Journal of Dynamic Systems Measurement and Control

This paper is concerned with the problem of H∞ estimation for networked control systems. Time delays and packet dropouts are considered simultaneously. The occurrence probability of each time delay is considered. The packet dropouts have the Bernoulli distributions. The system is modeled as Markovian jump linear systems with partly unknown transition probability. State observer is designed to estimate the practical state with H∞ feature. The estimation problem is cast into a set of linear matrix inequalities. An example is provided to illustrate the effectiveness and applicability of the proposed method.

This paper investigates fundamental performance limitations in the control of a combine harvester's header height control system. There are two primary subsystem characteristics that influence the achievable bandwidth by affecting the open loop transfer function. The first subsystem is the mechanical configuration of the combine and header while the second subsystem is the electrohydraulic actuation for the header. The mechanical combine + header subsystem results in an input-output representation that is underactuated and has a noncollocated sensor/actuator pair. The electrohydraulic subsystem introduces a significant time delay. In combination, they each reinforce the effect of the other thereby exacerbating the overall system limitation of the closed loop bandwidth. Experimental results are provided to validate the model and existence of the closed loop bandwidth limitations that stem from specific system design configurations.

Since torque in harmonic drives is transmitted by a pure couple, harmonic drives do not generate radial forces and therefore can be instrumented with torque sensors without interference from radial forces. The installation of torque sensors on the stationary component of harmonic drives (the Flexipline cup in this research work) produce backdrivability needed for robotic and telerobotic compliant maneuvers. Backdrivability of a harmonic drive, when used as torque increaser, means that the output shaft can be rotated via finite amount of torque. A high ratio harmonic drive is non-backdrivable because its output shaft cannot be turned by applying a torque on it. This article first develops the dynamic behavior of a harmonic drive, in particular the non-backdrivability, in terms of a sensitivity transfer function. The instrumentation of the harmonic drive with torque sensor is then described. This leads to a description of the control architecture which allows modulation of the sensitivity transfer function within the limits established by the closed-loop stability. A set of experiments on an active hand controller, powered by a DC motor coupled to an instrumented harmonic drive, is given to exhibit this method's limitations.

This article describes the dynamics, control, and stability of extenders, robotic systems worn by humans for material handling tasks. Extenders are defined as robot manipulators which extend (i.e., increase) the strength of the human arm in load maneuvering tasks, while the human maintains control of the task. Part of the extender motion is caused by physical power from the human; the rest of the extender motion results from force signals measured at the physical interfaces between the human and the extender, and the load and the extender. Therefore, the human wearing the extender exchanges both power and information signals with the extender. The control technique described here lets the designer define an arbitrary relationship between the human force and the load force. A set of experiments on a two-dimensional non-direct-drive extender were done to verify the control theory.

It is important to monitor the radial loads in hydropower units in order to protect the machine from harmful radial loads. Existing recommendations in the standards regarding the radial movements of the shaft and bearing housing in hydropower units, ISO-7919-5 (International Organization for Standardization, 2005, "ISO 7919-5: Mechanical Vibration-Evaluation of Machine Vibration by Measurements on Rotating Shafts-Part 5: Machine Sets in Hydraulic Power Generating and Pumping Plants," Geneva, Switzerland) and ISO-10816-5 (International Organization for Standardization, 2000, "ISO 10816-5: Mechanical Vibration-Evaluation of Machine Vibration by Measurements on Non-Rotating Parts-Part 5: Machine Sets in Hydraulic Power Generating and Pumping Plants," Geneva, Switzerland), have alarm levels based on statistical data and do not consider the mechanical properties of the machine. The synchronous speed of the unit determines the maximum recommended shaft displacement and housing acceleration, according to these standards. This paper presents a methodology for the alarm and trip levels based on the design criteria of the hydropower unit and the measured radial loads in the machine during operation. When a hydropower unit is designed, one of its design criteria is to withstand certain loads spectra without the occurrence of fatigue in the mechanical components. These calculated limits for fatigue are used to set limits for the maximum radial loads allowed in the machine before it shuts down in order to protect itself from damage due to high radial loads. Radial loads in hydropower units are caused by unbalance, shape deviations, dynamic flow properties in the turbine, etc. Standards exist for balancing and manufacturers (and power plant owners) have recommendations for maximum allowed shape deviations in generators. These standards and recommendations determine which loads, at a maximum, should be allowed before an alarm is sent that the machine needs maintenance. The radial bearing load can be determined using load cells, bearing properties multiplied by shaft displacement, or bearing bracket stiffness multiplied by housing compression or movement. Different load measurement methods should be used depending on the design of the machine and accuracy demands in the load measurement. The methodology presented in the paper is applied to a 40 MW hydropower unit; suggestions are presented for the alarm and trip levels for the machine based on the mechanical properties and radial loads.

