Actuator Noise Research Articles

Distributed boundary coverage with a team of networked miniature robots using a robust market-based algorithm

We study distributed boundary coverage of known environments using a team of miniature robots. Distributed boundary coverage is an instance of the multi-robot task-allocation problem and has applications in inspection, cleaning, and painting among others. The proposed algorithm is robust to sensor and actuator noise, failure of individual robots, and communication loss. We use a market-based algorithm with known lower bounds on the performance to allocate the environmental objects of interest among the team of robots. The coverage time for systems subject to sensor and actuator noise is significantly shortended by on-line task re-allocation. The complexity and convergence properties of the algorithm are formally analyzed. The system performance is systematically analyzed at two different microscopic modeling levels, using agent-based, discrete-event and module-based, realistic simulators. Finally, results obtained in simulation are validated using a team of Alice miniature robots involved in a distributed inspection case study.

μ Control for Satellites Formation Flying

In this paper, a μ controller is designed for a satellite formation flying system around the Earth based on an uncertainty model derived from a nonlinear relative position equation. In this model, nonzero eccentricity and varying semimajor axis are included as parametric uncertainties. J2 perturbation, atmospheric drag, and actuation and sensor noise are bounded by functional uncertainties. The μ controller design based on the nominal mission (an 800 km altitude circular reference orbit) is capable of achieving desired performance, is robust to uncertainties, and satisfies fuel consumption requirements even in a challenge nonnominal mission (a 0.1 eccentricity and 7,978 km semimajor axis elliptic reference orbit) with the same control gain. In this nonnominal mission, the designed μ controller is able to keep formation with almost the same level of the ΔV budget (43.86 m∕s∕year) as used in the nominal mission (39.65 m∕s∕year) . For comparison, linear quadratic regulator (LQR) and sliding mode controllers ...

Kalman Based Finite State Controller for Partially Observable Domains

A real world environment is often partially observable by the agents either because of noisy sensors or incomplete perception. Moreover, it has continuous state space in nature, and agents must decide on an action for each point in internal continuous belief space. Consequently, it is convenient to model this type of decision-making problems as Partially Observable Markov Decision Processes (POMDPs) with continuous observation and state space. Most of the POMDP methods whether approximate or exact assume that the underlying world dynamics or POMDP parameters such as transition and observation probabilities are known. However, for many real world environments it is very difficult if not impossible to obtain such information. We assume that only the internal dynamics of the agent, such as the actuator noise, interpretation of the sensor suite, are known. Using these internal dynamics, our algorithm, namely Kalman Based Finite State Controller (KBFSC), constructs an internal world model over the continuous belief space, represented by a finite state automaton. Constructed automaton nodes are points of the continuous belief space sharing a common best action and a common uncertainty level. KBFSC deals with continuous Gaussian-based POMDPs. It makes use of Kalman Filter for belief state estimation, which also is an efficient method to prune unvisited segments of the belief space and can foresee the reachable belief points approximately calculating the horizon N policy. KBFSC does not use an “explore and update” approach in the value calculation as TD-learning. Therefore KBFSC does not have an extensive exploration-exploitation phase. Using the MDP case reward and the internal dynamics of the agent, KBFSC can automatically construct the finite state automaton (FSA) representing the approximate optimal policy without the need for discretization of the state and observation space. Moreover, the policy always converges for POMDP problems.

Extensive study on the control of centrifugal compressor surge

This paper reports the results of an extensive study concerning surge instability in an industrial compression system and its dynamic suppression. Both numerical simulations and experiments have been used to analyse the system behaviour under unstable operating conditions and to compare different control devices for surge suppression. First, the characterization of surge is performed over the whole unstable operating range of a compression system based on a four-stage centrifugal compressor. The unsteady energy associated with the surge cycle is employed as an index of the surge intensity to allow for a quantitative approach to the problem. Subsequently, the behaviour and performance of a passive-type control system and of an active-type one are analysed and compared. The former consists of an innovative device based on an oscillating water column, whereas the latter is a high-gain type of feedback device implemented digitally. Experimental data show that the proposed passive device is effective not only in inhibiting surge development, but also in suppressing fully developed instability. The active device turns out to be more effective than the passive one, but under severe conditions it may fail because of actuator limitations and noise amplification. Finally, the relative merits and limitations of the two control systems are discussed with reference to their effectiveness range, flexibility, steady-state performance, installation, maintenance, and costs.

