High-gain Feedback Research Articles

Independence between the amount and structure of variability at low force levels

The purpose of the current experiment was to investigate the amount (standard deviation (S.D.) and coefficient of variation (CV)) and structure (approximate entropy (ApEn)) of force variability at very low force levels. Participants produced isometric force output of index finger abduction at five levels (0.4, 0.8, 1.0, 2.0, and 4.0 N) with high and low visual feedback gain. The findings showed that: subjects scaled their force output to the targets; S.D. increased non-linearly with force level and decreased with visual gain; and CV decreased with force level as well as visual gain. ApEn of the force output did not change as a function of force level, although the high gain increased ApEn in contrast to low gain. It is proposed that the recruitment of additional motor units at very low force levels does not significantly alter the structure of the force output, although it does increase the magnitude of force and its amount of variability. Overall, the findings provide evidence that the amount and structure of motor variability can be influenced by separate control processes at low force levels.

Monotonically convergent iterative learning control for linear discrete-time systems

In iterative learning control schemes for linear discrete time systems, conditions to guarantee the monotonic convergence of the tracking error norms are derived. By using the Markov parameters, it is shown in the time-domain that there exists a non-increasing function such that when the properly chosen constant learning gain is multiplied by this function, the convergence of the tracking error norms is monotonic, without resort to high-gain feedback.

Adaptive [formula omitted]-tracking for nonlinear higher relative degree systems

This paper proposes a relatively simple adaptive controller for nonlinear systems with higher relative degree. The controller achieves λ -tracking for a large class of nonlinear systems, i.e. it asymptotically stabilizes the system up to an error of at most λ which is chosen by the user. Only little information on the system is needed in the sense that no model needs to be known for the controller design, but only structural information like the relative degree and a lower bound on the positive high-frequency gain. The zero-dynamics does not need to be asymptotically stable, boundedness is sufficient. The controller consists of a high-gain observer, a high-gain observer-state feedback and a common adaptation of both high-gain parameters. The adaptation increases the gains of the observer and the state-feedback whenever the control objective, namely that the tracking error is of magnitude not larger than λ , is not attained. It is proved that the controller's adaptation converges and the control objective is achieved at least asymptotically.

Composition Control in Continuous Reactors

ABSTRACT A feedback control configuration for composition regulation in a continuous stirred tank reactor (CSTR) via manipulations of the jacket coolant/heating temperature, was studied. Under the assumptions that composition measurements are delayed and chemical kinetics are uncertain, a linear cascade (master/slave) control configuration is proposed, which leads to asymptotic regulation of the output composition about a given desired set point. The master control is derived by taking the reactor temperature as a virtual control input leading to low-gain linear PI feedback. The slave controller is derived by addressing a signal tracking problem that results in high-gain linear PI feedback. The final result is a cascade of linear PI feedbacks. The performance of the proposed control configuration is illustrated with numerical simulations of a methyl methacrylate polymerization reactor.

Robust output feedback regulation of minimum-phase nonlinear systems using conditional integrators☆

This paper is on the design of robust output feedback integral control for minimum-phase nonlinear systems with a well-defined relative degree. Previous work has shown how to design such controllers to achieve asymptotic regulation by a two-step process. First, robust control is designed to bring the trajectories to a small neighborhood of an equilibrium point. Within this neighborhood, the control then acts as a high-gain feedback that stabilizes the equilibrium point. The asymptotic regulation achieved by integral action happens at the expense of degrading the transient performance. In this paper, we present an approach to improve the transient performance. The control design is a continuous sliding mode control with integral action. However, the integrator is introduced in such a way that it provides integral action only “conditionally”, effectively eliminating the performance degradation . There are two main results in the paper: the first is asymptotic regulation and the second confirms the transient performance improvement by showing that the output feedback continuous sliding-mode control with integral action can be tuned to recover the performance of a state feedback ideal sliding mode control without integral action.

