Comparison of Controllers for Active Vibration Control of a Plate with Piezo-Patches As Sensors/Actuators
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Special Issue - 2015 International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 NCETEMS-2015 Conference Proceedings Comparison of Controllers for Active Vibration Control of A Plate with Piezo-Patches as Sensors/Actuators Neeraj Sehgal1 1Department of Mechanical Engineering, Ganga Institute of Technology and Management, Kablana, Jhajjar, Haryana, India Abstract:-- This work is aimed at the comparative study of p= relative to the plate structure classical controllers such as PID controllers and new s = relative to the sensor controllers (LQG and H∞ controllers) which are employed for sa = relative to the sensed voltage in the actuator the active vibration control of a cantilever plate with x = relative to x direction piezoelectric patches as sensors and actuators. These y= relative to y direction controllers are working for the purpose of vibration qq = relative to the stiffness suppression over the plate. The cantilever plate is embedded qΦ = relative to the piezoelectric stiffness with piezoelectric patches which are acting as actuators and ΦΦ = relative to the dielectric stiffness sensors. The position of patches may be collocated or non- Superscripts collocated depending upon the controller type. A comparison e = relative to the element among the PID, LQG and H∞ controllers for the same pupose S = relative to constant strain has been carried out. T = matrix transpose I. INTRODUCTION Keywords: PID, LQG, H∞, cantilever plate, piezoelectric patches, active vibration control. Active vibration control is the technique in which equal Nomenclature: and opposite force is applied to suppress the external vibrations. Industrial processes which are precise cannot a = half length of the finite element in x direction, m occur due to vibrations. Control of such vibrations is A = relative to surface area always being a field of curiosity for researchers. Today, b = half length of the finite element in y direction, m C = elastic constant, N/m2 there are different controllers which are employed for the Cs = piezoelectric sensor capacitance, F vibration suppuration such as Proportional integrative D = electric displacement vector, C/m2 differentiate, Linear quadratic Gaussian, Linear quadratic e = piezoeletric stress coefficient, C/m2 regulator and H∞ controllers etc. E = Young’s modulus, N/m2 f = force, N h = thickness, m K = stiffness matrix M = mass matrix q = displacement field vector qi = nodal displacement field, m k = kinetic energy, J Fig.1. Schematic diagram for Active Vibration Control u = displacement field in x direction, m Caruso G. et al.[1] studied the vibration control of an U = potential energy, J elastic cantilever plate, clamped on one side and excited by v = displacement field in y direction, m V = volume, m3 impulsive force acting on the free side. A modal model w = displacement field in z direction, m obtained by employing a suitable finite-element W = work, J formulation together with a modal reduction, was used in Greek Symbols the controller design. Qiu Z. C. et al.[2] used piezoelectric ε = strain field ceramics patches as sensors and actuators to control the σ = stress, N/m vibration of the smart flexible clamped plate. A method for ν = Poisson ratio optimal placement of piezoelectric actuators and sensors on θu = rotation about u-axis a cantilever plate was developed. Experimental set-up was ξ = dielectric tensor build for smart plate and results were found on it. C.M.A. ζ = nodal displacement vector Φ = electric potential, Volts Vasques[3] presented a comparative study between the ω = frequency, rad/s classical control strategies, amplitude velocity feedback ρ = material density, kg/m3 and constant gain, and optimal control strategies, linear Subscripts quadratic regulator (LQR) and linear quadratic Gaussian a = refers to the actuator (LQG) controller, is performed in order to investigate their b = relative to the body Volume 3, Issue 10 Published by, www.ijert.org 1 Special Issue - 2015 International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 NCETEMS-2015 Conference Proceedings effectiveness to diminish vibrations in beams with controller, while noise reduction and collocation of patches piezoelectric patches acting as sensors or actuators. is another requirement for LQG and H controller Vasudevan et. al.[4] showed the optimal control strategy respectively. By using MATLAB, a comparison among based on the full state dynamic observer to control these three controllers has been done by plotting graphs for vibrations of a beam under limited magnetic field intensity. different optimal positions of piezoelectric patches for PID and LQR based on full state observer can reduce respective controllers have been drawn. And a comparison settling time and tip deflection response of free vibration by these plots is discussed. oscillations. Shimon P. et al.