Covariance-based hardware selection-Part I: globally optimal actuator selection

A new covariance based formulation of the actuator selection problem is presented. The proposed optimization problem is aimed at finding the set of minimum cost actuator arrays such that there exists a linear feedback for which all closed-loop signals will satisfy pre-specified variance bounds. Through a linear matrix inequality (LMI) based transformation we exactly convert the original problem into a computationally attractive mixed integer convex program (MICP). The resulting MICP leads to the first computational scheme capable of calculating globally optimal solutions to the covariance based actuator selection problem. It is further shown that the formulation is general enough to incorporate extensions to the actuator noise and actuator dynamics cases. Finally, a set of examples are presented to illustrate the scheme as well as the scalability of required computational effort.

Modeling and sensorless control of an electromagnetic valve actuator

This paper presents the modeling and control of an electromagnetic valve actuator. The model is nonlinear and takes into account secondary nonlinearities like hysteresis, saturation, bounce and mutual inductance. Experimental methods for identifying parameters of the model are presented. Sliding mode control is utilized to reduce the seating velocity of the plunger as it strikes the core housing. This reduces actuator noise due to the high impact velocity of the plunger. In order to eliminate the need for position and velocity sensors, a nonlinear observer is developed that only employs coil current measurement. The position estimate is used as feedback to track a desired trajectory. The control objective is to minimize energy consumption and to reduce the seating velocity, which should improve actuator fatigue life and reduce impact noise. Simulation and experimental results are presented for an actuator designed and built in our laboratory. The experimental results show very good agreement with the analytical model.

Quasi‐Optimal Robust Stabilization of Control Systems

In this paper, we investigate the problem of semiglobal minimal time robust stabilization of analytic control systems with controls entering linearly, by means of a hybrid state feedback law. It is shown that in the absence of minimal time singular trajectories, the solutions of the closed‐loop system converge to the origin in quasi‐minimal time (for a given bound on the controller) with a robustness property with respect to small measurement noise, external disturbances, and actuator noise.

Robust optimal stabilization of the Brockett integrator via a hybrid feedback

The problem of semi-global minimal time robust stabilization of the Brockett integrator (also called Heisenberg system) is addressed and solved by means of a hybrid state feedback law. It is shown that the solutions of the closed-loop system converge to the origin, in quasi-minimal time (for a given bound on the controller), with a robustness property with respect to small measurement noises, external disturbances and actuator noises.

Unknown input proportional multiple-integral observer design for linear descriptor systems: application to state and fault estimation

In this note, the problem of observer design for linear descriptor systems with faults and unknown inputs is considered. First, it is considered that the fault vector function f is s~ times piecewise continuously differentiable. If the s~th time derivative of f is null, then s~ integral actions are included into a Luenberger observer, which is designed such that it estimates simultaneously the state, the fault, and its finite derivatives face to unknown inputs. Second, when the fault is not time piecewise continuously differentiable but bounded (like actuator noise) or s~th time derivative of fault is not null but bounded too, a high gain observer is derived to attenuate the fault impact in estimation errors. The considered faults may be unbounded, may not be determinist, and faults and unknown inputs may affect the state dynamic and plant outputs. Sufficient conditions for the existence of such observer are given. Results are illustrated with a differential algebraic power system.

Minimization of tape transient disturbances in track following tape drives with a disturbance observer

The primary purpose of the head servo in the track following tape drives is to track follow as accurately as possible during read/write operations in spite of disturbances such as tape edge movements or tape transients, internal and external vibrations transmitted to the head actuator and signal noise and dropouts. The track following and fine positioning is done using a position error signal (PES). Feedback controller design using proportional-integral-derivative (PID), lead-lag or estimator/controller techniques are used for maintaining accurate track following. This paper assumes that in addition to the PES signal, a head position signal is available for long seek, short seek, and track identification tasks, etc. In this paper, the development of a disturbance observer that supplements the nominal head servo controller in minimizing the effects of the tape transients is presented. The PES and the head position error signals are blended to provide a measure of the tape transient disturbance. This paper presents the theory of the disturbance observer and analyses to show the range of frequencies over which the disturbance observer will be effective. Finally, simulation results are presented for tape transients of various frequencies.