Regulation of nonlinear systems using conditional integrators

This paper studies the regulation of nonlinear systems using conditional integrators. Previous work introduced the tool of conditional integrators that provide integral action inside a boundary layer while acting as stable systems outside, leading to improvement in transient response while achieving asymptotic regulation in the presence of unknown constant disturbances or parameter uncertainties. The approach, however, is restricted to a sliding mode control framework. This paper extends this tool to a fairly general class of state feedback control laws, with the stipulation that we know a Lyapunov function for the closed-loop system. Asymptotic regulation with improvement in transient response is done by using the Lyapunov redesign technique to implement the state feedback control as a saturated high-gain feedback and introducing a conditional integrator to provide integral action inside a boundary layer. Improvement in the transient response using conditional integrators is demonstrated with an experimental application to the pendubot. Copyright © 2005 John Wiley & Sons, Ltd.

A NOVEL CONTROL STRUCTURE FOR DYNAMIC INVERSION AND TRACKING TASKS

A new structure for model inversion and tracking control tasks is introduced. It represents a two-degree of freedom controller, which unifies the principle of feedforward exact and high-gain feedback inversion, while preserving advantages of each.

Logic-based switching for robust control of minimum-phase nonlinear systems

We consider a single-input–single-output minimum-phase nonlinear system with large parametric uncertainty. The system can be represented globally in the normal form and our goal is to find a dynamic output feedback control law to ensure that the output (practically) asymptotically tracks a bounded smooth reference signal. Earlier work used high-gain observers with saturation to derive adaptive as well as robust control laws for this problem. The adaptive control law requires the nonlinear functions to be linearly parameterized in the unknown parameters and could have unsatisfactory transient performance for a large parameter set. The robust control law is based on a worst-case design and could be overly conservative. High gain feedback is needed to implement both controllers in the case when the parameter set is large. As a result, the robust and adaptive controllers may perform poorly in the presence of unmodeled dynamics and measurement noise. In order to reduce the controller gain and improve performance we propose a new approach based on partitioning the set of uncertain parameters into smaller subsets. Robust control laws are designed for each subset and logic based switching is used to choose the appropriate control law. The switching rule uses an estimate of the derivative of a Lyapunov function, which is provided by a high-gain observer.

Robust output feedback regulation of minimum-phase nonlinear systems using conditional integrators

This paper is on the design of robust output feedback integral control for minimum-phase nonlinear systems with a well-defined relative degree. Previous work has shown how to design such controllers to achieve asymptotic regulation by a two-step process. First, robust control is designed to bring the trajectories to a small neighborhood of an equilibrium point. Within this neighborhood, the control then acts as a high-gain feedback that stabilizes the equilibrium point. The asymptotic regulation achieved by integral action happens at the expense of degrading the transient performance. In this paper, we present an approach to improve the transient performance. The control design is a continuous sliding mode control with integral action. However, the integrator is introduced in such a way that it provides integral action only “conditionally”, effectively eliminating the performance degradation. There are two main results in the paper: the first is asymptotic regulation and the second confirms the transient performance improvement by showing that the output feedback continuous sliding-mode control with integral action can be tuned to recover the performance of a state feedback ideal sliding mode control without integral action.

Behavioral Approach Over A Lipschitz Bounded Set

In this article we discuss on a behavioral approach restricted over a set of functions whose second derivative are bounded to constant C. The condition is equavalent to the Lipschitz condition to the first derivative of the functions. At first characterization of the bounded set restricted by Lipschitz consatant is discussed. Several kinds of examples are introduced and the usefulness of the set is indicated. Secondly Levant VS differentiator is introduced. The principle of the differentiator is a high gain feedback with integrator in the feedback path. By choosing an appropriate parameters and switching speed, variable structure system can realize a high gain feedback system and practical differentiator can be composed. The choice of the parameters are closely related to the Lipschitz constant of the functions. Finally the invariant property of the function is discussed. The Levant differentiator can release the restriction of the properness of the system. Here we examine the conditions which ensure the application of non-proper systems. Discussion in the article is a challenge of the application of the behavioral approach to practical engineering problems. Appropriate restriction of the set of function might lead the behavioral approach from theoretical cite to practical engineering.

