Showing papers in "Journal of Dynamic Systems Measurement and Control-transactions of The Asme in 1997"
TL;DR: In this article, a lumped-parameter model of a piezoeletric stack actuator was developed to describe actuator behavior for purposes of control system analysis and design, and in particular for control applications requiring accurate position tracking performance.
Abstract: A lumped-parameter model of a piezoeletric stack actuator has been developed to describe actuator behavior for purposes of control system analysis and design, and in particular for control applications requiring accurate position tracking performance. In addition to describing the input-output dynamic behavior, the proposed model explains aspects of nonintuitive behavioral phenomena evinced by piezoelectric actuators, such as the input-output rate-independent hysteresis and the change in mechanical stiffness that results from altering electrical load. Bond graph terminology is incorporated to facilitate the energy-based formulation of the actuator model. The authors propose a new bond graph element, the generalized Maxwell resistive capacitor, as a lumped-parameter causal representation of rate-independent hysteresis. Model formulation is validated by comparing results of numerical simulations to experimental data.
245 citations
TL;DR: In this paper, negative input shaping is used to reduce residual vibration in computer controlled machines by convolving a sequence of impulses with a desired system command and the resulting shaped input is then used to drive the system.
Abstract: Input shaping reduces residual vibration in computer controlled machines by convolving a sequence of impulses with a desired system command The resulting shaped input is then used to drive the system The impulse sequence has traditionally contained only positively valued impulses However, when the impulses are allowed to have negative amplitudes, the rise time can be improved Unfortunately, excitation of unmodeled high modes and overcurrenting of the actuators may accompany the improved rise time Solutions to the problem of high-mode excitation and overcurrenting are presented Furthermore, a simple look-up method is presented that facilitates the design of negative input shapers The performance of negative shapers is evaluated experimentally on two systems; one driven by a piezo actuator and the other equipped with DC motors
240 citations
TL;DR: In this paper, a 6-DOF magnetically levitated joystick was used to emulate stiff walls and stick-slip friction with a 6DOF PD controller, and it was shown that the PD controller severely limits achievable wall damping and stiffness.
Abstract: This technical brief addresses issues of mechanical emulation of stiff walls and stick-slip friction with a 6-DOF magnetically levitated joystick. In the case of stiff wall emulation, it is shown that the PD control implementation commonly used severely limits achievable wall damping and stiffness. It is also shown that the perceived surface stiffness can be increased without loss ofstability by applying a braking force pulse when crossing into the wall. For stick-slip friction, Karnopp's model was implemented using a PD controller within the stick friction threshold. Even though the PD controller allows some motion during the stick phase, the haptic feedback provided is remarkably similar to stick-slip friction.
215 citations
TL;DR: In this article, a design process is presented that generates input shapers with insensitivity-to-time-delay ratios that are much larger than traditionally designed input shaper, and the advantages of the new shapers are demonstrated with computer simulations and their performance is verified with experimental results from the MIT Middeck Active Control Experiment, which was performed on board the Space Shuttle Endeavor.
Abstract: Input shaping is a method for reducing residual vibrations in computer-controlled machines. Vibration is eliminated by convolving an input shaper, which is a sequence of impulses, with a desired system command to produce a shaped input. The shaped input then becomes the command to the system. Requiring the vibration reduction to be robust to modeling errors and system nonlinearities is critical to the success of the shaping process on any real system. Input shapers can be made very insensitive to parameter uncertainty; however, increasing robustness usually increases system delays. A design process is presented that generates input shapers with insensitivity-to-time-delay ratios that are much larger than traditionally designed input shapers. The advantages of the new shapers are demonstrated with computer simulations and their performance is verified with experimental results from the MIT Middeck Active Control Experiment, which was performed on board the Space Shuttle Endeavor.
170 citations
TL;DR: In this article, a lumped-parameter model for describing the dynamics of vapor compression cycles is presented, in which the dynamics associated with the two heat exchangers, i.e., the evaporator and the condenser, are modeled based on a moving-interface approach by which the position of the two-phase/single-phase interface inside the one-dimensional heat exchanger can be properly predicted.
