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Initial Experiments on the EndPoint Control of Flexible one Link
 Robot,"Proceedings of The International Journal of Robotics Research
, 1984
"... It has been known for some time (Gevarter 1970) that if a flexible structure is controlled by locating every sensor exactly at the actuator it will control, then stable operation is easy to achieve. Nearly all commercial robots are controlled in this way, for this reason. So are most flexible spacec ..."
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Cited by 111 (1 self)
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It has been known for some time (Gevarter 1970) that if a flexible structure is controlled by locating every sensor exactly at the actuator it will control, then stable operation is easy to achieve. Nearly all commercial robots are controlled in this way, for this reason. So are most flexible spacecraft. Conversely, when one attempts to control a flexible structure by applying control torques at one end that are based on a sensor at the other end, the problem of achieving stability is severe. Solving it is an essential step for better control in space: the spaceshuttle arm is a cogent example. The next generation of industrial robots will also need such control capability, for they will need to be much lighter in weight (to achieve quick response with modest energy), and they will need to achieve greater precision by employing endpoint
Experimental implementation of extended multivariable ppf control on an active structure
 IEEE Transactions on Control Systems Technology
"... Abstract—This paper reports experimental implementation of an extended positive position feedback (PPF) controller on an active structure consisting of a cantilevered beam with bonded collocated piezoelectric actuators and sensors. Stability conditions for PPF control are rederived to allow for a fe ..."
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Cited by 19 (12 self)
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Abstract—This paper reports experimental implementation of an extended positive position feedback (PPF) controller on an active structure consisting of a cantilevered beam with bonded collocated piezoelectric actuators and sensors. Stability conditions for PPF control are rederived to allow for a feedthrough term in the model of the structure. This feedthrough term is needed to ensure that the system’s inbandwidth zeros are captured with reasonable accuracy. The set of stabilizing PPF controllers is shown to be a convex set characterized by a set of linear matrix inequalities. A number of multivariable PPF controllers are designed and successfully implemented on the structure. Index Terms—Flexible structures, multivariable systems, piezoelectric transducers, positive position feedback (PPF), vibration control. I.
Resonant control of structural vibration using chargedriven piezoelectric actuators
 IEEE Trans. Control Syst. Technol
, 2005
"... Abstract—Driving piezoelectric actuators by charge, or current rather than voltage is known to significantly reduce the hysteretic nature of these actuators. Although this feature of piezoelectric transducers has been known to the researchers for some time, still voltage amplifiers are being used as ..."
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Cited by 12 (8 self)
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Abstract—Driving piezoelectric actuators by charge, or current rather than voltage is known to significantly reduce the hysteretic nature of these actuators. Although this feature of piezoelectric transducers has been known to the researchers for some time, still voltage amplifiers are being used as the main driving mechanism for piezoelectric devices. This is due to the perceived difficulty in building charge/current amplifiers capable of driving highly capacitive loads such as piezoelectric actuators. Recently, a new charge amplifier has been proposed which is ideal for driving piezoelectric loads used in applications such as active damping of vibration. Consequently, it is now possible to effectively, and accurately control the charge deposited on the electrodes of a piezoelectric transducer, and thereby avoid hysteresis altogether. This paper further investigates properties of piezoelectric transducers driven by charge sources when used with resonant controllers for structural vibration control applications. The paper reports experimental results of a multivariable resonant controller implemented on a piezoelectric laminate cantilever beam. Index Terms—Charge control, flexible structures, hysteresis, piezoelectric, resonant controllers, vibration control. I.
Autonomous vibration suppression using online polezero identification
 Proceedings of the ASME Adaptive Structures and Materials Symposium
, 2000
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Mechanical and controloriented design of a monolithic microgripper using a new topological optimization method
 IEEE/ASME Transactions on Mechatronics
, 2009
"... Abstract — This paper presents a new method developed for the optimal design of piezoactive compliant micromechanisms. It is based on a flexible building block method, called FlexIn, which uses an evolutionary approach, to optimize a trusslike planar structure made of passive and active building bl ..."
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Cited by 5 (1 self)
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Abstract — This paper presents a new method developed for the optimal design of piezoactive compliant micromechanisms. It is based on a flexible building block method, called FlexIn, which uses an evolutionary approach, to optimize a trusslike planar structure made of passive and active building blocks, made of piezoelectric material. An electromechanical approach, based on a mixed finite element formulation, is used to establish the model of the active piezoelectric blocks. From the first design step, in addition to conventional mechanical criteria, innovative controlbased metrics can be considered in the optimization procedure to fit the openloop frequency response of the synthesized mechanisms. In particular, these criteria have been drawn here to optimize modal controllability and observability of the system, which is particularly interesting when considering control of flexible structures. Then, a planar monolithic compliant microactuator has been synthesized using FlexIn and prototyped. Finally, simulations and experimental tests of the FlexIn optimally synthetized device demonstrate the interests of the proposed optimization method for the design of microactuators, microrobots, and more generally for adaptronic structures. Index Terms — Actuator design, balanced gramian, compliant mechanisms, controllability, microgripper, microrobotics, observability,
Analog implementation of an integral resonant control scheme
, 2008
"... Integral resonant control (IRC) has been introduced as a high performance controller design methodology for flexible structures with collocated actuator–sensor pairs. IRC has a simple structure and is capable of achieving significant damping, over several modes, while guaranteeing closedloop stabil ..."
