Active vibration control of a space truss using a lead zirconate titanate stack actuator

Transcription

1 355 Technical Note Active vibration control of a space truss using a lead zirconate titanate stack actuator G Song 1, J Vlattas 2, S E Johnson 2 and B N Agrawal 2 1 Department of Mechanical Engineering, The University of Akron, Ohio, USA 2 Department of Aeronautics and Astronautics, US Naval Postgraduate School, Monterey, California, USA Abstract: This paper presents design, implementation and experimental results of active vibration control of Naval Postgraduate School (NPS) space truss using a piezoelectric ceramic stack actuator. The NPS space truss represents a flexible spacecraft structure that may support interferometer, antenna and other vibrationsensitive instrumentation. To simulate the effects of a spacecraft disturbance on the truss, a proof mass actuator is incorporated on the structure to excite the truss. To reduce the vibrations caused by the proof mass actuator, an active strut member is installed along a diagonal of the base bay of the truss. The active strut element consists of a piezoelectric ceramic actuator stack, a force transducer and mechanical interfaces. An integral plus double-integral force controller is designed to suppress vibration of the truss. Experimental results demonstrate that the active piezoceramic strut actuator can effectively reduce truss vibration. Keywords: active vibration control, piezoceramic material, flexible spacecraft, space truss 1 INTRODUCTION The current trend of spacecraft design is to use large, complex and lightweight space structures to achieve increased functionality at a reduced launch cost. Truss-type structures such as those envisioned for the International Space Station will be more increasingly used. Truss-type space structures can support interferometer, antenna and other vibration-sensitive instrumentation. Because of launch constraints, these truss structures are lightweight. The combination of large and lightweight design results in these space structures being flexible and having low frequency fundamental modes. These modes might be excited in a variety of tasks such as slewing, pointing manoeuvres and docking with other spacecraft. The induced vibration must be effectively suppressed to satisfy stringent requirements for attitude control and vibrationsensitive missions, such as a space-based interferometer. This poses a challenging task for spacecraft designers. One promising method for this problem is to use the technology of smart structures, which employs embedded actuators and sensors, and microprocessors that analyse the responses from the sensors and to command the actuators to apply The MS was received on 1 April 21 and was accepted after revision for publication on 7 August 21. Corresponding author: Department of Mechanical Engineering, The University of Akron, 244 Sumner Street, ASEC-17D, Akron, OH , USA. localized strains to ensure that the system responds in a desired fashion [1 3]. Piezoelectric materials are commonly used as actuators (compensators) in smart structures since they have advantages such as high stiffness, high bandwidth, high efficiency, light weight, no moving parts and easy implementation. A commonly used piezoceramic is lead zirconate titanate (PZT), which has a strong piezoeffect. The use of an active PZT strut for vibration suppression has already been demonstrated for a number of specific space applications [4 7]. This paper presents the design, implementation and experimental results of active vibration control of the Naval Postgraduate School (NPS) space truss using a PZT stack actuator. The NPS space truss represents a flexible spacecraft structure that may support interferometer, antenna and other vibration-sensitive instrumentation. The truss consists of 12 cubic bays arranged in a T configuration mounted to a base plate. The structure is approximately 3.76 m in length,.35 m wide and.7 m tall. The bare truss weighs kg. To simulate the effects of a spacecraft disturbance on the truss, a proof mass actuator is incorporated on the structure to excite the truss s vibrational modes. For active suppression of the vibrations caused by the proof mass actuator, an active strut member is installed along a diagonal of the base bay of the truss. This location has the highest modal strain energy (MSE) according to the finite element model. The active strut element consists of a low cost, commercially available piezoelectric ceramic actuator G121 # IMechE 21 Proc Instn Mech Engrs Vol 215 Part G