Abstract: This paper presents a new lumped-parameter model for describing the dynamics of vapor compression cycles. In particular, the dynamics associated with the two heat exchangers, i.e., the evaporator and the condenser, are modeled based on a moving-interface approach by which the position of the two-phase/single-phase interface inside the one-dimensional heat exchanger can be properly predicted. This interface information has never been included in previous lumped-parameter models developed for control design purpose, although it is essential in predicting the refrigerant superheat or subcool value. This model relates critical performance outputs, such as evaporating pressure, condensing pressure, and the refrigerant superheat, to actuating inputs including compressor speed, fan speed, and expansion valve opening. The dominating dynamic characteristics of the cycle around an operating point is studied based on the linearized model. From the resultant transfer function matrix, an interaction measure based on the Relative Gain Array reveals strong cross-couplings between various input-output pairs, and therefore indicates the inadequacy of independent SISO control techniques. In view of regulating multiple performance outputs in modern heat pumps and air-conditioning systems, this model is highly useful for design of multivariable feedback control.
166 citations
TL;DR: In this article, a robust motion control algorithm using partial state feedback for a class of nonlinear systems in the presence of modelling uncertainties and external disturbances is introduced, where the effects of these uncertainties are combined into a single quantity called perturbation.
Abstract: This work introduces a new robust motion control algorithm using partial state feedback for a class of nonlinear systems in the presence of modelling uncertainties and external disturbances. The effects of these uncertainties are combined into a single quantity called perturbation. The major contribution of this work comes as the development and design of a robust observer for the state and the perturbation which is integrated into a Variable Structure Controller (VSC) structure. The proposed observer combines the procedures of Sliding Observers (Slotine et al, 1987) with the idea of Perturbation Estimation (Elmali and Olgac, 1992). The result is what is called Sliding Perturbation Observer (SPO). The VSC follows the philosophy of Sliding Mode Control (SMC) (Slotine and Sastry, 1983). This combination of controller/observer gives rise to the new routine called Sliding Mode Control with Sliding Perturbation Observer (SMCSPO). The stability analysis shows how the algorithm parameters are scheduled in order to assure the sliding modes of both controller and observer. A simplified form of the general design procedure is also presented in order to ease the practical applications of SMCSPO. Simulations are presented for a two-link manipulator to verify the proposed approach. Experimental validation of the methodology is also performed on a PUMA 560 robot. A superior control performance is obtained over some full state feedback techniques such as SMC and Computed Torque Method.
133 citations
TL;DR: In this paper, the authors proposed a delayed position feedback within the absorber section of the structure to impart ideal resonance features to the absorbber, which is shown to be real-time tunable to time varying disturbance frequencies.
Abstract: The Delayed Resonator (DR) and Dual Frequency Fixed Delayed Resonator (DFFDR) are newly introduced control techniques for active vibration absorption. Both methods propose a delayed position feedback within the absorber section of the structure to impart ideal resonance features to the absorber. When installed on an oscillating primary body, they form notch filters at their resonance frequencies attenuating the response of the primary structure. The DR absorber is shown to be real-time tunable to time varying disturbance frequencies. In this article, a number of new issues are considered. First, the basic theory is modified for acceleration feedback instead of position, which was originally proposed for the DR methodology. Second, the new absorption methods are implemented on distributed parameter structures which are under high frequency excitation (around 1 KHz). Stability of the combined structure is studied on a reduced order multi-degree-of-freedom primary structure together with the DR absorber. Experimental tests are conducted on a steel beam to verify the analytical findings. Piezoelectric actuators are used both to generate harmonic disturbances and to implement the control. The correspondence observed between the theoretical and experimental results is encouraging. The efficiency of the DR and DFFDR absorption techniques is demonstrated.
121 citations
TL;DR: In this article, a new PID controller for the position and trajectory control of pneumatic actuators based on the sliding mode control approach is proposed, which is simple, easy to implement, and robust to payload and parametric variations.
Abstract: Pneumatic robot manipulators are characterized by high-order, time-variant actuator dynamics, nonlinearities due to compressibility of air, external disturbances such as static and Coulomb friction, and wide range of payload variations. Conventional PID controllers suffer from problems of gain tuning under these conditions. In this paper, a new control algorithm is proposed for the position and trajectory control of pneumatic actuators based on the sliding mode control approach. The stability of motion is proved for the case of a linear, time-invariant switching surface. A disadvantage of using sliding mode control for third- and higher-order mechanical systems is the need for acceleration feedback. In this paper, to overcome this difficulty we propose the use of differential pressure. The proposed controller is simple, easy to implement, and robust to payload and parametric variations. The effectiveness of the new scheme for position and trajectory control is illustrated by experiments on an industrial piston-driven cylindrical actuator with proportional valves.
