiency of the controller and show that the fractional-order controller has better stability robustness than the integer-order controller. 1. Introduction Flexible structures have attracted increasing attentions for many applications because of their weights and production costs. However, the flexibility leads to unwanted vibration problems. Thus, vibration control is usually needed. Over the past few decades, active vibration control has drawn more interest from researchers since it can effectively suppress the vibration [1, 2]. A large part of the active vibration control research has used piezoelectric materials for actuation and sensing. Advantages of using piezo-actuators/sensors include nanometer scale resolution, high stiffness, and fast response. Piezo-actuators have been proven to be useful in suppressing structural vibration [3, 4]. Stabilization of flexible structures can be easily done by collocating the sensors and the actuators. However, the collocated control configuration is not always feasible in practice and its performance is not always satisfactory. Thus, noncollocated control has been investigated [5, 6]. However, noncollocated control results in a nonminimum-phase closed-loop system because the separation between the actuator and the sensor creates an input-output delay, which can deteriorate stability of the closed-loop system. Fractional calculus is a 300-year-old mathematical topic [7, 8]. However, its practical applications have just recently been explored. Recently, fractional-order control has been attracting interest. It has been illustrated that fractional-order controllers yield superior performance to integer-order controllers [9, 10]. This paper presents a simple approach to improve the delay-margin of the noncollocated vibration control of piezo-actuated flexible beams using a fractional-order proportional-integral-derivative (PID) controller. The rest of the paper is organized as follows. Section 2 provides some preliminaries. Section 3 describes the piezo-actuated flexible beam that is used as an experimental test bench. Section 4 presents a finite element model of the

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