2 356 G SONG, J VLATTAS, S E JOHNSON AND B N AGRAWAL stack, a force transducer and mechanical interfaces. It replaces a truss member and acts as a load-carrying member as well as an actuating member. With the proof mass actuator and the active PZT strut member, the truss weighs kg. By using the force transducer as a sensor and the PZT stack as an actuator, an integral plus doubleintegral force controller is designed to suppress vibration of the truss. A dspace digital data acquisition and real-time control system along with Matlab/Simulink is used to implement the control design in real time. To assist measuring vibrations across the truss, three-axis accelerometers are used. Experimental results demonstrate that the active strut member with a piezoceramic stack actuator can effectively suppress truss vibration by using an integral plus double-integral force controller. 2 PIEZOELECTRIC CERAMIC MATERIAL AND PZT STACK ACTUATOR A piezoceramic material possesses the property of piezoelectricity, which describes the phenomenon of generating an electric charge in a material when subjected to a mechanical stress (direct effect) and, conversely, generating a mechanical strain in response to an applied electric field. This property prepares piezoceramic materials to be able to function as both sensors and actuators. The advantages of piezoceramic materials include high efficiency, no moving parts, fast response and being compact. A commonly used piezoceramic is PZT, which has a strong piezo-effect. PZT can be fabricated into different shapes to meet specific geometric requirements. PZT materials are often used as both sensors and actuators, which can be integrated into structures. The PZT actuation strain can be on the order of 1 ístrain. Within the linear range PZT actuators produce strains that are proportional to the applied electric field/voltage. These features make them attractive for structural control applications. A common way to use PZT is the stacked design. In this design, the active part of the positioning element consists of a stack of ceramic discs separated by thin metallic electrodes. Each ceramic disc lies between two electrode surfaces, one of which is connected to the control voltage and the other to the ground. Maximum operating voltage is proportional to the thickness of the discs. The individual discs and electrodes are connected to each other with epoxy cement and are hermetically sealed on the outside with highly insulating materials. Stack elements can withstand high pressure and show the highest stiffness of all piezoactuator designs. Since the ceramics cannot withstand large pulling forces, spring-preloaded actuators are used. Stack models can be used for static and dynamic operation. In this experiment, a PZT stack actuator (model P-843) manufactured by Physik Instrumente is used. This preloaded PZT actuator is a high resolution linear translator for static and dynamic applications. It provides submillisecond response and subnanometre resolution. The translators are equipped with high reliability multilayer PZT ceramic stacks protected by an internally spring-preloaded non-magnetic stainless steel case. The actuator provides a displacement up to 9 ím, a push force up to 8 N and a pulling force up to 3 N [8]. 3 THE NPS SPACE TRUSS The NPS space truss structure (Fig. 1) is composed of 12 cubic bays assembled from a combination of 161 elements that begin and terminate in an aluminium node ball. It is a result of collaboration between NPS and the Naval Research Laboratory. There are a total of 52 node balls constituting the truss [9]. The structure is approximately 3.76 m in length,.35 m wide and.7 m tall (from the base plate). These 12 cubic bays are a combination of battens/ longerons and diagonals. Longerons run down the length of the structure, battens compose the vertical elements and diagonals run diagonally from one line of longerons to an adjacent line. Collectively, all of the aforementioned elements will be referred to as struts. Each strut is made of homogeneous aluminium and is composed of several parts: the tube, outer sleeve, bolt, standoff and nut. Each strut begins and terminates in an aluminium node ball. The experimental set-up for the NPS space truss is displayed in Fig. 2. To excite the vibration of the truss, a Fig. 1 NPS space truss (with numbered nodes) Proc Instn Mech Engrs Vol 215 Part G G121 # IMechE 21

3 ACTIVE VIBRATION CONTROL OF A SPACE TRUSS USING A PZT STACK ACTUATOR 357 Fig. 2 Active vibration control experimental set-up proof mass actuator called LPACT is used. As shown in Fig. 2, the LPACT is mounted between nodes 14 and 52 to achieve the maximum excitation effect. To achieve active suppression of the vibration of the truss, a smart strut (Fig. 3) which consists of a force sensor and a PZT stack actuator is installed between nodes 35 and 27 in the base bay (Fig. 4). This smart strut replaces a regular strut member. This location experiences the greatest MSE for the truss s second mode as identified by a finite element model [9, 1] and is selected to mount the smart strut. A Trek 5/75 voltage amplifier is used to power the PZT stack actuator. The mass properties of the bare and the modified truss are shown in Table 1. A more detailed description of the truss and its finite element model can be found in references [9] and [1]. The truss response is measured by the active strut force sensor and with four Kistler accelerometers that are mounted across the truss. Accelerometers were mounted at nodes 26 and 41 because they were located at the extreme ends of the truss and represent the points that will experience the maximum displacement for the first and second mode shapes of the truss. Likewise, two more accelerometers were located at nodes 18 and 49, where the third and fourth mode shapes Fig. 4 The smart strut installed between nodes 27 and 35 in the base bay have the most power. The dspace system along with Matlab/Simulink is used for digital data acquisition and real-time control. Fig. 3 The smart strut 4 ACTIVE VIBRATION CONTROL OF NPS SPACE TRUSS 4.1 Frequency response identification Prior to designing the active controller, it is necessary to identify the frequency response of the truss system, whose input is the PZT actuator and whose output is the force sensor. The frequency response function of the actuator sensor system was obtained using an HP-35665A digital signal analyser. Pink noise, generated by the signal analyser, was applied to the piezoceramic actuator through the Trek voltage amplifier. The frequency response of the actuator and sensor assembly from to 2 Hz is displayed in Fig. 5 [1]. G121 # IMechE 21 Proc Instn Mech Engrs Vol 215 Part G