A design methodology capable of dealing with nonlinear systems containing parameter uncertainty is presented. A generalized sensitivity analysis is incorporated which utilizes sampling of the parameter space and statistical inference. For a system with j adjustable and k nonadjustable parameters, this methodology (which includes an adaptive random search strategy) is used to determine the combination of j adjustable parameter values which maximizes the probability of the performance indices simultaneously satisfying design criteria given the uncertainty in the k nonadjustable parameters.

In many practical applications unbalanced rotating machinery cause vibrations that transmit large oscillatory forces to the system foundation. Using ad hoc optimization schemes tuned isolators and absorbers have traditionally been designed to suppress system vibration levels by attempting to minimize the peak frequency response of the force/displacement transmissibility system transfer function. In this paper we formulate the classical isolator and absorber vibration suppression problems in terms of modern system theoretic criteria involving H₂ (shock response), mixed H₂/H_∞ (peak frequency response), and mixed H ₂/L₁ (worst-case amplitude response) performance measures

In this paper the application of the damped least-squares method to the resolved-acceleration control is experimentally examined on a 2-DOF planar manipulator In order to decrease the position error introduced by the damping, only small singular values are damped. The symbolical expressions of the singular value decomposition of the Jacobian matrix were utilized in order to decrease the computational burden. Position error along the work-space boundary was only 15% greater than along the trajectories inside the reachable workspace

Although serial manipulator arms modeled with rigid links show full system controllability in the joint space, this condition does not necessarily hold for flexible robotic systems. In particular, in certain robot configurations, called inaccessible robot positions, one or more of the flexibilities may not be accessed directly by the actuators. This condition deteriorates system performance as reported earlier by the authors (Tosunoglu et al., 1988, 1989). The present study addresses the relationship between the accessibility and controllability concepts and establishes accessibility as a distinct concept from controllability. Although the theoretical framework is developed for n-link, spatial manipulators modeled with m oscillation components, example case studies demonstrate the concepts on one- and two-link arms for brevity. Specifically, it is shown that although in accessibility and uncontrollability may coincide in certain instances (as shown on a one-like arm), counter examples may be found where an arm in an inaccessible position can simultaneously demonstrate full system controllability (as shown on a two-link arm).

This paper presents a new adaptive controller designed for rigid-body robots including motor dynamics. The effects of motor dynamics have attracted attentions from a number of researchers. The available controllers able to ensure stable tracking in the presence of motor dynamics need acceleration feedback, or at least an acceleration observer. This means additional computing power and expenses in the hardware implementation. The proposed adaptive controller does not need an observer to avoid the acceleration feedback. It generates a continuous control signal with its closed-loop stability proven in the Lyapunov sense

In the absence of plant parameter uncertainty feedforward controllers can be synthesized to achieve perfect continuous tracking. When a plant has uncertainties it is in general impossible to achieve such perfect tracking. Investigated in this paper is the role played by feedforward controllers in the presence of plant uncertainties. The authors show that the use of feedforward controllers cannot improve the tracking error beyond what is achievable with a properly designed feedback loop, over all plant uncertainties. Including preview in the feedforward will not alter the situation either. The authors present two methods of designing robust compensators so that the tracking error due to uncertainties will be made small in some sense in the frequency domain and will have zero error in the steady state.

We propose a new control strategy for on-off valve controlled pneumatic actuators and robots with focus on the position accuracy. A mathematical model incorporating pneumatic process nonlinearities and nonlinear mechanical friction has been developed to characterize the actuator dynamics; this model with a few simplifications is then used to design the controller. In our control scheme, one valve is held open and the other is operated under the pulse width modulation mode to simulate the proportional control. An inner loop utilizing proportional-plus-integral control is formed to control the actuator pressure, and an outer loop with displacement and velocity feedbacks is used to control the load displacement. Also, a two staged feedforward force is implemented to reduce the steady state error due to the nonlinear mechanical friction. Experimental results on a single degree of freedom pneumatic robot indicate that the proposed control system is better than the conventional on-off control strategy as it is effective in achieving the desired position accuracy without using any mechanical stops in the actuator.