91 citations
TL;DR: In this article, it was shown that the cumulative compliance of the out-of-bandwidth modes and not the modes themselves is required to converge the zeros of the open-loop system and the poles of the closed loop system.
Abstract: Colocated, output feedback is commonly used in the control of reverberant systems. More often than not, the system to be controlled displays high modal density at a moderate frequency, and thus the compliance of the out-of-bandwidth modes significantly influences the performance of the closed-loop system at low frequencies. In the assumed modes approach, the inclusion principle is used to demonstrate that the poles of the dynamic system converge from above when additional admissible functions are used to expand the solution. However, one can also interpret the convergence of the poles in terms of the zeros of the open-loop system. Since colocated inputs and outputs are known to have interlaced poles and zeros, the effect of modification to the structural impedance locally serves to couple the modes of the system through feedback. The poles of the modified system follow loci defined by the relative location of the open-loop poles and zeros. Thus, as the number of admissible functions used in the series expansion is increased, the interlaced zeros of the colocated plant tend toward the open-loop poles, causing the closed-loop poles to converge from above as predicted by the inclusion principle. The analysis and results presented in this work indicate that the cumulative compliance of the out-of-bandwidth modes and not the modes themselves is required to converge the zeros of the open-loop system and the poles of the closed-loop system.
90 citations
TL;DR: In this paper, the design and performance of an active controller for a pantograph which collects current for a high-speed train are considered, and a dynamic model of the pantograph/catenary system is described and control objectives are established.
Abstract: The design and performance of an active controller for a pantograph which collects current for a high-speed train are considered. A dynamic model of the pantograph/ catenary system is described and control objectives are established. A design which incorporates a frame-actuated controller and requires only a single measurement is described. Over an array of train speeds, the contact force variation with the actively controlled pantograph is 50 percent less than for the equivalent passive pantograph system.
78 citations
TL;DR: In this article, a constant-magnitude force (produced by a mass in a gravity field) is randomly moved through the sensing space while raw data is continuously gathered, and the motion of the force vector (the motion) and the calibration matrix (the shape) are simultaneously extracted by singular value decomposition.
Abstract: We present a new technique for multi-axis force/torque sensor calibration called shape from motion. The novel aspect of this technique is that it does not require explicit knowledge of the redundant applied load vectors, yet it retains the noise rejection of a highly redundant data set and the rigor of least squares. The result is a much faster, slightly more accurate calibration procedure. A constant-magnitude force (produced by a mass in a gravity field) is randomly moved through the sensing space while raw data is continuously gathered. Using only the raw sensor signals, the motion of the force vector (the motion) and the calibration matrix (the shape) are simultaneously extracted by singular value decomposition. We have applied this technique to several types offorce/torque sensors and present experimental results for a 2-DOF fingertip and a 6-DOF wrist sensor with comparisons to the standard least squares approach.
TL;DR: In this paper, three neural networks are developed, one for system identification, the second for on-line state estimation, and the third for vibration suppression, which can identify, estimate, and suppress the vibration of a composite structure by the embedded piezoelectric sensor and actuator.
Abstract: Smart structure with build-in sensor(s) and actuator(s) that can actively and adaptively change its physical geometry and properties has been considered one of the best candidates in vibration control applications. Implementation of neural networks to system identification and vibration suppression of a smart structure is conducted in this paper. Three neural networks are developed, one for system identification, the second for on-line state estimation, and the third for vibration suppression. It is shown both in analysis and in experiment that these neural networks can identify, estimate, and suppress the vibration of a composite structure by the embedded piezoelectric sensor and actuator. The controller is also shown to be robust to system parameter variations.
TL;DR: In this article, the authors discuss the application of a class of discrete-time sliding mode controllers (DSMC) which was previously shown to be robustly stable in the case of linear plants.
Abstract: This paper discusses the application of a class of discrete-time sliding mode controllers (DSMC) which was previously shown to be robustly stable. Further insight into design and performance of DSMC is obtained considering the case of linear plants. A simple numerical example is used to illustrate the properties of this technique.
TL;DR: In this article, a digital robust controller is designed via Quantitative Feedback Theory (QFT) to maintain a constant cutting force in the presence of parametric uncertainty for a time varying end milling process.
Abstract: In this work, a digital robust controller is designed via Quantitative Feedback Theory (QFT) to maintain a constant cutting force in the presence of parametric uncertainty for a time varying end milling process. The QFT controller is designed using the delta transform method for discrete systems. The controller is designed to limit the overshoot and settling time of the cutting force levels over a range of cutting parameters. Models are presented for the cutting process and machine dynamics including parametric uncertainty, and these models are used to develop a controller which meets given tracking and regulation specifications for all plant values. Experimental results are obtained by implementing the controller on a milling machine.
