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ISA Transactions 51 (2012) 834–840

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ISA Transactions
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F. Hong, C.K. Pang / ISA Transactions 51 (2012) 834–840

As the sensing voltage is much smaller than the driven voltage
ap...
836

F. Hong, C.K. Pang / ISA Transactions 51 (2012) 834–840

Fig. 2. Improved indirect-driven self-sensing actuation (IDS...
F. Hong, C.K. Pang / ISA Transactions 51 (2012) 834–840

¼ ÀaÀ1 bY 2 ðtÞ r 0
s

837

ð12Þ

which is negative semi-definite,...
838

F. Hong, C.K. Pang / ISA Transactions 51 (2012) 834–840

10
Gain (dB)

5
0
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−10
IDSSA

−15
103

104

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F. Hong, C.K. Pang / ISA Transactions 51 (2012) 834–840

0.4
Open−loop
Plant model

20
0
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−40
102

103

PES (500 nm/V)
...
840

F. Hong, C.K. Pang / ISA Transactions 51 (2012) 834–840

10
Base−line PI
Adaptive+IDSSA

Gain (dB)

5

0

−5

−10

−1...
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Robust vibration control at critical resonant modes using indirect-driven self-sensing actuation in mechatronic systems

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This paper presents an improved indirect-driven self-sensing actuation circuit for robust vibration control of piezoelectrically-actuated flexible structures in mechatronic systems. The circuit acts as a high-pass filter and provides better self-sensing strain signals with wider sensing bandwidth and higher signal-to-noise ratio. An adaptive non-model-based control is used to compensate for the structural vibrations using the strain signals from the circuit. The proposed scheme is implemented in a PZT-actuated suspension of a commercial dual-stage hard disk drive. Experimental results show improvements of 50% and 75% in the vibration suppression at 5.4kHz and21 kHz respectively, compared to the conventional PI control.

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Transcript of "Robust vibration control at critical resonant modes using indirect-driven self-sensing actuation in mechatronic systems"