A two degree of freedom vehicle model is analyzed for its performance sensitivity as a function of the system's feedback gains. Three measures of performance, namely, sprung mass isolation, suspension travel, and tire contact force variation are examined. The varied feedback gains are the spring stiffness, the passive damping coefficient, and the active damping coefficient. Both frequency response and RMS response of the performance variables are considered and surfaces are formed to examine output sensitivity to suspension feedback. The results show that RMS vehicle isolation is increased by both softening the suspension and adding active damping.

In this paper an implementation of an adaptive control law for a pneumatic actuator is presented. Pneumatic actuators are of particular interest for robotic applications because of their large force output per unit weight, and their low cost. Stabilization of a pneumatic actuator is difficult if a high bandwidth closed-loop system is desired. This is because of the compressibility of air, and of the nonlinear characteristics of air flowing through a variable area orifice. Further complications arise from the geometry of the mechanism because the equations of motion are highly nonlinear. The order of the dominant dynamics is shown to vary with the position of the mechanism.

Hydraulic servovalve controlled systems contain many time-varying dynamic characteristics that are difficult to model. Controllers for such systems must either adapt to these changing parameters or be robust enough to handle the parameter variations. In order to achieve the highest possible bandwidth, an adaptive controller is developed for the system that uses full-state feedback for simultaneous parameter identification and tracking control. This controller takes into account the hydraulic fluid compressibility with an online identification scheme. Experimental results demonstrate a four fold improvement in bandwidth as compared to a conventional fixed gain proportional controller

Deals with asymptotic tracking of linear systems with actuator saturation in the presence of disturbances. Both reference inputs and disturbances are assumed to belong to a class which may be regarded as the zero-input response of a linear system. The controller includes an anti-windup term which reduces the degradation in the system performance due to saturation. The stability of the overall system is established based on the Lyapunov stability theory. The proposed scheme is evaluated for a two axis motion control system by simulation

A closed form solution for the time optimal control of a dual actuator disc drive system that takes into account the physical constraint limiting the relative motion of the fine and coarse actuator has been derived. The result is useful for determining track seeking strategies for high performance optical discs. The application of the necessary conditions to a simplified model of the compound actuator is presented and a solution derived.

This paper describes a new approach to the control of heating, ventilating and air-conditioning(HVAC) system. In the conventional method for controlling HVAC systems, the occupant adjusts the reference input whenever the condition are uncomfortable. The reference input must be periodically adjusted because the controlled variable does not accurately reflect the comfort of the specific occupant. The fundamental concept of the approach described in this paper is that the controller learns to predict the actual thermal sensation of the specific use by tuning parameters of a model of thermal sensation. The parameters are adjusted with respect to the actual thermal sensation ratings of the specific occupant so that with time the model accurately reflects the comfort of the specific occupant. The stability of the controller is maintained by utilizing a priori information about the parameters of the model of thermal sensation. The method is implemented on a residential heat pump air conditioner. Experiments using human subjects verify the usefulness and feasibility of the method.

Some examples of low-order adaptive controllers are considered. Simple arguments are used to show that the instability properties of adaptive controllers are not necessarily the result of some unmodeled dynamics. The particular low-order adaptive controllers maintain stability within the same admissible gain bounds as the corresponding stationary linear controllers. Solutions are proposed to improve robustness of adaptive controllers

An adaptive sliding mode control design method is proposed for discrete nonlinear systems where explicit knowledge of the system dynamics is not available. Three layer feedforward neural networks are used as function approximators for the unknown dynamics. The control law is designed based on the outputs of the approximators, and the sliding surface is chosen as a stable polynomial of the system outputs. Convergence of the state trajectories into a small sliding sector is proved. The method is applied to the internal combustion (IC) engine idle speed control problem. Simulation and experimental results are provided