[5] presented an efficient II. PID CONTROLLER: controller for vibration control in a fully clamped plate and an experiment between control methodologies and A. A proportional-integral-derivative controller (PID actuators was done. Theoretical and experimental studies controller): were undertaken with verifying results. Chhabra et. A proportional-integral-derivative controller (PID al.[6][7] presented the active vibration control of beam like controller) is a control loop feedback structures with laminated piezoelectric sensor and actuator mechanism (controller) widely used in vibration control layers bonded on top and bottom surfaces of the beam. The contribution of the piezoelectric sensor and actuator layers techniques. A PID controller calculates an error value as on the mass and stiffness of the beam has been considered the difference between a measured process variable and a desired set point value. Manipulated variable is used to with modeling of the structure in a state space form. The minimize the error by adjusting the process. The PID designing of state/output feedback control by Pole controller algorithm involves three separate constant placement technique and LQR optimal control approach parameters: the proportional, are exercised to achieve the desired control. Feedback Gain was find out by using Hybrid Multiobjective Genetic the integral and derivative values, Algorithm-Artificial Neural Network. Pradeep et.al.[8][9] denoted P, I, and D. Simply put, these values can be interpreted in terms of time: P depends on presented the work deals with the mathematical the present error, I on the accumulation of past errors, formulation and the computational model for vibration and D is a prediction of future errors, based on current rate control of a beam with piezoelectric smart structures. A successful scheme of analyzing and designing piezoelectric of change. The response of the controller can be explained smart structures with control laws is developed. Mukherjee in terms of the responsiveness of the controller to an error, the degree to which the controller overshoots the set point, A. et al.[10] studied the active vibration control of stiffened and the degree of system oscillation.( Neeraj et. al.[16]) plates. The stiffened plate was formulated with finite element and piezoelectric effects. A velocity feedback algorithm was employed. Numerical examples for vibration control of isotropic and orthotropic stiffened plates were presented. Chhabra et. al.[11] showed that active vibration control of beam like structures with distributed piezoelectric actuator and sensor layers bonded on top and bottom surfaces of the beam. The control effect can be improved by locating the patches optimally. The Fig.2: Block Diagram of PID controller piezoelectric patches are placed on the free end, middle end and fixed end. The study is done through simulation in B. PID Controller Theory: MATLAB for various controllers like POF, PID and Pole The PID controller is named after its three correcting Placement technique. Varun et. al.[12] studied the active terms, whose sum constitutes the manipulated variable vibration control in the cantilever beam with collocated (MV). The proportional, integral, and derivative terms are sensors/actuators by using fuzzy controller. Amit et. al. summed to calculate the output of the PID controller. [13] studied the basic techniques for analysis of active vibration control using piezoelectric sensor and actuator. A Defining as the controller output, the final form of smart cantilever plate with the Neural Network and LQG the PID algorithm is: controller is developed. Neeraj et. al.[14] presented various ( ) ( ) ( ) optimization techniques which for the optimal placement of 푢 푡 = 푀푉 푡 = 퐾푝푒 푡 + 푡 푑 piezoelectric sensors/actuators on a smart structure for 퐾 ∫ 푒(휏)푑휏 + 퐾 푒(푡) 푖 0 푑 푑푡 active vibration control. And also how these optimization techniques can be implemented is studied. Meta-heuristic where approaches such as Genetic algorithms, swarm intelligence, Kp: Proportional gain, a tuning parameter simulated annealing, tabu search, and other recent approaches are explained. Ki: Integral gain, a tuning parameter In this paper, different controllers used in active vibration Kd: Derivative gain, a tuning parameter control are stated. Classical controller like PID and new e: Error = SP- PV controllers like LQG and H∞ controllers with their formulations are explained. The terms like proportional, t: Time or instantaneous time (the present) integrate and derivative are taken as parameters in PID Volume 3, Issue 10 Published by, www.ijert.org 2 Special Issue - 2015 International Journal of Engineering Research