  1. 1. ISA Transactions 51 (2012) 834–840 Contents lists available at SciVerse ScienceDirect ISA Transactions journal homepage: www.elsevier.com/locate/isatrans Research Article Robust vibration control at critical resonant modes using indirect-driven self-sensing actuation in mechatronic systems Fan Hong a, Chee Khiang Pang b,n a b Data Storage Institute, A*STAR, 5 Engineering Drive 1 (Off Kent Ridge Crescent, NUS), Singapore 117608, Republic of Singapore Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore 117583, Republic of Singapore a r t i c l e i n f o a b s t r a c t Article history: Received 29 November 2011 Received in revised form 19 May 2012 Accepted 7 June 2012 Available online 4 July 2012 This paper presents an improved indirect-driven self-sensing actuation circuit for robust vibration control of piezoelectrically-actuated flexible structures in mechatronic systems. The circuit acts as a high-pass filter and provides better self-sensing strain signals with wider sensing bandwidth and higher signal-to-noise ratio. An adaptive non-model-based control is used to compensate for the structural vibrations using the strain signals from the circuit. The proposed scheme is implemented in a PZT-actuated suspension of a commercial dual-stage hard disk drive. Experimental results show improvements of 50% and 75% in the vibration suppression at 5.4 kHz and 21 kHz respectively, compared to the conventional PI control. & 2012 ISA. Published by Elsevier Ltd. All rights reserved. Keywords: Piezoelectricity Self-sensing actuation Strain signal Vibration control Critical resonant mode Mechatronics 1. Introduction Mechatronic systems are highly compatible integration of mechanics, electronics, control systems, and computer science [1], which appear widely in industrial applications such as intelligent robots, aerospace crafts, and consumer electronics, etc. To meet the growing demand for high-performance and low-cost mechatronic products, continual improvements in R&D such as servo evaluation and mechanical structure optimization are essential [2], especially for portable devices requiring ultrahigh data capacities and ultra-strong disturbance rejection capabilities [3,4]. In recent decades, lightweight flexible structures are widely used in mechatronic systems to achieve high-speed and highaccuracy performance with low-energy consumption. These flexible structures can be found in a wide range of applications such as high-density data storage devices [5,6], flexible robotic arms [7,8], or high-speed nanopositioners [9,10], etc. However, due to the inherent low structural damping and light weight, these flexible structures may suffer from disturbance induced structural vibrations at critical resonant modes [11]. These vibrations would degrade the positioning accuracy severely and prolong n Corresponding author. Tel.: þ65 6516 7942; fax: þ65 6779 1103. E-mail address: justinpang@nus.edu.sg (C.K. Pang). the settling time, and therefore need to be properly compensated for [12]. Active vibration control schemes were developed using additional sensors such as in [13–16]. Basically, sensors were attached on the mechanical structures to measure the acceleration or strain signals, and the measured signals were fed back to the inner loop to actively compensate for the structural vibrations of the flexible structures. In particular, active vibration control incorporated with Pb–Zr–Ti (PZT) material as actuators/sensors has attracted many research interests [17,18]. PZT material has become one of the popular choices in vibration control and noise suppression applications due to their efficiency in converting mechanical energy into electrical energy, and vise versa [19]. In addition, it possesses favourable features such as high sensitivity, high working bandwidth, and low-level noise at high frequency range. In traditional approaches, PZT material has been used solely as sensors or actuators [20–22], where separated circuitries were required for sensors and actuators respectively. The idea of self-sensing actuation (SSA) was concurrently proposed in [23,24], where the PZT elements were used as sensors and actuators simultaneously to reduce implementation cost and complexity, achieving truly collocated control. In these works, conventional RC bridge circuits were used to extract the strain signals from the PZT elements, with good applications appeared in [25–27] where the strain signals were used to provide active damping of the vibrations of PZT-actuated suspension in dual-stage hard disk drives (HDDs). 0019-0578/$ - see front matter & 2012 ISA. Published by Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.isatra.2012.06.004