Robust stabilization of chained systems via hybrid control

The problem of global robust exponential stabilization of nonholonomic chained systems is addressed and solved by means of a hybrid state feedback control law. It is shown that the control law yields global exponential stability and global robustness against a class of small measurement errors, actuator noises and exogenous disturbances.

Noise-induced bias in last principal component modeling of linear system

Last principal component (LPC) modeling relies on principal component transformation, and utilizes the eigenvectors associated with the last (smallest) principal components. When applied to experimental data, it may be considered an alternative to least squares based estimation of model parameters. Experimental results in the literature (cited in the body of the paper) suggest that LPC modeling is inferior to LS, in terms of estimation bias, in the presence of noise. Other results show that LPC produces unbiased estimates only in a very special case. In this paper, we derive explicit expressions for noise-induced bias in LPC-based identification. We investigate static systems with input actuator and measurement noise, and discrete dynamic systems with output measurement noise. We show that, indeed, LPC-based estimates are biased even when LS-based ones are not, and when the LS estimate is also biased, the LPC estimate has the LS bias plus an additional term. The theoretical results are supported by simulation studies.

Exact temperature tracking for hyperthermia: a model-based approach

In this paper, the inverse dynamics method for generating feedforward inputs and reference trajectories to achieve exact tracking for general linear time-invariant MIMO systems is explicitly derived. The method is applied to the task of generating input powers to achieve exact temperature tracking at multiple locations within a tumor during hyperthermia treatments. A number of important issues are considered: 1) robustness of the control schemes to parameter variation; 2) effect of additive sensor and actuator noise; 3) effect of using reduced order model estimators; and 4) effect of fast desired trajectories on the accuracy of output tracking. The inverse dynamics method is shown to be significantly more accurate when fast trajectories are desired. The results of this simulation study show that model-based inverse dynamics control is promising for clinical application. In addition, the inverse dynamics method derived can also be applied to other general linear MIMO systems.

Steady-state optimal discrete-time control of first-order systems with actuator noise variance linearly related to actuator signal variance

In this paper, the steady-state discrete-time optimal LQG control problem is considered when the noise variance of an actuator depends linearly on the variance of the actuator signal. A first-order system is analyzed in the case of noise-free and noisy output measurements. In the standard LQG problem the actuator noise variance is assumed to be known and constant before the design of the feedback gain. Consequently, the standard LQG design can lead to the deterioration of the system performance in the considered case.

Parameter identification of robot arm with repetitive control

In parameter identification of robot manipulators, measurement noise from acceleration and velocity, together with unmodelled dynamics, are the main sources of errors in the least-squares estimation and can also considerably increase the time necessary for parameter convergence. Instead of using Instrumental Variables or filtered estimates of the acceleration, we discuss the application of a repetitive controller in order to minimize estimation bias caused by measurement noise. We prove that the controller converges to a neighbourhood of the desired trajectory, taking into account measurement and actuator noise. Thus, desired values of acceleration and velocity can be used in the regression vector as estimates of their real values. The method is applied in the parameter estimation of a direct-drive arm, experimental issues are discussed and the validity of the results are experimentally verified.

