Error Feedback Control Research Articles

Some new algebraic criteria for chaos synchronization of Chua's circuits by linear state error feedback control

AbstractThe research on the sufficient criterion for chaos synchronization of the master–slave Chua's circuits by linear state error feedback control has received much attention and some synchronization criteria for special control matrix were proposed. In this paper, the above synchronization issue is investigated in the situation of general linear state error feedback controller with propagation delay of control signals from the master Chua's circuit. First of all, a master–slave synchronization scheme for Chua's circuits with propagation delay is given and the relevant error system is derived. Using a quadratic Lyapunov function and frequency domain method, three new algebraic synchronization criteria for the synchronization scheme with general control matrix are proven. They are applied to derive the synchronization criteria for simple control matrices. Some examples are given to show the sharpness of these new criteria compared with the known criteria. Copyright © 2006 John Wiley & Sons, Ltd.

GRAPHICS-BASED CONTROL DESIGNS FOR NONMINIMUM-PHASE NONLINEAR SYSTEMS SUBJECT TO INPUT AND OUTPUT CONSTRAINTS

ABSTRACT This article deals with the output regulation of nonminimum-phase systems subject to input and output constraints. Through the off-line static data reconciliation algorithm for a class of stable nonlinear bioreactors, the static feedforward control can ensure constant disturbance attenuation in spite of input multiplicities and actuators constraints. Under the pseudo-steady-state error diagnoses and a graphics-based mechanism for disturbance estimation, the proposed error feedback control scheme will induce the piecewise output regulation. Based on the “intelligent” algorithm for tuning improvement, the closed-loop simulation shows that the piecewise control strategy turns out to be robust against the unknown disturbances.

Feedback and Feedforward Output Regulation of Bounded Uniformly Continuous Signals for Infinite‐Dimensional Systems

This article presents a state space output regulation theory for linear infinite‐dimensional systems (with bounded control, observation, and feedthrough operators) in which the reference and disturbance signals are bounded and uniformly continuous. Output regulation problems are posed and solved for both feedforward and error feedback controllers. Furthermore, under certain assumptions necessary conditions are obtained for those controllers which solve these output regulation problems. One consequence of these necessary conditions is a generalization of the well‐known internal model principle. A key feature in our theory is that the exogenous system generating the reference and disturbance signals is infinite‐dimensional.

A new output feedback synchronization theorem for a class of chaotic systems with a scalar transmitted signal

This paper proposes a new, simple and yet applicable output feedback synchronization theorem for a large class of chaotic systems. We take a linear combination of drive system state variables as a scale-driving signal. It is proved that synchronization between the drive and the response systems can be obtained via a simple linear output error feedback control. The linear feedback gain is a function of a free parameter. The approach is illustrated using the Rössler hyperchaotic systems and Chua's chaotic oscillators.

Sensorimotor mapping affects movement correction deficits in early Huntington’s disease

Huntington's disease (HD) is associated with early voluntary movement problems linked to striatal dysfunction. In pointing movements, HD increases the irregularity of the terminal part of movements, suggesting a dysfunction in error feedback control. We tested this hypothesis in movements requiring continuous feedback control. Patients in the early stages of HD and controls traced as fast and accurately as possible circles within a 5-mm annulus on a digitizing tablet when visual feedback of the hand and the circle was direct or indirect (through a monitor). Patients deviated more often from the annulus and showed larger corrections toward the circle than controls when using indirect visual feedback but not with direct visual feedback. When velocity requirements were removed, patients showed little change in these control problems. These results suggest that HD does not affect error feedback control in all movements and that the striatal contribution to voluntary movement is sensitive to sensorimotor mapping.

FREQUENCY DOMAIN CRITERION FOR CHAOS SYNCHRONIZATION OF LUR'E SYSTEMS VIA LINEAR STATE ERROR FEEDBACK CONTROL

Some frequency domain criteria for chaos synchronization of Lur'e system by linear state error feedback control are proposed and applied to design the controller that synchronizes the master-slave Chua's circuits coupled by linear state error feedback. A simple synchronization controller is obtained.

FUZZY ROBUST TRACKING OF A BIOREACTOR

A model-based robust control scheme is applied to a continuous bioreactor operating in an non stationary regime. The proposed control algorithm is a fuzzy robust error feedback controller that allows tracking several profiles of the substract concentration, while maintaining the stability conditions of the process. A numerical case study is simulated to test the robustness properties of the proposed controller in the face of parameter uncertainties and changes on load disturbances.