A Wide Bandwidth Isolation Amplifier Design Using Current Conveyors

In this paper, the dual-channel optocoupler and current conveyors are employed to achieve the wide bandwidth isolation amplifier. The high gain feedback technique and pole-zero compensation are applied to overcome the inherent nonlinear characteristics of optocouplers and to obtain a good transient response. Its bandwidth is up to 570 kHz with linear transfer characteristics. The maximum noise signal level in the frequency range up to 1.25 MHz is less than 31.6 μV. The mathematical model of proposed isolation amplifier is verified with experimental and simulation results. The dynamic responses and static characteristics are also demonstrated with experimental results.

Adaptive stabilization of the sine‐Gordon equation by boundary control

AbstractThis paper is concerned with adaptive global stabilization of the sine‐Gordon equation without damping by boundary control. An adaptive stabilizer is constructed by the concept of high‐gain output feedback. The closed‐loop system is shown to be locally well‐posed by the Banach fixed point theorem and then to be globally well‐posed by the Lyapunov method. Moreover, using a multiplier method global exponential stabilization of the system is proved. Copyright © 2004 John Wiley & Sons, Ltd.

Nonlinear System Identification and Learning Control of Flexible Arm with one degree of freedom using Neural Networks

This paper studies control methods of a flexible arm with one degree of freedom in order to suppress both vibration due to step movement and residual vibration due to signal noise. When using the conventional PD control methods, these two problems become adverse problems. Namely, the residual vibration becomes large when high gain feedback is used to improve response during suppressing the vibration of the step movement. Moreover, this system becomes a nonlinear system because the deformation of the flexible arm is large by use of soft elastic material. Neural Network (NN) is used as both a simulator and a controller with a view of nonlinear and learning ability. In this study, On-line learning of NN is impossible as the flexible arm breaks by fatigue on many repetitions of learning. Therefore, Off-line learning is employed and the NN simulator is used because of the nonlinear mapping ability for Neuro-controller training. As to the Neuro-controller training, repetitive learning method is proposed, which gives excellent performance of the Neuro-controller by improving both the simulator and controller in turn. This proposed method can give excellent results for the adverse problem of suppressing both the vibration of due to the step movement and the residual vibration due to the signal noise.

高次相対次数を有する非線形時変システムに対するハイゲイン適応出力フィードバック制御

This paper deals with a controller design problem for time-varying nonlinear systems with a higher order relative degree. A robust adaptive tracking control for uncertain time-varying nonlinear systems with stable zero dynamics will be proposed based on the high-gain adaptive output feedback and the backstepping strategies. The proposed method is useful in the case where only the output signal is available.

Feed Drives of NC Machine Tools Influenced by Base Vibration (1st Report)

Owing to high gain feedback control and feedforward control technology, servo response of the feed drives in NC machine tools is getting faster than that of conventional drives. However, when a large table including column or gantry is positioned by high response servo control, structural vibrations in low frequency domain are inspired and deteriorate the motion accuracy. Especially overshoot and vibration with low damping tend to appear in motion trajectory at acceleration and deceleration points. Such vibrations are likely to be generated by the dynamic combination of the machine structure as a rigid body and the floor foundation as a elastic spring and a damping. In this paper, a feed drive under the influence of base dynamics is investigated in a existing horizontal machining center by using FEM and experimental modal analysis. By creating a servo simulation model with the drive and base, vibrations at positioning are estimated and have a good agreement with measured ones. By analyzing the servo model it is found that the vibration is due to the coupling of base dynamics and feed dynamics.

Laser frequency stabilization by locking to a LISA arm

We analyze a technique for suppressing laser frequency noise for the laser interferometer space antenna (LISA) gravitational wave detector. We demonstrate that the laser frequency can be stabilized to a LISA arm by high gain feedback. It is shown that the feedback bandwidth is not limited by the 33 second round-trip propagation time and example frequency controller designs are presented.