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Cited by 3 (2 self)
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Integral resonant control (IRC) has been introduced as a high performance controller design methodology for flexible structures with collocated actuator–sensor pairs. IRC has a simple structure and is capable of achieving significant damping, over several modes, while guaranteeing closedloop stability of the system in the presence of unmodeled outofbandwidth dynamics. IRC can be an ideal controller for various industrial damping applications, if packaged in a simple easytoimplement electronic module. This work proposes an analog implementation of the IRC scheme using a single OpAmp circuit. The objective is to show that with simple analog realization of the modified IRC scheme, it is possible to damp a large number of vibration modes. A brief discussion about the modeling, circuit considerations, implementation and experimental results is presented in order to validate the usefulness and practicality of the proposed analog IRC implementation. 1. Background Flexible structures are employed in a variety of industrial, scientific and defense applications [1–4]. These structures
Integral control of collocated smart structures
"... This paper introduces a simple and robust technique for vibration control in smart structures with collocated sensors and actuators. The technique is called Integral Resonant Control (IRC). We show that by adding a direct feedthrough to a collocated system, the transfer function can be modified fro ..."
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Cited by 1 (0 self)
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This paper introduces a simple and robust technique for vibration control in smart structures with collocated sensors and actuators. The technique is called Integral Resonant Control (IRC). We show that by adding a direct feedthrough to a collocated system, the transfer function can be modified from containing resonant poles followed by interlaced zeros, to zeros followed by interlaced poles. This structure permits the direct application of integral feedback and results in good stability and damping performance. To alleviate the problems due to unnecessarily high controller gain below the first mode, a slightly complicated secondorder controller is also discussed. A piezoelectric laminate cantilever beam used to test the proposed control scheme exhibits up to 24 dB modal damping over the first eight modes.
A survey of control issues . . .
, 2007
"... Nanotechnology is the science of understanding matter and the control of matter at dimensions of 100 nm or less. Encompassing ..."
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Nanotechnology is the science of understanding matter and the control of matter at dimensions of 100 nm or less. Encompassing
Active Control of Mechanical Vibrations in a Circular Disk
"... Mechanical vibration is a common phenomenon observed in the operation ..."
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Physical Interpretation of Transfer Function Zeros for Simple Control Systems with Mechanical Flexibilities
"... A new type of sliding surface for a variable structure control system is proposed to achieve fast and accurate path tracking in a class of nonlinear secondorder multiinput dynamical systems. Thesurface is adaptable to arbitrary initial conditions, and movable towards a predetermined surface. The ..."
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A new type of sliding surface for a variable structure control system is proposed to achieve fast and accurate path tracking in a class of nonlinear secondorder multiinput dynamical systems. Thesurface is adaptable to arbitrary initial conditions, and movable towards a predetermined surface. The movement is executed in a stepwise manner according to the trajectory of representative points. We call it a moving sliding surface (MSS). Using the MSS favorable fast tracking is accomplished without increasing the magnitude of the discontinuous control gain. A twodegreeoffreedom robotic manipulator subjected to external disturbances is considered to demonstrate the efficacy of the proposed method. I Introduction In recent years, much attention has been given to controller design for path tracking utilizing the theory of variable structure systems (VSS) It is also known that the gradients (slopes in case of secondorder systems) of .most of conventional sliding surfaces are usually determined in ad hoc manner. Ashchepkov (1983) established and proved the necessary conditions of optimality of the sliding surface in the sense of speed. For given initial conditions and properly designed controller, the optimal value of slope of the surface to get fast regulation of the states was determined by minimizing the quadratic performance index. In this paper, we formulate an optimal sliding surface in the sense of motion speed before introducing a new sliding surface. The optimal surface is constructed by evaluating a position tracking error performance index in both the reaching and sliding phases. The relationship between the peformance index, slope of the surface, and discontinuous control gain is presented. Then we introduce a new sliding surface adaptable to arbitrary initial conditions. The surface is initially designed to pass given initial errors and subsequently is moved toward a predetermined surface via rotating or/and shifting. We call it a moving sliding surface (MSS) compared with the