TL;DR: In this article, the authors presented a robust force tracking control of a flexible gripper driven by a piezoceramic actuator characterizing its durability and quick response time.
Abstract: This paper presents a robust force tracking control of a flexible gripper driven by a piezoceramic actuator characterizing its durability and quick response time. The mathematical governing equation for the proposed system is derived by employing Hamilton’s principle and a state space control model is subsequently obtained through the modal analysis. Uncertain parameters such as frequency variation are included in the control system model. The sliding mode control theory which has inherent robustness to the system uncertainties is adopted to design a force tracking controller for the piezoceramic actuator. Using the output information from a tip force sensor, a full-order observer is constructed to estimate state variables of the system. Force tracking performances for desired trajectories represented by sinusoidal and step functions are evaluated by undertaking both simulation and experimental works. In addition, in order to illustrate practical feasibility of the proposed method, a two-fingered gripper is constructed and its performance is demonstrated by showing a capability of holding an object.
TL;DR: In this paper, a new approach of transporting a flexible beam handled by two manipulators to a desired position/orientation while suppressing its vibration, and simultaneously controlling the internalforces between the manipulators and the beam to avoid any damage on the system is presented.
Abstract: This paper presents a new approach of transporting a flexible beam handled by two manipulators to a desired position/orientation while suppressing its vibration, and simultaneously controlling the internalforces between the manipulators and the beam to avoid any damage on the system The algorithm combines impedance control and an I-type force feedback into one scheme by designing a proper response of the interaction force No information about the vibration is used in the controller The asymptotic stability is investigated by using LaSalle theorem, based on the vibration dynamics of the beam approximated by m assumed modes (m → ∞) Simulations demonstrate the validity of the proposed method
TL;DR: It is shown why ordinary sample-and-hold generates an active contact interface, and ways of improving the feeling of the interface are provided, and a suite of numerical methods for improving the performance of rendering of surfaces by force reflection are developed.
Abstract: An important problem in the field of force-reflecting systems and telerobotics is poor rendering of contact, particularly of contact with stiff surfaces. There are numerous possible sources of poor performance, including poor contact models, sampling errors, and delays due to computation or data transmission. In this paper we examine effects due to sample-and-hold, which is a fundamental property of both the discrete domain and also of the sensors and power amplifiers used in a force-reflecting system. We propose sample-and-hold be generalized to sample-estimate-hold. We show why ordinary sample-and-hold generates an active contact interface, and provide ways of improving the feeling of the interface. We have developed a suite of numerical methods for improving the performance of rendering of surfaces by force reflection. We have conducted both simulations and experiments to demonstrate the efficacy of the proposed scheme. Our contributions are a new method of digitally processing force data, and a systematic method for coupling force-processing systems that run at different rates.
TL;DR: In this paper, a technique for control system design that provides robust stability in the presence of bounded modeling errors is presented, which is a discrete-time version of a well known sliding mode control technique with saturation functions.
Abstract: This paper presents a technique for control system design that provides robust stability in the presence of bounded modeling errors The proposed method is a discrete-time version ofa well known sliding mode control technique with saturation functions that generates the boundary layer without requiring either matched uncertainties or smooth functions It is shown that the boundary layer can be made attractive and that the boundary layer thickness is bounded under mild conditions It is also shown that asymptotic stability can be guaranteed if the available model is assumed to be perfect An example is used to illustrate the proposed design technique
TL;DR: In this article, the authors demonstrate that a properly designed continuous sliding mode controller (CSLM) is capable of accuracies of better than ±02 mm and maintain performance when the load mass is varied by upwards of a factor of 10.
Abstract: Sliding mode control has been promoted as a means to overcome the nonlinearities associated with pneumatic positioning systems Previously published performance results have been disappointing with reported accuracies of only ±5 mm and poor tracking of the sliding surface New experimental results demonstrate that a properly designed continuous sliding mode controller (CSLM) is capable of accuracies of better than ±02 mm Further, the CSLM controller is able to maintain performance when the load mass is varied by upwards of a factor of 10 Direct comparison to a conventional pro-portional differential pressure controller provides evidence that CSLM is indeed more robust than comparable controllers for this application
TL;DR: In this article, a path-tracking controller for a load-haul-dump mining vehicle is designed using a geometric approach recently developed in the context of car- and tractor-trailer-like vehicles.