  2. 2. F. Hong, C.K. Pang / ISA Transactions 51 (2012) 834–840 As the sensing voltage is much smaller than the driven voltage applied on the PZT elements, the quality of the signal, i.e., the signal-to-noise ratio (SNR) is a concern [28]. Conventional RC bridge circuits suffer from poor common-mode signal rejection so that the bridge is hard to be balanced. To tackle this problem, an Indirect-Driven Self-Sensing Actuation (IDSSA) circuit was proposed in [29], where operational amplifiers were used to drive the PZT actuators indirectly rather than by the input voltage (actuation voltage). By doing so, the SSA circuit has provided sensing signals with higher SNR. In this paper, the IDSSA circuit is further improved so that the circuit acts as a high-pass filter, resulting in better self-sensing performance in terms of wider sensing bandwidth and higher SNR compared to conventional SSA circuits and its earlier version in [29]. The improved circuit is then used to suppress the structural vibrations at critical resonant modes of the PZT-actuated suspension of a commercial dual-stage HDD. Rather than directly feeding back the strain signal, an adaptive non-model-based control [30] is used to enhance the performance of vibration suppression. The rest of the paper is organized as follows. Section 2 presents the characteristics of the PZT elements and the schematic of the improved IDSSA circuit. The controller with an add-on adaptive strain feedback is designed in Section 3. The effectiveness of the proposed adaptive control with IDSSA circuit is evaluated by extensive experiments on a PZT-actuated suspension of a commercial dual-stage HDD in Section 4. Section 5 gives conclusive remarks. 835 Fig. 1. Conventional SSA circuit. 2.2. Conventional SSA circuit The structure of the conventional SSA circuit is shown in Fig. 1, where the PZT element is modeled as a sensing voltage source vp in series with an equivalent capacitor Cp. The driving voltage vin is applied to the PZT element directly, and the sensing voltage vp generated from the strain of PZT element can be extracted by balancing the bridge circuit. The circuit can be analyzed by deriving the Laplace transform of v1 ðtÞ and v2 ðtÞ as V 1 ðsÞ ¼ Cp ½V ðsÞÀV p ðsފ C p þC 1 in V 2 ðsÞ ¼ C eq V ðsÞ C eq þ C 2 in 2. Indirect-driven self-sensing actuation (IDSSA) circuit In this section, the characteristics of the PZT element and the structure of conventional SSA circuit are briefly reviewed, followed by the IDSSA circuit design. 2.1. PZT element The electromechanical equations of the PZT element can be written as [23] S ¼ sE T þdE p ð2Þ P where S, T, D, and E are the strain, the applied mechanical stress, the charge density, and the uniform electric field of the PZT element respectively. sE and E represent the elastic compliance and the permittivity of the PZT element respectively. d and e are the PZT constants. From Eq. (2), the uniform electric field Ep in the PZT element can be written as E À eS ð3Þ E Assume that the PZT element is a rectangular solid with length lp, width bp, and thickness hp. The voltage v measured across the PZT element can be obtained by multiplying Eq. (3) by hp, i.e., v ¼ Ep hp ¼ If C 1 =C 2 ¼ C p =C eq , the sensing voltage Vp(s) can be decoupled from the control input Vin(s) and is proportional to circuit output Vo(s) as V o ðsÞ ¼ D ¼ eS þ EE D V o ðsÞ ¼ V 2 ðsÞÀV 1 ðsÞ C eq Cp Cp ¼ À V p ðsÞ V in ðsÞ þ C eq þ C 2 C p þ C 1 Cp þ C1 ð1Þ p Ep ¼ The circuit output Vo(s) is then calculated as Dhp E À eShp E 9 qin qp À 9vin Àvp Cp Cp ð4Þ where D9qin =A is the charge density due to the applied voltage vin with A ¼ lp  bp being the polarization area of the PZT element, eS9qp =A is the polarization charge density due to the