This paper presents the development of a resolved motion adaptive control which adopts the ideas of "resolved motion rate control" [4] and "resolved motion acceleration control" [6] to control a manipulator in Cartesian coordinates for various loading conditions. The proposed adaptive control is performed at the hand level and is based on the linearized perturbation system along a desired hand trajectory. The controlled system is characterized by feedforward and feedback components which can be computed separately and simultaneously. The feedforward component resolves the specified positions, velocities, and accelerations of the hand into a set of values of joint positions, velocities, and accelerations from which the nominal joint torques are computed using the Newton-Euler equations of motion to compensate all the interaction forces among the various joints. The feedback component consisting of recursive least square identification scheme and an optimal adaptive self-tuning controller for the linearized system computes the perturbation torques which reduce the manipulator hand position and velocity errors along the nominal hand trajectory. The feasibility of implementing the proposed adaptive control using present day low-cost microprocessors is explored.

This paper describes, an adaptive fuzzy sliding mode control (AFSMC) method applied to the control of the vertical motion of a minehunting ROV (remotely operated vehicle). The effects of parameter variation of the ROV are considered, and performance and robustness to uncertainty is assessed. The proposed control methodology addresses the fundamental issues of stability, performance requirements and model variation within a single framework. The effectiveness of the technique is demonstrated by its ability to decouple pitch and heave of the ROV subjected to parameter variation

An adaptive control scheme is proposed for controlling a certain class of nonlinear, uncertain systems. When a local approximation of the nonlinear system function using its Taylor's expansion is possible, this scheme provides an adaptation law to estimate such an approximation. With the help of a properly designed sampling rule, the neighborhood of approximation can be moved from time to time in order to capture the fast changing system dynamics. Several modifications are also made in the control law to avoid exciting the un-modelled dynamics, to reduce the noise sensitivity and to accommodate various signal levels in the system response. Performance and important features of the proposed controller are illustrated through simulations of some dynamic systems

The conventional linear digital control fails to provide precise positioning of a control object under the influence of static friction, Coulomb friction and backlash. This paper presents an adaptive pulse width control (PWC) scheme. This scheme is developed based on the relationship between the displacement of a control object due to a single pulse input and the pulse width. The coefficient appearing in this relationship is estimated by a parameter adaptation algorithm. Sufficient conditions for asymtotic stability of this adaptive scheme is developed using Popov hyperstability theorem. This adaptive PWC is tested on a laboratory positioning table and is shown to be effective.

A systematic way to combine an adaptive control design technique and sliding mode control methodology for trajectory tracking control of robot manipulators in the presence of parametric uncertainties and external disturbance is developed in this paper. Continuous sliding mode controllers without the unpleasant reaching transient and chattering problem are first developed by using a dynamic sliding mode. Transient performance is guaranteed and globally uniform ultimate boundedness (GUUB) stability is obtained. A conventional adaptive scheme is also developed for comparison. With some modifications to the conventional adaptation law, the control law is redesigned by combining the design methodologies of adaptive control and sliding mode control. The suggested controller preserves the advantages of both methods, namely, asymptotic stability of adaptive systems for parametric uncertainties and GUUB stability with guaranteed transient performance of sliding mode control for both parametric uncertainties and external disturbances. The control law is continuous and the chattering problem of sliding mode control is avoided. A priori knowledge of the bounds of the parameter uncertainties and external disturbances is assumed. Experimental results illustrate the effectiveness of the proposed methods.

A problem common to all mechanical systems with rotating shafts, including active magnetic bearing (AMB) systems, is the synchronous vibration caused by mass unbalance. Autobalancing compensation case AMB actuators to spin a rotor about its inertial axis and thus eliminate the centrifugal forces due to mass unbalance. However, because mass unbalance is modelled as a sinusoidal sensor disturbance occurring below loop bandwidth frequency, no available compensation method reduces vibration yet preserves the desired loop frequency response. Adaptive forced balancing (AFB) solves this problem and has been applied to single-end, AMB suspensions¿the SISO case. This paper extends AFB compensation to the MIMO case. Simulations of a double-end, AMB suspension verify the success of our method.

The design of a stable adaptive controller and observer for a class of nonlinear systems is considered. Stable adaptive observer designs in the existing literature are generally based on the assumption that the nonlinearities in the system dynamics are functions of measured variables and inputs. In this work, a broader class of nonlinear systems that contain the product of an unmeasurable state and an unknown parameter are considered. The nonlinear system is transformed into a suitable form which allows for the design of a stable adaptive controller and a stable nonlinear observer using a parameter dependent Lyapunov function. The design process is shown on a simple example and then extended to the general case. Simulation results on two distinct examples are shown and discussed for the proposed scheme.