Abstract: A path-tracking controller for a load-haul-dump mining vehicle is designed using a geometric approach recently developed in the context of car- and tractor-trailer-like vehicles. This controller is made up of a kinematic component computing the velocities required of the vehicle for satisfactory path-tracking, and a dynamic component determining the propulsion and steering that are necessary to acquire these velocities. Prospects for practical implementation appear to be promising from an operational, a technological, and an economic point of view.
TL;DR: In this paper, a robust control strategy for the trajectory tracking control of multi-link elastic robot manipulators is proposed, where the robustness against both of the structured uncertainty caused by nonlinear mechanical structure and the unstructured one caused by elasticity of links is taken into account in designing controllers.
Abstract: In this paper, a robust control strategy is proposed for the trajectory tracking control of multi-link elastic robot manipulators. The robustness against both of the structured uncertainty caused by the nonlinear mechanical structure and the unstructured one caused by elasticity of links is taken into account in designing controllers. For this purpose the model of elastic robot manipulators is decomposed into the slow model and the fast model by using an integral manifold approach. The slow controller, which is robust against the structured uncertainty, is designed for the slow model on the basis of VSS theory. On the other hand, the fast controller, which is robust against the unstructured uncertainty, is designed for the fast model on the basis of H control theory. Then the composite control is constructed with the slow controller and the fast controller. Some results of numerical simulations are presented to show the effectiveness of this design procedure.
TL;DR: In this article, the stability and performance robustness of adaptive open-loop control algorithms with respect to structured uncertainty are derived. But the analysis of stability and robustness is restricted to the case of active magnetic bearings.
Abstract: Recent experimental results have demonstrated the effectiveness of adaptive open-loop control algorithms for the suppression of unbalance response on rotors supported in active magnetic bearings. Herein, tools for the analysis of stability and performance robustness of this algorithm with respect to structured uncertainty are derived. The stability and performance robustness analysis problems are shown to be readily solved using a novel application of structured singular values. An example problem is presented which demonstrate the efficacy of this approach in obtaining tight bounds on stability margin and worst case performance.
TL;DR: In this paper, a five-parameter nonlinear proportional and integral (PI) compensator is proposed for linear time-invariant single-input single-output (SISO) systems.
Abstract: In this paper, linear time-invariant single-input single-output (SISO) systems that are stabilizable by a (linear) proportional and integral (PI) compensator are considered. For such systems a five-parameter nonlinear PI compensator is proposed. The parameters of the proposed compensator are tuned by solving an optimization problem. The optimization problem always has a solution. Additionally, a general non-linear PI compensator is proposed and is approximated by easy-to-compute compensators, for instance, a six-parameter nonlinear compensator. The parameters of the approximate compensators are tuned to satisfy an optimality condition. The superiority of the proposed nonlinear PI compensators over the linear PI compensator is discussed and is demonstrated for a feedback system.
TL;DR: In this article, an accelerometer placement scheme to determine the angular velocities and accelerations of a rigid body is presented, and it is shown that the least number of uniaxial accelerometers required in a sensor array is nine.
Abstract: An accelerometer placement scheme to determine the angular velocities and accelerations of a rigid body is presented. We show that the least number of uniaxial accelerometers required in a sensor array to uniquely determine the angular velocities in a moving frame is nine.
TL;DR: In this paper, the authors derived the nonlinear integro-differential equations describing the transverse and rotational motions of a nonuniform Euler-Bernoulli beam with end mass attached to a rigid hub, and investigated the effects of both the linear and nonlinear elastic rotational couplings.
Abstract: The nonlinear integro-differential equations, describing the transverse and rotational motions of a nonuniform Euler-Bernoulli beam with end mass attached to a rigid hub, are derived. The effects of both the linear and nonlinear elastic rotational couplings are investigated. The linear couplings are exactly accounted for in a decoupled Euler-Bernoulli beam model and their effects on the eigensolutions and response are significant for a small ratio of hub-to-beam inertia. The nonlinear couplings with a resultant stiffening effect are negligible for small angular velocities. A discretized model, suitable for the study of large angle, high speed rotation of a nonuniform beam, is presented. The optimal control moment for simultaneous vibration suppression of the beam at the end of a prescribed rotation is determined. Influences of the nonlinearity, nonuniformity, maneuver time, and inertia ratio on the optimal control moment and system response are discussed.