Input constrained funnel control with applications to chemical reactor models

Error feedback control (in the presence of input constraints) is considered for a class of exothermic chemical reactor models. The primary control objective is regulation of a setpoint temperature T ∗ with prescribed accuracy: given λ>0 (arbitrarily small), ensure that, for every admissible system and reference setpoint, the regulation error e=T−T ∗ is ultimately smaller than λ (that is, || e( t)||< λ for all t sufficiently large). The second objective is guaranteed transient performance: the evolution of the regulation error should be contained in a prescribed performance funnel F around the setpoint temperature T ∗ . A simple error feedback control with input constraints of the form u(t)= sat [ u ̄ , u ̄ ] (−k(t)[T(t)−T ∗]+u ∗) , u ∗ an offset, is introduced which achieves the objective in the presence of disturbances corrupting the measurement. The gain k( t) is a function of the error e(t)=T(t)−T ∗ and its distance to the funnel boundary. The input constraints u ̄ , u ̄ have to satisfy certain feasibility assumptions in terms of the model data and the operating point T ∗ .

Temperature Control of the Batch Polypropylene Reactor by ADRC

A new control method called Active-Disturbance Rejection Controller (ADRC) is proposed for temperature control of a batch polypropylene reactor in this paper. This controller is mainly composed of three parts, i.e. "extended state observer" (ESO), input reference signal tracking-differentiator (TD) and a non-linear state error feedback (NLSEF) control law. The simulation results have shown that ADRC can obtain quite good performances with the process uncertain. As the control algorithm in DCS ADRC is developed and tested for a batch polypropylene reactor in a local Petro-Chemical plant. The experiment results have indicated that the controller can give much better dynamic responses than the other control algorithms conducted several years ago.

Saccade adaptation in response to altered arm dynamics.

The delays in sensorimotor pathways pose a formidable challenge to the implementation of stable error feedback control, and yet the intact brain has little trouble maintaining limb stability. How is this achieved? One idea is that feedback control depends not only on delayed proprioceptive feedback but also on internal models of limb dynamics. In theory, an internal model allows the brain to predict limb position. Earlier we had found that during reaching, the brain estimates hand position in real-time in a coordinate system that can be used for generating saccades. Here we tested the idea that the estimate of hand position, as expressed through saccades, depends on an internal model that adapts to dynamics of the arm. We focused on the behavior of the eyes as perturbations were applied to the unseen hand. We found that when the hand was perturbed from stable posture with a 100-ms force pulse of random direction and magnitude, a saccade was generated on average at 182 ms postpulse onset to a position that was an unbiased estimate of real-time hand position. To test whether planning of saccades depended on an internal model of arm dynamics, arm dynamics were altered either predictably or unpredictably during the postpulse period. When arm dynamics were predictable, saccade amplitudes changed to reflect the change in the arm's behavior. We suggest that proprioceptive feedback from the arm is integrated into an adaptable internal model that computes an estimate of current hand position in eye-centered coordinates.

Robust Nonlinear Control of a Forced Oscillating Chemical Reactor

A model-based robust control scheme is applied to a continuous stirred-tank polymerization reactor operating in an oscillatory regime to produce a polymer for a wide range of polymer properties. The proposed control algorithm is a robust error feedback controller that allows us to track the oscillatory profile of the monomer conversion with predetermined amplitude and frequency while maintaining the reactor temperature at a constant set-point. A case study is simulated to test the robustness properties of the proposed controller in the face of load disturbances and parameter variations and uncertainties.

Radial Error Feedback Control for Bar Turning in CNC Turning Centers1

In-process measurement and control of CNC machines can improve machining accuracy while increasing productivity and eliminating waste in a cost effective way. This paper describes an in-process measurement and control system called radial error feedback control (REFC) for bar turning in CNC turning centers. REFC was designed to compensate for the radial error due to the time-varying bar deflection caused by the cutting force, which moves along the bar at a constant velocity. In a dry cutting environment, a noncontact laser sensor was used to directly measure the radial error of the workpiece while it is being cut. To compensate for the radial error, a gain-scheduled Kalman filter for prediction together with PI control law was designed, based on a time-varying model of the deflection of the bar. Analytical modelling (using classical beam vibration theory) was employed to develop a simple model for the bar bending. For non-uniform bars finite element modelling can be used. Experimental results show that the dimensional and geometric accuracy of the workpiece is substantially improved by this radial error feedback control technique.