4 358 G SONG, J VLATTAS, S E JOHNSON AND B N AGRAWAL Table 1 Mass properties of the bare and the modified truss Quantity Mass (kg) Component Bare Modified masses Bare Modified Part name truss truss (kg) truss truss Node balls Longerons Diagonals LPAC strut Active strut Screw Total mass Frequency (Hz) Frequency (Hz) Fig. 5 Frequency response ( 2 Hz) By examining the frequency response and magnitude phase plots, the frequency of the dominant mode below 7 Hz is determined to be at Hz. Since most disturbance sources on a spacecraft have frequencies less than 7 Hz, the most significant mode under 7 Hz was targeted. The mode at Hz will be the target frequency for vibration suppression of the truss. In the magnitude portion of the frequency response plot, the first peak at 8.5 Hz is associated with the resonant frequency of the proof mass actuator, and vibration at this frequency will not be controlled. If this truss is equipped with two PZT struts, vibrations at and 12.5 Hz (associated with the second peak in the magnitude portion of the frequency response plot) can be controlled simultaneously. 4.2 Control system design In the literature, integral force control [4, 6, 7], robust control [11], linear quadratic Gaussian (LQG) control [3], adaptive control [12], the H 1 technique [13] and neural network control [14] have been reported for active vibration suppression of truss-like structures. Among these methods, integral force control has the advantages of inherent stability [6, 7], easy implementation and high efficiency [6]. In this paper, active truss control is designed using an integral plus double-integral force feedback control. Integral force control is chosen to provide a 98 phase shift between the PZT actuator and the measured force in the frequency of interest. A block diagram of the closed-loop control of the NPS truss is displayed in Fig. 6. The controller is composed of two feedback paths: integral control and double-integral control. Both paths are summed and passed through a saturator that limits maximum output voltage and prevents possible damage to the piezoceramic stack once the signal is amplified by the Trek 5/75 voltage amplifier. The output signal is then combined with a positive bias voltage that provides a preload for the active strut after amplification with the Trek 5/75 amplifier. The bandpass filter in the design is used to prevent the amplification of low frequency signal and high frequency noise. The bandpass filter is centred at Hz, which is the target mode. Proc Instn Mech Engrs Vol 215 Part G G121 # IMechE 21

5 ACTIVE VIBRATION CONTROL OF A SPACE TRUSS USING A PZT STACK ACTUATOR 359 Truss Accel. Trek 5/75 Volt. Amplifier Active Strut Force Tranducer Disturbance _ iigain ò ò Bandpass Filter Bias Voltage igain Simulink Controller ò Fig. 6 Block diagram of the control design 4.3 Experimental results The active control experiment is conducted to evaluate the effectiveness of the controller. During the experiment, the proof mass actuator (LPACT) excites the truss at Hz. The smart strut with integral and double-integral control is used to suppress the induced vibration. The controller is designed using Matlab/Simulink and downloaded to the digital signal processor of the dspace system. The input signal is received from the force sensor via an analogue-to-digital converter (ADC). The digital signal processor then processes this signal and generates a command, which is sent to the Trek voltage amplifier through a digital-to-analogue converter (DAC). Both the ADC and the DAC are hardware components of dspace. The TRACE module of the dspace system enables realtime data acquisition and the Cockpit module provides near real-time controller parameter adjustment. The format of each test is identical. All tests are 2 s in duration. At the commencement of each test no actuating signal is being applied to the controller. The first 5 s is uncontrolled. At the 5 s point, the active vibration suppression kicks in. A time of 15 s was judged sufficient for any transients to die out and to allow the system to achieve steady state. The degree of control effectiveness is evaluated by the reduction (in db) of the power spectral density at the modal frequency of the controlled versus uncontrolled force sensor response for each test. The specific test configurations (gain values) along with the results are detailed in Table 2. The best results were those of test 3 that resulted in a power reduction of db. The power spectral density comparison for this case is displayed in Fig. 7. The time responses of the force sensor and node 41 for this test are displayed in Fig. 8. It is clear that the magnitude of vibrations at the base bay measured by the force sensor and at node 41 measured by Table 2 the three-axis accelerometer have been significantly decreased after the active control takes effect at 5 s. Overall, vibration reduction of the truss is achieved in each case and the PZT stack actuator along with integral and doubleintegral control is found to be effective. 5 CONCLUSION Active control tests variations in gain parameters Integral Double-integral Power Reduction Test gain gain (db) The NPS space truss simulates a flexible space structure, which may support interferometer, antenna, and other vibration-sensitive instrumentation. The truss consists of 12 cubic bays arranged in a T configuration mounted onto a base plate. To simulate the effects of a spacecraft disturbance on the truss a proof mass actuator is incorporated on the structure to excite the truss s vibrational modes. An active strut element consisting of a piezoelectric actuator stack and a force transducer can replace a truss member and act as a load-carrying member as well as a force actuator. An integral plus double-integral force controller is designed to suppress specific modal vibrations across the entire length of the truss. The active vibration control experiments, using a single piezoelectric strut, validated the use of integral plus double-integral force feedback as a means of actively suppressing the vibration on the NPS space truss using one G121 # IMechE 21 Proc Instn Mech Engrs Vol 215 Part G