conventional one, for instance, employed by a II. Optimal Sliding Surfaces Consider typical coupled secondorder nonlinear system described by where/€ R,x(0 €R 2 '", u(t) € R"', and x 0 = x{t 0 ) are the initial conditions given at initial time toThe control problem is to get We see that the tracking error becomes zero for any initial conditions provided that there exists a control u k (t) so as to cause the error trajectory to slide along the surface defined by (3). This can be achieved by satisfying the sliding condition 154 /Vol. 116, MARCH 1994 Transactions of the ASME Copyright © 1994 by ASME We construct such a discontinuous control u k (t) from the concept of equivalent control where k k might be any positive number. Then the tracking problem reduces to the following equation. e2k\(t) = e 2k (t) From the trajectory behavior of the error states e 2k~\ (t) and e 2k (t) in the sense of convergence speed to zero, we may assume s k (t 0 ) > 0. Then, we obtain the solution of equation (ii) the sliding phase (t>t ks ) where In the sense of standard deviation of the position tracking error (Ashchepkov, 1983) we may choose performance index J k as follows. Minimizing J k , we can obtain optimal value of c k (or k k ) with given initial errors (v ku v k2 ) and k k (or c k ). Ill Moving Sliding Surface We see from previous section that the sliding surface defined by the Eq. III.l Rotating Sliding Surface. Let us define the rotating sliding surface as Sk(t)=Ck(t)e 2 k.i(t)+e 2k (t) Sk(to)=(s k ) 0 = {c k )oe 2k \(to)+e 2k (to). (10) We obviously see that the surface initially goes through the initial errors e(t 0 ) with the corresponding slope (c k ) 0 . In other words, the RP initially lies on the surface (s k ) 0 as shown in (t) < 0 for e 6 R 2 4, t e (t ks , «>). Herein s k is defined by Step 1. We determine an appropriate constant (A r ) k required to rotate the surface and, define (refer to Step Step 5. We stop rotation according to the following condition, i. III.2 Shifting Sliding Surface. We define the shifting sliding surface as where (c k ) p is the slope of the predetermined sliding surface (s k ) p , and ct k (t) is the timevarying intercept of the e 2k axis. The surface initially goes through given initial errors with appropriate initial intercept {a k \ as shown in Theorem 2. Step 1. We determine an appropriate constant (A s ) k required to shift the surface and define (refer to Step 2. We calculate the initial intercept (a k ) 0 satisfying the equation (s k )o = 0 according to given initial errors e(t 0 ); (a*)o = {c k )oe 2 ki(k) + e 2k (t 0 ). Step 3. The shifting direction is determined from the value of (a^) 0 , i.e., if (a k ) Q >0; downward, and if (a k ) 0 < 0; upward. Step From intuition, we may combine the RSS and the SSS to get better results in the sense of fast tracking time. For instance, if the initial errors are located in the unstable zone, the SSS is used until the RP enters the stable zone, and subsequently RSS is employed throughout. Consequently, we may define the moving sliding surface (MSS) The intercept a*(0 = 0 for the RSS and the slope c k (t)=(c k ) p for the SSS. IV Application to a Robotic Manipulator To illustrate the efficiency of the proposed method, we consider a twodegreeoffreedom manipulator studied by Fu and Liao (1990) (see +a)} yl(t)+ Ul (t)+d x (t)]/[^ + M\ yi = [2liiy l (t)+M(y l U)+a)} Mt) y 2 {t) + u 2 (t)+d 2 (t)] The control objective is to force x 2k^\ (t) to asymptotically track the desired trajectories x 2 k1(0Thus, the control inputs U\(f) and u 2 {f) should be determined so that the trajectory error is forced to zero asymptotically, for any initial conditions. Accordingly, in view of Though the control problem is multiinput, it is treated as m singleinput problems; the kth sliding surface s k (t) depends only upon e 2k X (t) and e 2k {t). Hence, from the concept of equivalent control the discontinuous control laws satisfying the sliding condition can be obtained as follows: And the desired trajectory x 2k \ (t) is chosen to be where the value of constant slope c k is chosen as 5 for k = 1, 2. It is noted that the surfaces (20) are exactly same as ones employed by On the other hand, from the responses obtained by employing the proposed MSS we see that the tracking behavior is impressively improved without increment of the discontinuities in the control input. For this simulation, the following From the surface trajectories of the MSS, we know that the RP never crosses the surface during the reaching phase. V Conclusions The new type of the sliding surface called a moving sliding surface (MSS) has been proposed to improve the tracking behavior of the secondorder nonlinear systems. The MSS was designed first to pass given initial errors and to subsequently move towards a predetermined sliding surface via rotating or/ and shifting. The existence of sliding mode with the MSS has been proved and several salient features were presented. Employing the MSS, it was possible to remarkably lessen the tracking time without increasing undesirable chattering of the control input signals. It has been shown that the proposed method could be applied to both singleinput and multiinput systems. In multiinput systems, each sliding surface moves independently according to arbitrary given initial errors. References Ashchepkov, L. T., 1983, "Optimization of Sliding Motion in a Discontinuous System," Automation and Remote Control, Vol. 44, No. 11, pp. 3037. Cohn, D. L., 1980, Measure Theory, Birkhauser, Boston. Elmali, H., and