strain, and C p 9ðEAÞ=hp is the capacitance of the PZT element. It can be seen from Eq. (4) that the voltage measured across the PZT element is a subtraction of the sensing voltage vp from the applied voltage vin. An SSA circuit shall be designed to extract the sensing voltage vp which is proportional to the strain of the PZT element. Cp V p ðsÞ Cp þ C1 As pointed out in [26], the PZT actuators with conventional SSA circuit require more power input for actuation than those without it. To handle this problem, an IDSSA circuit was proposed in [29], which employed op-amps to drive the PZT actuators indirectly so that the load burden on the implementation hardware was lessened. The IDSSA circuit is further improved in Section 2.3. 2.3. Improved IDSSA circuit design Based on the original design in [29], the IDSSA circuit is further improved by adding capacitors and resistors in the feedback loops of op-amps such that the circuit acts as a high-pass filter as shown in Fig. 2, resulting in better self-sensing performance in terms of wider sensing bandwidth and higher SNR compared to conventional SSA circuits. The sensing voltage vp generated from the strain of the PZT element can be decoupled from vin as shown in the following derivations. The Laplace transform of v1 ðtÞ and v2 ðtÞ is derived as C 1 C p R1 R2 s2 þ C 1 R2 s V 1 ðsÞ ¼ 1 þ V ðsÞ C 1 C 2 R1 R2 s2 þðC p þ C 1 þ C 2 ÞR1 s þ 1 in À ðC p =C 2 Þs2 V p ðsÞ s2 þðC p þ C 1 þ C 2 Þ=ðC 1 C 2 R2 Þs þ 1=ðC 1 C 2 R1 R2 Þ
  3. 3. 836 F. Hong, C.K. Pang / ISA Transactions 51 (2012) 834–840 Fig. 2. Improved indirect-driven self-sensing actuation (IDSSA) circuit. V 2 ðsÞ ¼ 1 þ C 3 C eq R3 R4 s2 þ C 3 R4 s V in ðsÞ C 3 C 4 R3 R4 s2 þ ðC eq þ C 3 þ C 4 ÞR1 s þ1 The circuit output Vo(s) is given by V o ðsÞ ¼ Fig. 3. Head suspension assembly of a commercial dual-stage HDD. R6 R7 þ R8 R7 Á V 2 ðsÞÀ V 1 ðsÞ R5 þR6 R8 R8 The components are chosen to be 8 C 1 ¼ C 2 ¼ C 3 ¼ C 4 ¼ C eq ¼ C p R1 ¼ R2 ¼ R3 ¼ R4 R5 ¼ R8 : R6 ¼ R7 ¼ kR5 Therefore, the bridge circuit is balanced and Vp(s) is decoupled from Vin(s) as 2 V o ðsÞ ks ¼ V p ðsÞ s2 þ 2zð2pf c Þs þ ð2pf c Þ2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi where f c ¼ 1=2p C 1 C 2 R1 R2 , z ¼ C 1 C 2 R1 R2 ðC 1 þC 2 þC p Þ= 2C 1 C 2 R2 , and k are the cut-off frequency, damping ratio, and gain of the high-pass filter, respectively. Neutral axis PZT 3. Adaptive non-model-based controller design The proposed IDSSA circuit is used for vibration control at the critical resonant modes of the PZT-actuated suspension. Rather than directly feeding back the strain signal, an adaptive nonmodel-based control is used to enhance the performance of vibration suppression. In this section, the structure of the PZTactuated suspension is analyzed, followed by the adaptive algorithm with its stability proof. 3.1. PZT-actuated suspension Fig. 3 shows the head suspension assembly of a commercial dual-stage HDD, where the PZT-actuated suspension is mounted on the base-plate of the Voice Coil Motor (VCM) actuator for fine positioning. The suspension can be modeled as a flexible beam with length l, width b, and thickness h as shown in Fig. 4, for simplicity but without loss of generality. Assume that the cross-section of the suspension is a symmetrical area (in y2z plane) which is perpendicular to the neutral plane (in x2z plane). Therefore, the strain ex generated in the x2y ^ plane can be calculated as 2 ^ ex ¼ Àz ^ ^ d wðx,tÞ ^ dx Fig. 4. PZT-actuated suspension modeled as a flexible beam (Top: top view; bottom: side view). The proposed IDSSA circuit is used to extract the strain signal of the PZT-actuated suspension. The strain signal can then be used for adaptive non-model-based controller design to compensate for the structural vibrations at the critical resonant modes. 3.2. Adaptive non-model-based control Fig. 5 shows the block diagram of the control system with the add-on adaptive control, where the base-line control is composed of a PI control and notch filters, and an adaptive non-model-based control is used in the add-on strain feedback loop to enhance the performance of vibration suppression at the critical resonant modes of the PZT-actuated suspension. The adaptive non-model-based control is derived based on an energy function [30] as ½Ek ðtÞ þ Ep ðtފÀ½Ek ð0Þ þEp ð0ފ ¼ Z t _ vðtÞwðtÞ dt ð5Þ 0 2 ^ ^ where wðx,tÞ is the displacement of in x2y plane and z is the distance from the neutral axis to a point of interest in the beam as shown in Fig. 4. where Ek(t) and Ep(t) are the total kinetic and potential energy of the system at time t, Ek ð0Þ and Ep ð0Þ are the initial kinetic and _ potential energy of the system at time 0. vðtÞ and wðtÞ are the external input and velocity respectively. The time derivative of