6 36 G SONG, J VLATTAS, S E JOHNSON AND B N AGRAWAL 1 Power Spectral Density - Controlled vs Uncontrolled (Trial 1) Power Spectrum Magnitude (db) Frequency (Hz) Fig. 7 Power spectral density plot of test 3.5 PCB Force Sensor - Time Data (v) x 1-3 Node 41 - X-Axis - Time Data (v) Node 41 - Y-Axis - Time Data (v) Node 41 - Z-Axis - Time Data (v) Fig. 8 Time responses of the force sensor and node 41 for test 3 active strut. The maximum response power reduction for the controlled versus the uncontrolled case is db. The average reduction was on the order of db at various gain settings. ACKNOWLEDGEMENT The authors would like to thank Dr Bosse for his help in setting up the NPS space truss. Proc Instn Mech Engrs Vol 215 Part G G121 # IMechE 21

7 ACTIVE VIBRATION CONTROL OF A SPACE TRUSS USING A PZT STACK ACTUATOR 361 REFERENCES 1 Crawley, E. F. and de Lius, J. Use of piezoelectric actuators as elements of intelligent structures. Am. Inst. Aeronaut. Astronaut. J., 1987, 25(1), Crawley, E. F. and Lazarus, K. B. Induced strain actuation of isotropic and anisotropic plates. Am. Inst. Aeronaut. Astronaut. J., 1991, 29(6), Crawley, E. F. Intelligent structures for aerospace: a technology overview and assessment. Am. Inst. Aeronaut. Astronaut. J., 1994, 32(8), McClelland, R., Lim, T.-W., Bosse, A. B. and Fisher, S. Implementation and feedback controllers for vibration suppression of a truss using active struts. In Proceedings of the International Society of Optical Engineering Conference on Smart Structures and Materials, San Diego, California, 1996, pp Won, C. C., Sulla, L., Sparks, D. W. and Belvin, W. K. Application of piezoelectric devices to vibration suppression. J. Guidance, Control, Dynamics, November December 1994, 17(6), Preumont, A., Dufour, J. P. and Malikian, C. Active damping by local force feedback with piezoelectric actuators. J. Guidance, Control, Dynamics, March April 1992, 15(2), Fanson, J. L., Blackwok, G. H. and Chu, C.-C. Active member control of precision structures. In Proceedings of the AIAA Conference on Structures, Structural Dynamics, and Materials, 1989, pp Products for Micropositioning. Catalog 111, Physik Instrumente. 9 Andberg, B. K. Modal testing and analysis of the NPS space truss. MS thesis, Naval Postgraduate School, September Johnson, S. E. and Vlattas, J. Modal analysis and active vibration control of the Naval Postgraduate School space truss. MS thesis, Naval Postgraduate School, June Petitjean, B. and Leblhan, D. Robust control of a satellite truss structure. In Tenth International Conference on Adaptive Structures and Technologies, Paris, France, 2, pp Zhang, L. and Liu, F. Active damping enhancement of flexible intelligent truss structures. Proc. SPIE, 2, 3985, Pai, M. C. and Sinha, A. Sliding mode control of vibration in a flexible structure via estimated states and H 1 í techniques. In Proceedings of the 2 American Control Conference, Chicago, Illinois, 2, Vol. 2, pp Bosse, A., Lim, T. W. and Shelley, S. Modal filters and neural networks for adaptive vibration control. J. Vibr. Control, May 2, 6(4), G121 # IMechE 21 Proc Instn Mech Engrs Vol 215 Part G