A Real-Time State Predictor in Motor Control: Study of Saccadic Eye Movements during Unseen Reaching Movements

Theoretical motor control predicts that because of delays in sensorimotor pathways, a neural system should exist in the brain that uses efferent copy of commands to the arm, sensory feedback, and an internal model of the dynamics of the arm to predict the future state of the hand (i.e., a forward model). We tested this theory under the hypothesis that saccadic eye movements, tracking an unseen reaching movement, would reflect the output of this state predictor. We found that in unperturbed reaching movements, saccade occurrence at any time t consistently provided an unbiased estimate of hand position at t + 196 msec. To investigate the behavior of this predictor during feedback error control, we applied 50 msec random-force perturbations to the moving hand. Saccades showed a sharp inhibition at 100 msec after perturbation. At approximately 170 msec, there was a sharp increase in saccade probabilities. These postperturbation saccades were an unbiased estimator of hand position at saccade time t + 150 msec. The ability of the brain to guide saccades to the future position of the hand failed when a force field unexpectedly changed the dynamics of the hand immediately after perturbation. The behavior of the eyes suggested that during reaching movements, the brain computes an estimate of future hand position based on an internal model that relies on real-time proprioceptive feedback. When an error occurs in reaching movements, the estimate of future hand position is recomputed. The saccade inhibition period that follows the hand perturbation may indicate the length of time it takes for this computation to take place.

Tracking with prescribed transient behaviour

Universal tracking control is investigated in the context of a class S of M-input, M-output dynamical systems modelled by functional differential equations. The class encompasses a wide variety of nonlinear and infinite-dimensional systems and contains – as a prototype subclass – all finite-dimensional linear single-input single-output minimum-phase systems with positive high-frequency gain. The control objective is to ensure that, for an arbitrary -valued reference signal r of class W 1,∞ (absolutely continuous and bounded with essentially bounded derivative) and every system of class S, the tracking error e between plant output and reference signal evolves within a prespecified performance envelope or funnel in the sense that for all t ≥ 0, where φ a prescribed real-valued function of class W 1,∞ with the property that φ(s) > 0 for all s > 0 and . A simple (neither adaptive nor dynamic) error feedback control of the form $u(t)=- \alpha ({\varphi}(t)\|e(t)\|)e(t)$ is introduced which achieves the objective whilst maintaining boundedness of the control and of the scalar gain .

Multi-tiered control for undergraduate mechatronics

As mechatronics has gained popularity, the use of more sophisticated control in the design of computer controlled systems has also increased. It is reasonable to teach mechatronics using a gradually increasing complexity in control approach, beginning with discrete and combinational logic and progressing to error feedback control. This work presents an overview of the controls taught in the mechatronics course at Iowa State University and focuses on the introduction of control concepts appropriate for undergraduate mechanical engineers.

Minimum effort dead‐beat control of linear servomechanisms with ripple‐free response

A new and systematic approach to the problem of minimum effort ripple-free dead-beat (EFRFDB) control of the step response of a linear servomechanism is presented. There is specified a set of admissible discrete error feedback controllers, complying with general conditions for the design of ripple-free dead-beat (RFDB) controllers, regardless of the introduced degree of freedom, defined as the number of steps exceeding their minimum number. The solution is unique for the minimum number of steps, while their increase enables one to make an optimal choice from a competitive set of controllers via their parametrization in a finite-dimensional space. As an objective function, Chebyshev's norm of an arbitrarily chosen linear projection of the control variable was chosen. There has been elaborated a new, efficient algorithm for all stable systems of the given class with an arbitrary degree of freedom. A parametrized solution in a finite space of polynomials is obtained through the solution of a standard problem of mathematical programming which simultaneously yields the solution of a total position change maximization of servomechanism provided that a required number of steps and control effort limitation are given. A problem formulated in this way is consecutively used in solving the time-optimal (minimum-step) control of a servomechanism to a given steady-state position with a specified limitation on control effort. The effect of EFRFDB control on the example of a linear servomechanism with torsion spring shaft, with the criterions of control effort and control difference effort, is illustrated and analysed. Copyright © 2001 John Wiley & Sons, Ltd.