Application of the recurrent multilayer perceptron in modeling complex process dynamics

A nonlinear dynamic model is developed for a process system, namely a heat exchanger, using the recurrent multilayer perceptron network as the underlying model structure. The perceptron is a dynamic neural network, which appears effective in the input-output modeling of complex process systems. Dynamic gradient descent learning is used to train the recurrent multilayer perceptron, resulting in an order of magnitude improvement in convergence speed over a static learning algorithm used to train the same network. In developing the empirical process model the effects of actuator, process, and sensor noise on the training and testing sets are investigated. Learning and prediction both appear very effective, despite the presence of training and testing set noise, respectively. The recurrent multilayer perceptron appears to learn the deterministic part of a stochastic training set, and it predicts approximately a moving average response of various testing sets. Extensive model validation studies with signals that are encountered in the operation of the process system modeled, that is steps and ramps, indicate that the empirical model can substantially generalize operational transients, including accurate prediction of instabilities not in the training set. However, the accuracy of the model beyond these operational transients has not been investigated. Furthermore, online learning is necessary during some transients and for tracking slowly varying process dynamics. Neural networks based empirical models in some cases appear to provide a serious alternative to first principles models.

Empirical Model Development and Validation with Dynamic Learning in the Recurrent Multilayer Perceptron

A nonlinear multivariable empirical model is developed for a U-tube steam generator using the recurrent multilayer perceptron network as the underlying model structure. The recurrent multilayer perceptron is a dynamic neural network, very effective in the input-output modeling of complex process systems. A dynamic gradient descent learning algorithm is used to train the recurrent multilayer perceptron, resulting in an order of magnitude improvement in convergence speed over static learning algorithms. In developing the U-tube steam generator empirical model, the effects of actuator, process,and sensor noise on the training and testing sets are investigated. Learning and prediction both appear very effective, despite the presence of training and testing set noise, respectively. The recurrent multilayer perceptron appears to learn the deterministic part of a stochastic training set, and it predicts approximately a moving average response. Extensive model validation studies indicate that the empirical model can substantially generalize (extrapolate), though online learning becomes necessary for tracking transients significantly different than the ones included in the training set and slowly varying U-tube steam generator dynamics. In view of the satisfactory modeling accuracy and the associated short development time, neural networks based empirical models in some cases appear to provide a serious alternative to firstmore » principles models. Caution, however, must be exercised because extensive on-line validation of these models is still warranted.« less

Steady-state optimal controller with actuator noise variance linearly related to actuator signal variance

The linear-quadratic-Gaussian (LQG) method assumes that the covariance matrix of the actuator noise is given before the design of the feedback matrix. However, in practice, the actuator-noise covariance matrix may depend on the actuator signal energy, which depends on the feedback. Consequently, the feedback from LQG theory degrades the system performance. The authors investigate the steady-state optimal controller when the noise variance of an actuator is linearly related to the variance of an actuator signal. This control system could be much more precise and/or spend much less control energy than the one obtained through the use of the ordinary LQG method. >

Bounds on noise response of structures

Using continuum models, explicit closed-form formulas are developed for the RMS (attitude) error response of structures to sensor and actuator noise for collocated actuators/sensors as a function of both control gain parameters and structure parameters, for dissipative (PD) controllers, and performance bounds deduced therefrom. One conclusion is that the maximum attainable improvement in the RMS attitude response varying either structure parameters or control gains is 3 dB at most for the axial and torsion modes, the bending being essentially insensitive, whether the Bernoulli model or the anisotropic Timoshenko model is used. The results should be useful in CSI optimization in the preliminary design phase.

Compensator design for stability enhancement with collocated controllers

A continuum model rather than a finite element model is used. The optimal compensator design is formulated as a stochastic regulator problem and is shown to be solvable by the general infinite-dimensional theory developed by the author despite the lack of exponential stabilizability. Infinite-dimensional steady-state Riccati equations characterizing the feedback control gain and the Kalman filter gain operators can be solved explicitly. The associated performance indexes including the mean-square control-effort are calculated in closed form. As a first approximation, the compensator transfer function can be realized as a bank of bandpass filters in parallel centered at the undamped mode frequencies. Numerical calculations for the gain and bandwidths for a typical configuration are presented. The performance of the compensator is evaluated when in fact in the true model there is no actuator noise. The theoretical problem involved is to show that the infinite-dimensional stochastic process is asymptotically stationary. It is possible to calculate the steady-state covariance in closed form and thereby calculate performance indexes of interest explicitly, facilitating the choice of optimal design parameters. >