Development of a multistage laser frequency stabilization for an interferometric gravitational-wave detector

Laser frequency stabilization is essential for interferometric gravitational-wave detectors to attain their target sensitivity. We have designed a multistage laser frequency stabilization system which has been applied in the development of the TAMA 300 gravitational-wave detector in Japan. The control topology consisting of two cascaded loops were employed to secure high feedback gain and reliable detector operation and thus allow the best frequency stability and uninterrupted long-term observation. We achieved simultaneously a frequency stability of 5×10−5 Hz/Hz, and a common-mode rejection ratio (which reduces the coupling of frequency noise to spurious signals in the detector) of 37 dB. The developed system enabled us to operate TAMA 300 with sufficient sensitivity and stability that it had the potential to register gravitational-wave events. The system was confirmed to be suitable for a gravitational-wave detector from the observation run of TAMA 300.

Fundamental design limitations of the general control configuration

The theory of fundamental design limitations is well understood for the case that the performance variable is measured for feedback. In the present paper, we extend the theory to systems for which the performance variable is not measured. We consider only the special case for which the performance and measured outputs and the control and exogenous inputs are all scalar signals. The results of the paper depend on the control architecture, specifically, on the location of the sensor relative to the performance output, and the actuator relative to the exogenous input. We show that there may exist a tradeoff between disturbance attenuation and stability robustness that is in addition to the tradeoffs that exist when the performance output is measured. We also develop a set of interpolation constraints that must be satisfied by the disturbance response at certain closed right half plane poles and zeros, and translate these constraints into generalizations of the Bode and Poisson sensitivity integrals. In the absence of problematic interpolation constraints we show that there exists a stabilizing control law that achieves arbitrarily small disturbance response. Depending on the system architecture, this control law will either be high gain feedback or a finite gain controller that depends explicitly on the plant model. We illustrate the results of this paper with the problem of active noise control in an acoustic duct.

On gain adaptation in adaptive control

The adaptive high-gain output feedback strategy u(t)=-k(t)y(t), (d/dt)k(t)=/spl par/y(t)/spl par//sup 2/ is well established in the context of linear, minimum-phase, m-input m-output systems (A, B, C) with the property that spec(CB)/spl sub//spl Copf//sub +/; the strategy applied to any such linear system achieves the performance objectives of: 1) global attractivity of the zero state; and 2) convergence of the adapting gain to a finite limit. Here, these results are generalized in three aspects. First, the class of systems is enlarged to a class N/sub h/(/spl mu/), encompassing nonlinear systems modeled by functional differential equations, where the parameter h/spl ges/0 quantifies system memory and the continuous function /spl mu/:[0,/spl infin/)/spl rarr/[0,/spl infin/), with /spl mu/(0)=0, relates to the allowable system nonlinearities. Next, the linear control law is replaced by u(t)=-k(t)[y(t)+/spl mu/(/spl par/y(t)/spl par/)//spl par/y(t)/spl par/]y(t), wherein the additional nonlinear term counteracts the system nonlinearities. Then, the quadratic adaptation law is replaced by the law (d/dt)k(t)=/spl psi/(/spl par/y(t)/spl par/), where the continuous function /spl psi/ satisfies certain growth conditions determined by /spl mu/ (in particular cases, e.g., linear systems, a bounded function /spl psi/ is admissible). The above performance objectives 1) and 2) are shown to persist in the generalized framework.

Robust Adaptive Backstepping Control Based on High-Gain Feedback and Its Application to a CSTR Control

In this paper, we propose a robust adaptive control for uncertain nonlinear systems via backstepping procedure based on high gain feedback strategy. It is shown that one can design a stable adaptive control system provided that the uncertain nonlinearities can be evaluated by an unknown constant and a known nonlinear function which give upper bounds of uncertainties. The effectiveness of the proposed methods is demonstrated by a simulation for a CSTR model.