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Research Papers

Efficient Active Vibration Control of Smart Structures With Modified Positive Position Feedback Control Using Pattern Search Methods in the Presence of Instrumentation Phase Lead and Lag

[+] Author and Article Information
Rajiv Kumar

Director
Rayat Bahra College of Engineering and Nano
Technology for Women,
Hoshiarpur, Punjab 146104, India
e-mail: rkvashishat@yahoo.com

Contributed by the Dynamic Systems Division of ASME for publication in the Journal of Dynamic Systems, Measurement, and Control. Manuscript received December 19, 2011; final manuscript received April 13, 2013; published online July 19, 2013. Assoc. Editor: Nabil Chalhoub.

J. Dyn. Sys., Meas., Control 135(6), 061001 (Jul 19, 2013) (12 pages) Paper No: DS-11-1395; doi: 10.1115/1.4024603 History: Received December 19, 2011; Revised April 13, 2013

For active vibration control applications, positive position feedback (PPF) type controller is quite suitable. These controllers are of low order so are easy to implement in practice. These controllers avoid the problem of control spillover also. However, a systematic design methodology is not available for the design of these controllers. For multimode vibration control applications, in the presence of instrumentation, controller design becomes even more difficult. In the present paper, a systematic design procedure has been suggested to design the PPF controller. The proposed controller is designed by minimizing the H2 or H norm of the closed loop (CL) system. The direct search methods based on pattern search technique has been used. The controller designed in this way can provide uniform damping to all the modes. The problems caused by the instrumentation (i.e., phase lead and lag) and time delay actually present in the control loop can be completely eliminated. Since, the controller is designed by minimizing the H norm of the closed loop system, it is robust in nature. With the proposed methodology, the use of other complicated frequency domain techniques to design the controller can be avoided.

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Figures

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Fig. 1

Geometry of the flexible beam with PZT actuator and PVDF sensor

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Fig. 2

Effect of feed-through term on the FRF of the flexible beam

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Fig. 3

Schematic for experimental setup for system identification

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Fig. 4

Comparison of “FEM” and “Experimental” results

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Fig. 5

Block diagram of PPF control: (a) block diagram of simple PPF control and (b) block diagram of efficient PPF control

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Fig. 6

Block diagram of lead/lag compensator circuit

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Fig. 7

(a) Flow chart for efficient PPF controller design (compact) and (b) flow chart for efficient PPF controller design (detailed)

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Fig. 8

Frequency response function of the system with GA based optimal PPF controller (type-I and type-II)

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Fig. 9

Frequency response function of the system (with LP and HP filters) using PS based optimal PPF controllers designed without considering the filters in the loop (type-I and type-II)

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Fig. 10

Effect of considering the filters and system delay in the design of PS based optimal PPF controllers

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Fig. 11

Frequency response function of the open and closed loop system using various types of PS based optimal PPF controllers along with compensator (with filters and system delay in the system)

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Fig. 12

Effect of system delay from 1 ms to 10 ms on the closed loop system with PS based optimal controller (type-II) (close up for the second mode)

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Fig. 13

Simulations based time domain response of the open and closed loop system with PS based optimal

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Fig. 14

Transfer function for compensation circuits for various types PPF controllers

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Fig. 15

Open and closed loop response using PPF control with H norm minimization

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Fig. 16

Schematic of experimental setup

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Fig. 17

Experimental time domain response of the open and closed loop system with digitized PS based optimal PPF controller (type-II), digitized at 1.3 kHz (with and without compensator)

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Fig. 18

Experimental time domain response of the open and closed loop system with digitized PS based optimal PPF controller (type-III), digitized at 1.3 kHz for a random force applied at the free end

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