A PUMA 560 industrial robot has been retrofitted with an open-architecture controller. An adaptive control scheme that incorporates actuator dynamics has been implemented on this robot testbed. The overall low level control scheme is based on the complete robot-actuator dynamics, and consists of a modified regressor-based adaptive algorithm and a feedforward compensation scheme for actuator dynamics. It is shown by a Lyapunov-like analysis that, under this control scheme, the tracking error of a general robot is bounded. Experiments carried out show that the performance of the robot, with the adaptive control scheme, is significantly improved when properly compensated for actuator dynamics.

This paper considers the implementation of an adaptive algorithm for periodic disturbance cancellation. It is shown that the maximum rate of adaptation can be calculated precisely based on measurements of the system's frequency response. The response of the closed-loop system to additional disturbances can also be computed on that basis. The results are verified experimentally on a high track density magnetic disk drive. Excellent matching between the theoretical and experimental results is observed. An improved method is also proposed that leads to faster convergence of the adaptive algorithm and better disturbance rejection capabilities. The results of this paper significantly enhance the ability of the control engineer to design and analyze adaptive feedforward algorithms for a variety of applications where periodic disturbances are encountered.

The slewing motion of a truss arm driven by a V-gimbaled control-moment-gyro is studied. The V-gimbaled control-moment-gyro consists of a pair of gyros that must precess synchronously. The feedback linearization technique is utilized to partially linearize the nonlinear nominal model, where two specific output functions are chosen to satisfy the system tracking and synchronization requirements. The system tracking dynamics are bounded by properly determining system indices and command signals. For the partially linearized system, the backstepping tuning function design approach is employed to design an adaptive nonlinear controller. The dynamic order of the adaptive controller is reduced to its minimum. The performance of the proposed controller is verified by simulation.

An advanced control strategy, based on the principles of Self-Adjusting Model Algorithmic Control (SAMAC), for regulating the energy input to a nonlinear electric arc furnace system is presented in this paper. The SAMAC strategy is an extension of Model Algorithmic Control (MAC) designed to accommodate the nonlinear and time-varying characteristics of the arc furnace process. Simulation results show that SAMAC yields an improved performance over both the traditional MAC strategy and a conventional analog control system (typical of many existing furnace installations) in terms of commonly used classical measures of response characteristics, including speed of response, settling time, overshoot, cumulative error, and sensitivity to variations in plant parameter values (robustness).

This paper deals with the development of a fault-free model of the pneumatic subsystem Of an air brake system that is used in commercial vehicles. Our objective is to use this model in brake control and diagnostic applications. The development of a diagnostic system would be useful in automating enforcement inspections and also in monitoring the condition of the brake system in real-time. This paper presents a detailed description of the development of this model and of the experimental setup used to corroborate this model for various realistic test runs.

This paper deals with the response of a distributed air transmission line with laminar flow subjected to an impulse, step, or arbitrary periodic excitation. The rational is based on the inverse Fourier transform: R(¿) = F^-1 {G(j¿) * P 1 (j¿)} where R(¿) is the response, G(j¿) the system frequency function, and P 1 (j¿) the frequency spectrum of the input function. For input flow prediction, G(j¿) is the input admittance. G(j¿) represents the transfer function for pressure calculation. The predicted dynamics of a blocked and an open line subjected to arbitrary periodic excitation are compared with experimental measurements.

This paper presents a control theory, for a large class of nonlinear systems, including analog, digital, and hybrid systems. The control theory is developed from a new system model that can be used to model nonlinear systems that cannot be modeled with the state space equations.

An approach is presented for the analysis and design of controllers and observers for high-dimensional systems using pole allocation and matrix perturbation theory. Development of a feedback control law that leads to a desired closed-loop configuration is a prohibitive task computationally, especially for large-order systems. Existing pole allocation algorithms can handle only low-order models. In this paper, matrix perturbation theory is used to provide an estimate of the system eigensolution, which is consequently used to analyze and design the closed-loop controller. The accuracy of the control (or observer) design depends on how small a perturbation the controls (or observer gains) are on the uncontrolled system, and it is assessed qualitatively by considering Gerschgorin's disks and the system eigensolution.