  4. 4. F. Hong, C.K. Pang / ISA Transactions 51 (2012) 834–840 ¼ ÀaÀ1 bY 2 ðtÞ r 0 s 837 ð12Þ which is negative semi-definite, i.e., the closed-loop system is energy dissipative and stable. Since the stability condition in (12) is independent of system dynamics, the control system is robust against plant uncertainties. 4. Performance evaluation Fig. 5. Block diagram of the control system with the add-on adaptive control. Eq. (5) is _ _ _ E k ðtÞ þ E p ðtÞ ¼ vðtÞwðtÞ ð6Þ _ _ where E k ðtÞ and E p ðtÞ are the time derivatives of the kinetic and potential energy respectively. The adaptive non-model-based control v(t) is designed as the combination of a PI control and an adaptive strain feedback term, which is expressed as Z t Z t vðtÞ ¼ Àkp wðtÞÀki wðtÞ dtÀkf f ðtÞ f ðtÞ dt ð7Þ 0 0 where kp, ki 4 0 are proportional and integral gains respectively, f(t) is a signal reflecting the deformation of the controlled plant, e.g., the strain, which should be chosen such that it is zero when the controlled plant is static without deformation. The gain kf 4 0 is for the add-on strain feedback loop, where larger kf leads to faster transient performance but undesired high-gain control and more energy consumption, and vice versa. An adaptive tuning for kf can be achieved by setting kf ¼ Y 2 ðtÞ, and Ys(t) is s updated by Z t _ _ Y s ðtÞ ¼ aY s ðtÞwðtÞf ðtÞ f ðtÞ dtÀbY s ðtÞ ð8Þ 0 where a 40 sets the updating rate, b 40 is introduced to avoid divergence of the integral gains in the presence of various disturbances and plant uncertainties. With the b-term, Ys(t) acts Rt _ as a first order filter of the aY s ðtÞwðtÞf ðtÞ 0 f ðtÞ dt and thus it will not diverge. Note that PI control is used in Eq. (7) rather than PD control in [30]. The integral term is used to eliminate the steady-state error. To accommodate the extra term, the integral gain is chosen 2 as ki ¼ k0 ðtÞ, where k0 ðtÞ is adaptively tuned by Z t _ _ k 0 ðtÞ ¼ gk0 ðtÞwðtÞ wðtÞ dt ð9Þ The adaptive control with the proposed IDSSA circuit is implemented in the PZT-actuated suspension of a commercial dual-stage HDD. The objective is to robustly suppress the structural vibrations at the critical resonant modes of the PZT-actuated suspension. The schematic of the experimental setup is shown in Fig. 6. A PZT-actuated suspension from a dual-stage commercial HDD is used in the experiment test. The effective stroke of the PZTactuated suspension is around 7150 nm with 710 V input range. A Laser Doppler Vibrometer (LDV) from Polytec is used to measure the lateral displacement of the slider without disk rotation. The resolution of the LDV is set at 500 nm/V. Control algorithms are implemented in dSPACE by setting the sampling frequency at 60 kHz. Control signals are applied to the PZTactuated suspension through a Piezo Amplifier (amplification  20, Piezo Systems, Inc.). Fig. 7 captures the actual experimental setup placed on a vibration-free table. 4.1. Self-sensing performance of the IDSSA circuit The proposed IDSSA circuit is implemented in a Printed Circuit Board (PCB) as shown in Fig. 8, which is used to extract the strain signal of the PZT-actuated suspension produced by PZT elements. AD827JN with dual op-amps is chosen due to its high unity-gain bandwidth and high performance. Both op-amps are connected in the non-inverting configuration so that the PZT elements can be driven indirectly by negative input terminal of op-amp rather than by input voltage directly [29]. In addition, a difference amplifier is implemented by another op-amp chip LF356N. A grid 0 where g 40 sets the updating rate of k0 ðtÞ. The stability of the closed-loop system with the add-on adaptive control is proven as follows. The Lyapunov function candidate is chosen as 1 1 1 2 VðtÞ ¼ Ek ðtÞ þ Ep ðtÞ þ kp wðtÞ2 þ aÀ1 Y 2 ðtÞ þ gÀ1 k0 ðtÞ s 2 2 2 ð10Þ Using Eq. (6), the time derivative of V(t) is _ _ _ _ _ V ðtÞ ¼ vðtÞwðtÞ þ kp wðtÞwðtÞ þ aÀ1 Y s ðtÞY s ðtÞ þ gÀ1 k0 ðtÞk 0 ðtÞ ð11Þ Substituting Eqs. (7)–(9) into (11) yields Z t Z t _ _ V ðtÞ ¼ Àkp wðtÞÀki wðtÞ dtÀkf f ðtÞ f ðtÞ dt wðtÞ 0 0 Z t _ f ðtÞ dtÀbY s ðtÞ þ aÀ1 Y s ðtÞ aY s ðtÞwðtÞf ðtÞ 2 _ _ þkp wðtÞwðtÞ þ k0 ðtÞwðtÞ Z 0 0 t wðtÞ dt Fig. 6. Schematic diagram of the self-sensing vibration control system.