Minimum effort dead‐beat control of linear servomechanisms with ripple‐free response

AbstractA new and systematic approach to the problem of minimum effort ripple‐free dead‐beat (EFRFDB) control of the step response of a linear servomechanism is presented. There is specified a set of admissible discrete error feedback controllers, complying with general conditions for the design of ripple‐free dead‐beat (RFDB) controllers, regardless of the introduced degree of freedom, defined as the number of steps exceeding their minimum number. The solution is unique for the minimum number of steps, while their increase enables one to make an optimal choice from a competitive set of controllers via their parametrization in a finite‐dimensional space. As an objective function, Chebyshev's norm of an arbitrarily chosen linear projection of the control variable was chosen. There has been elaborated a new, efficient algorithm for all stable systems of the given class with an arbitrary degree of freedom. A parametrized solution in a finite space of polynomials is obtained through the solution of a standard problem of mathematical programming which simultaneously yields the solution of a total position change maximization of servomechanism provided that a required number of steps and control effort limitation are given. A problem formulated in this way is consecutively used in solving the time‐optimal (minimum‐step) control of a servomechanism to a given steady‐state position with a specified limitation on control effort. The effect of EFRFDB control on the example of a linear servomechanism with torsion spring shaft, with the criterions of control effort and control difference effort, is illustrated and analysed. Copyright © 2001 John Wiley &amp; Sons, Ltd.

Contouring control of machine tool feed drive systems: a task coordinate frame approach

We show that contouring performance can be viewed as a regulation problem in a moving task coordinate frame that is attached to the desired contour. By transforming the machine tool feed drive dynamics to this task coordinate frame, a control law is designed to assign different dynamics to the tangential and normal directions. The transformation also illustrated the effect of contour curvature and feed rate in the control action as well as the system dynamics in the task coordinate frame. The resulting control law consists of a linear time-varying proportional-plus-derivative (PD) position error feedback control law and a linear time invariant trajectory feedforward control law. Experimental results of the proposed control law on the motion axes of a machining center, Matsuura MC510V, showed significant improvement of the contouring accuracy compared to the existing servo controller as well as the successful decoupling between the tangential dynamics and the normal (contouring) dynamics for feedrate up to 6 m/min (4 in/s).

Lorentz Magnetic Levitation for Haptic Interaction: Device Design, Performance, and Integration with Physical Simulations

A new Lorentz force magnetic levitation haptic interface device has been developed and integrated with real-time 3-D rigid-body simulations for detailed, responsive interaction with dynamic virtual environments. An ideal haptic interface device would enable remote or simulated objects to be sensed and manipulated in 6 degrees of freedom (DoF) in the same manner as real physical objects, with the same micrometer level of detail and kHz bandwidth response that the user can sense. To approach this level of performance requires stiff lightweight moving parts, responsive actuators, high-resolution sensors, a fast control system, and a real-time simulation closely integrated with the device. Lorentz levitation is well suited to high-performance, tool-based haptic interaction because noncontact actuation and sensing provide motion and force feedback in 6 DoF with the simple dynamics of a single moving part at high control bandwidths and sensitivity. New actuation and sensing subsystem designs greatly increase the user range of motion over previous maglev devices. The motion range of the new device is ± 12.5 mm in translation and ± 7.5 deg in rotation to accommodate haptic fingertip motion tasks. The device has a measured closed-loop position bandwidth of more than 100 Hz in each DoF, a maximum stiffness of 25.0 N/mm, and a position resolution of 5-10 μm. Virtual coupling and intermediate representation methods were implemented to combine the simulation and the device controller and maximize the realism of haptic user interaction when computational resources are limited. In our system, the device controller must cycle several times faster than the simulation to generate stiff constraints during stable levitation. With virtual coupling, the updated position and orientation data from the interface device and the simulated tool act as error and velocity feedback control setpoints for each other. With the contact point intermediate representation method, a list of current tool contact points and directions is generated at each update of the simulation so that the device controller can evalute contact constrains locally and change impedance to respond to user motions at the fast control rate rather than the slower simulation rate. The contact point intermediate representation provides a crisper, more responsive feeling than virtual coupling during interaction but is not as easily stabilized. Experimental data from the virtual coupling and a modified contact point intermediate representation are presented.

Mixed internal model-based and feedforward control for robust tracking in nonlinear systems

The purpose of this paper is to compare different features of two approaches to the problem of tracking-prescribed trajectories in a nonlinear system, and to propose a possible merger of these approaches in what is called here the problem of “Asymptotically Robust Perfect Tracking”. The latter is the problem of designing a feedforward /error-feedback control law achieving perfect tracking in case the initial conditions of the system /exosystem are known and compatible with perfect tracking, and asymptotic tracking in all other cases.