The problem of explicitly determining the worst persistent input disturbance that a closed loop system can tolerate under prespecified state and control constraints is studied. Verification of designs specifically aimed at maximizing the size of persistent bounded disturbances while satisfying system constraints, typically requires extensive simulations because the exact nature of the worst input is not known. In this paper the exact nature of the worst input is completely characterized for both SISO and MIMO cases. A finite number of specific impulse responses of the closed loop system determines the worst persistent input disturbance. In the case of a SISO system with n state constraints (|x i | ¿ ß i ), a, control constraint (|u| ¿ ß u ) and an output constraint (|y| ¿ ß o ), n + 2 impulse responses are generaly needed. With this new result the large number of simulations that is typically needed for design verification can be significantly reduced. Three examples illustrate how the new characterization can be utilized.

This paper uses almost decoupling theory to obtain a systematic solution to the MIMO-QFT problem by an n times solution of the SISO-QFT sensitivity constraint problem. This is in contrast to the current MIMO-QFT formulation that requires an n² times solution for the elements of the closed loop transfer matrix. The problem is also in a form where direct comparison with H^¿ control is feasible. However, due to the use of unstructured perturbation description, this design route along with all H^¿ based design methods will invariably produce more conservative (higher bandwidth) controllers than classical QFT.

A two degree of freedom (1/4 car model) is used to evaluate alternative linear control laws. Control laws considered are full state feedback, sprung mass absolute velocity feedback and an LQG regulator using suspension defelection as the measurement. It is shown that all three can yield improvements to the sprung mass ride quality but that overall the LQG regulator using suspension deflection provides the best trade-off between ride quality, suspension packaging and road holding constraints.

In this work, we consider the control of platoons of cooperating nonholonomic vehicles. Using techniques based on redundant manipulator control, the platoon is treated as a single entity with a set of platoon-level objectives. The class of tricyclelike robots, with limits on steering and speed, is chosen because it represents a vast class of real, nonholonomic vehicles beyond the basic differential drive. The method presented uses platoon redundancy to limit the impact of vehicle constraints on the platoon-level objectives. A simulation study is presented to show the efficacy of the method.

A nonlinear, lumped parameter pantograph model including geometric and coulomb friction nonlinearities and variable stiffness has been developed. The model performance has been compared with experimental dynamic response data measured on a prototype pantograph. Responses of the model and the experimental data including subharmonic and harmonic resonances are in close agreement for motions excited by comparable forcing functions for input frequencies of 0 to 12 Hz. The model has been used to identify the primary parameters and nonlinear effects which influence dynamic pantograph performance.

Modeling of heat exchangers using true bond graphs with temperature and rate of change of entropy as power variables is presented. Techniques used for modeling of irreversabilities and compressible flows are shown. The results of two and three lump models are compared with experimental results, with the agreement between these low order models and the experimental results being good. This paper shows how well a three lump model (6th order) can predict the dynamics of an actual reversal of flow. Heat exchanger response to mass flow rate oscillation is presented.

Catastrophic and premature bearing failure caused by excessive thermally-induced bearing preload is a major design problem for spindle bearings of high-speed machine tools. Due to a lack of a low cost and easy to maintain on-line preload measuring technique, the traditional solution is to limit the maximum spindle speed and the initial bearing preload. This solution is incompatible with the need to increase machining productivity, which requires increasing the spindle speed, and product quality (surface finish, dimensional accuracy), which requires increasing (or at least not decreasing) the preload to keep the spindle system stiff. This paper proposes a solution that is compatible with increased productivity and quality. A dynamic state observer has been developed based on a preload model derived from physical laws of heat transfer and thermoelasticity to estimate the spindle bearing preload via low cost thermocouples attached to the bearing outer ring and the spindle housing. A systematic procedure to determine the observer gains is developed to account for modeling errors, unknown parameters, nonlinearities, and measurement noise. The modeling errors are particularly significant in this problem because factors like bearing skidding, wear, and lubricant deterioration are not easily modeled, and the observer must be designed to be insensitive to them. A unique modeling error compensator idea is introduced to null-out the modeling errors. The preload observer has been successfully validated on two different bearing configurations for a wide range of speeds and running conditions.