TL;DR: In this paper, the authors focus on the problem of controlling the manipulator in order to track a desired object trajectory, while guaranteeing that contact forces are controlled so as to comply with contact constraints at every instant.
Abstract: Although most of the literature on manipulation systems deals with systems with as many degrees of freedom as the dimension of their task space, or even with more (redundant manipulators), kinematically defective manipulation systems are often encountered in robotics, in particular when dealing with simple industry-oriented grippers, or when the whole surface of the manipulator limbs is exploited to constrain the manipulated object, as in “whole-arm” manipulation. Kinematically defective systems differ from nondefective and redundant manipulation systems in many ways, some of which have been addressed in the literature. In this paper, we focus on one of the central problems of manipulation, i.e., controlling the manipulator in order to track a desired object trajectory, while guaranteeing that contact forces are controlled so as to comply with contact constraints (friction bounds, etc.) at every instant. We attack this problem by an unified approach that is appropriate for manipulation systems with general kinematics. When dealing with kinematically defective systems, it is not possible to assign arbitrary trajectories of object motions and contact forces. To understand what restrictions position and force reference trajectories should exhibit in order to be feasible by a given system, is the central issue of this work.
TL;DR: In this article, the authors combine finite element discretization techniques with bond graph methods to simplify the model formulation process, as compared to alternative schemes based on weighted residual solutions of the governing partial differential equations.
Abstract: A wide range of engineering problems involve porous media modeling. General porous media models are highly nonlinear, geometrically complex, and must account for energy transfer between fluid and solid constituents normally modeled in distinct Lagrangian and Eulerian reference frames. Combining finite element discretization techniques with bond graph methods greatly simplifies the model formulation process, as compared to alternative schemes based on weighted residual solutions of the governing partial differential equations. The result generalizes existing numerical models of porous media and current network thermodynamics/bond graph theory.
TL;DR: In this article, a robust controller design methodology for a class of uncertain, multivariable, regulating systems required to maintain a prespecified operating condition within hard time domain tolerances despite a vector of step disturbances is presented.
Abstract: Presented in this paper is a robust controller design methodology for a class of uncertain, multivariable, regulating systems required to maintain a prespecified operating condition within hard time domain tolerances despite a vector of step disturbances. The design methodology is a frequency domain approach and is based on sequential loop design where a Gauss elimination technique facilitates the various design steps. The specific class of systems addressed are those which can be modeled as square, multivariable systems with parametric uncertainty. One restriction imposed is that the system and its inverse are stable for all plant parameter combinations. The key features of this design methodology include (i) the design of fully populated controller matrix, (ii) the ability to design for system integrity, and (iii) the direct enforcement of hard time domain tolerances through frequency domain amplitude inequalities.
TL;DR: In this article, the predictive control law is obtained by minimizing a quadratic function of the tip tracking error, the elastic deflection, and the input torque of the flexible macro-micro manipulator.
Abstract: This paper presents a new approach to end-point trajectory control of flexible macro-micro manipulator based on nonlinear inversion and predictive control techniques. In this approach, precise control of the end-effector trajectory is accomplished by the inverse controller of the rigid micro manipulator, and the predictive controller steers the end point of the flexible macro manipulator with limited elastic oscillation. The predictive control law is obtained by minimizing a quadratic function of the tip tracking error, the elastic deflection, and the input torque of the flexible macro manipulator. The feedback parameters of the predictive controller are chosen such that zero dynamics are asymptotically stable. The combination of the inverse and the predictive controllers accomplishes precise end-effector trajectory tracking and elastic mode stabilization. These results are applied to a planar macro-micro manipulator system consisting of one flexible link and two micro rigid links. Simulation results are presented to show that in the closed-loop system time varying end point trajectory control and elastic mode stabilization are accomplished.
TL;DR: In this paper, an inversion state transformation is applied to the system so that the DRE associated with the transformed system becomes forward in the sense that its boundary condition is set at the initial time of operation (t = t 0 ).
Abstract: This paper presents a new state feedback control design for linear time-varying systems. In conventional control designs such as the LQ optimal control, the state feedback gain is calculated off-line by solving a Differential Riccati Equation (DRE) backwards with the boundary condition set at some future time. The apparent disadvantage of using a backward DRE is that future information of the system matrices is required to find the state feedback gain at every time instant. In this paper, an inversion state transformation is applied to the system so that the DRE associated with the transformed system becomes forward in the sense that its boundary condition is set at the initial time of operation (t = t 0 ). As a result, the forward DRE can be calculated on-line without using future information of the system matrices.