  5. 5. 838 F. Hong, C.K. Pang / ISA Transactions 51 (2012) 834–840 10 Gain (dB) 5 0 −5 −10 IDSSA −15 103 104 Phase (deg.) −80 −100 −120 −140 −160 −180 103 Fig. 7. Experimental setup on the vibration-free table. 104 Frequency (Hz) Gain (dB) Fig. 9. Frequency response of the proposed IDSSA circuit. 20 10 0 −10 −20 −30 −40 103 IDSSA LDV 104 Phase (deg.) 100 0 −100 −200 −300 103 104 Frequency (Hz) Fig. 8. PCB of the IDSSA circuit. Fig. 10. Self-sensing performance of IDSSA circuit (solid-line: V IDSSA =V in ; dashedline: V LDV =V in ). Table 1 Values of circuit components. Component Value Cp C 1 ¼ C 2 ¼ C 3 ¼ C 4 ¼ C eq R1 ¼ R2 ¼ R3 ¼ R4 R5 ¼ R8 R6 ¼ R7 4.84 nF 4.84 nF 8 kO 1 kO 4:7 kO of pin holes on the board is used for plugging in suitable passive components to balance the circuit and adjust the circuit amplification gain. As most of the critical resonant modes of the PZTactuated suspension lie above 5 kHz and the circuit is designed to act as a high-pass filter, the cut-off frequency, damping ratio, and gain of the circuit are set as f c ¼ 4:5 kHz, z ¼ 1:5, and k¼4.7 respectively. The values of components are listed in Table 1. The corresponding frequency response of the IDSSA circuit, i.e., V o ðsÞ=V p ðsÞ, is measured and plotted in Fig. 9. Note that the output provides a quadruple amplification of the sensing voltage, i.e., vo ¼ 4vp in the effective working bandwidth 4.5–30 kHz. The self-sensing performance of the proposed IDSSA circuit is evaluated by conducting the experiments in an open-loop configuration. The suspension is actuated by PZT actuator by injecting swept sine signal vin through piezo amplifier, while the strain signal vIDSSA is collected from the sensing circuit. The frequency response of V IDSSA =V in is then obtained and benchmarked against V LDV =V in , with V LDV being the lateral displacement of the slider measured by LDV. The comparison is shown in Fig. 10, and confirms that the proposed IDSSA circuit is able to detect almost all the critical resonant modes of the PZT-actuated suspension. 4.2. Vibration suppression at critical resonant modes Note that in this experiment, only the PZT actuation loop is active and the VCM actuation loop is disabled. A nominal controller, i.e., a PI controller in series with four notch filters at 5.4 kHz, 16 kHz, 20.9 kHz and 25.6 kHz, is first designed to stabilize the system. As can be seen from Fig. 11, the resulting open-loop achieves the gain cross-over frequency at around 1.5 kHz with sufficient gain margin and phase margin, as well as the DC gain around 25 dB. Fig. 12 shows that the base-line loop system is able to track a 25 Hz square wave.
  6. 6. F. Hong, C.K. Pang / ISA Transactions 51 (2012) 834–840 0.4 Open−loop Plant model 20 0 −20 −40 102 103 PES (500 nm/V) 40 Gain (dB) 839 104 Base−line PI 0.2 0 −0.2 −0.4 0 1 2 3 4 5 6 0 0.4 −200 −400 −600 −800 102 103 Frequency (Hz) 104 0.1 0.06 −0.2 0 1 2 3 4 Time (sec) 5 6 7 x 10−3 0.4 PES (500 nm/V) 0.04 0.02 0 −0.02 Base−line PI 0.2 0 −0.2 −0.4 −0.04 −0.06 0 1 2 3 4 5 0.02 0.04 0.06 Time (sec) 0.08 0.1 Fig. 12. Step response of the base-line loop system. PES (500 nm/V) 0 Adaptive+IDSSA 0.2 0 −0.2 −0.4 Remark 1. In order to eliminate the steady-state tracking error, the open-loop shall ideally have a DC gain of 40–50 dB. However, for the plant model such as the PZT-actuated suspension with a low DC gain of around À 10 dB, the controller should be designed to have a DC gain as high as around 50–60 dB. With such a highgain control, the PZT actuator will saturate easily. To avoid saturation, therefore, the controller is designed to have a comparatively lower DC gain. Remark 2. To prevent saturation of the