The simplest technique of decoupling the normalized equations of motion of a linear nonclassically damped second-order system is to neglect the off-diagonal elements of the normalized damping matrix. In this paper, the error introduced in the system response due to this decoupling technique is studied. Conditions are derived under which the solution of an approximately decoupled system is "close" to the exact solution of the system.

Computer numerically controlled (CNC) multi-axis bending is a new metal forming technology used to fabricate long slender structural workpieces of arbitrary shape and cross section. Although this process can achieve high levels of flexibility and productivity over conventional forming processes, generating a control program to produce a desired shape is a laborious process involving the trial-and-error by a skilled engineer. A systematic method was developed to replace the manual control method. Since multi-axis bending is inherently a local deformation process, the concept of intrinsic part representation from differential geometry is applied as a basis to develop the part geometric model and process model. After being compensated for springback and die offset, the model is used to compute a set of initial control commands. The effectiveness of the model is demonstrated experimentally.

A dynamical model and a control architecture are developed for the closed-chain motion of two N -joint manipulators holding a rigid object in a three-dimensional workspace. Dynamic and kinematic constraints are determined and combined with the equations of motion of the manipulators to obtain a dynamical model of the entire system in the joint space. Reduced-order equations of motion and a functional relation for the generalized contact forces are developed. The problem of solving the reduced-order model for the forward and inverse dynamics is discussed. Control laws are determined so as to decouple the force-controlled and position-controlled degrees of freedom during motion of the system

The results of a study on the combined joint motion control, vibration control, and force control of a constrained rigid-flexible robot arm for both regulation and tracking are presented. A nonlinear modified Corless-Leitmann controller is proposeed for control of the flexible motion using only joint actuators. Experimental studies, which demonstrate the effectiveness of the proposed method, are described.

A new actuation method for one-link flexible arms is presented. The endpoint control of a flexible arm has been known to be a nonminimum phase system due to the noncollocated sensor and actuator. By relocating the actuator near the endpoint, the system can be changed to a minimum phase system. In order to implement this, transmission mechanisms are developed which transform the actuator torque to appropriate force and torque and transmit them to an appropriate point on the arm link. Exact pole-zero configurations are analyzed with regard to the location of the actuation point and the type of transmissions. We then develop an integrated design method, which allows for relocating zeros for an improved control performance. A prototype flexible arm is designed based on the design guidelines and open loop and closed loop tests are made to verify the effectiveness.

A manipulator design theory for reduced dynamic complexity is presented. The kinematic structure and mass distribution of a manipulator arm are designed so that the inertia matrix in the equation of motion becomes diagonal and/or invariant for an arbitrary arm configuration. For the decoupled and invariant inertia matrix, the system can be treated as linear, single-input, single-output systems with constant parameters. As a result, the control of the manipulator arm is simplified, and, more importantly, control performance can be improved due to the reduced dynamic complexity. First, the problem of designing such an arm with the decoupled and/or configuration-invariant inertia matrix is defined. The inertia matrix is then analyzed in relation to the kinematic structure and mass properties of the arm links. Necessary conditions for the manipulator arm to possess a decoupled and/or configuration-invariant inertia matrix are obtained. Using the necessary conditions, we find the kinematic structure and mass properties for which the inertia matrix reduces to a constant, diagonal form. For 2 and 3 degree-of-freedom arms, possible arm designs for decoupled and/or invariant inertia matrices are then determined.

This paper presents an optimal solution to the problem of tracking controller design for a category of direct-drive robot arms, mechanically constructed to have invariant and decoupled joint actuator dynamics. For good tracking behavior, the controller uses future reference positions of a joint to anticipate the changes in reference velocity. An explicit acceleration feedforward term is avoided improving the power to noise ratio of the control signal. For good regulation behavior, the controller uses position and velocity feedback. An integral of error term is also avoided, reducing the probability of the occurence of limit cycle oscillations caused by saturation of the actuator torque rating.

We present a model for an array of microcantilevers that are used in atomic force microscopy and nano-scale manufacturing. The microcantilevers are connected to each other through a common base, and are individually actuated. The sensors are also integrated on each microcantilever. This system is an example of a spatially-invariant system with a distributed array of sensors and actuators. We exploit the spatial invariance of the problem to design optimal H₂ controllers for this array. An analytic expression for the optimal controller is derived in the transformed domain, and estimates of the coupling range of the controller is obtained