PZT actuator due to the signal drifting of LDV measurement, a 50 Hz square wave with amplitude of 0.025 mV is injected to the ‘‘trig-in’’ port. Note that the spikes in Fig. 12 are due to the ‘‘trig in’’ signal, not the actual displacement of the plant. To show the vibration suppression capability of the adaptive scheme, sinusoidal signals with amplitude of 0.01 V at two frequencies, i.e., 5.4 kHz and 20.9 kHz are injected as disturbance respectively at the output. Note that only kf is tuned for simplicity. The parameters in Eq. (8) are chosen as a ¼ 1 and b ¼ 5. As can be seen from Fig. 13, the nominal control (top) is unable to attenuate the disturbance, while more than 50% improvement can be achieved by the adaptive control (bottom) with the settling time being 6 Â 10 À 3 s. Similarly, the disturbance rejection 6 x 10−4 0.4 −0.08 −0.1 0 Fig. 13. Transient response of vibration suppression at 5.4 kHz. Reference Base−line PI 0.08 Adaptive+IDSSA 0.2 −0.4 Fig. 11. Frequency response of base-line open-loop transfer function. Displacement (500 nm/V) 7 x 10−3 PES (500 nm/V) Phase (deg.) 200 0 1 2 3 4 5 Time (sec) 6 x 10−4 Fig. 14. Transient response of vibration suppression at 20.9 kHz. performance at the other frequency of 20.9 kHz is improved by 75% with the settling time of 5 Â 10 À 4 s as shown in Fig. 14. To explore the effect of the adaptive control and IDSSA circuit in the frequency range of interest, the sensitivity functions with and without the adaptive control and IDSSA circuit are plotted in Fig. 15. Note that the sensitivity function with the adaptive control is measured at steady-state, i.e., after the adaptive law is converged at each frequency. Fig. 15 shows that better gain attenuation is achieved at the critical resonant modes by the adaptive control, which confirms the improved disturbance rejection performance of the scheme in time domain. Remark 3. In the mass production of PZT-actuated structures for mechatronic systems, significant perturbations exist in the natural frequencies, damping ratios, and residues of the critical resonant modes of the PZT-actuated structures. Compared to conventional high gain control schemes such as peak filter method, the adaptive control with IDSSA circuit is more robust against these perturbations due to: (1) the strain signal is
  7. 7. 840 F. Hong, C.K. Pang / ISA Transactions 51 (2012) 834–840 10 Base−line PI Adaptive+IDSSA Gain (dB) 5 0 −5 −10 −15 103 104 Frequency (Hz) Fig. 15. Sensitivity functions with and without the adaptive control and IDSSA circuit. proportional to the mechanical deformation, i.e., the sensing signal of the IDSSA circuit varies along with the perturbations of the critical resonant modes of the PZT-actuated structures; and (2) the adaptive control is independent of plant dynamics. 5. Conclusions In this paper, an indirect-driven self-sensing actuation (IDSSA) circuit has been proposed for robust vibration control at the critical resonant modes of PZT-actuated structures in mechatronic systems. The proposed circuit employed op-amps to act as a high-pass filter and provide better self-sensing strain signals with wider sensing bandwidth and higher signal-to-noise ratio. Rather than directly feeding back the strain signal, an adaptive non-model-based control was used to enhance the performance of robust vibration control. The proposed IDSSA circuit with adaptive control was implemented in the PZT-actuated suspension of a commercial HDD, and the experimental results showed improved performance in vibration suppression at the critical resonant modes. Acknowledgments This work was supported in part by Singapore MOE AcRF Tier 1 Grant R-263-000-564-133. The authors would like to thank X. Wang and G. Dai in Department of Electrical and Computer Engineering, National University of Singapore, for their help in the experiments. References [1] de Silva CW. Mechatronics: an integrated approach. Boca Raton: CRC Press; 2004. [2] Pang CK, Ng TS, Lewis FL, Lee TH. Managing complex mechatronics RD: a systems design approach. IEEE Transactions on Systems, Man, and Cybernetics—Part A 2012;42(1):57–67. [3] Yamaguchi T, Hirata M, Pang CK, editors. 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