Saturated Feedback Research Articles

Stability Properties and Effects of Measurement Disturbances on Antiwindup PI-and PID-Control

Different forms of discrete time controllers with integral action, control signal saturation and antiwindup feedback (i.e. Plaw, PlawD, Plaw-P cascade, I-aw with observer based feedback) are investigated. It is shown that high gain antiwindup is not required and that low antiwindup gain does not significantly diminish the stability properties as long as it is not lower than a given threshold. Results are given for the steady state control error offset induced by stationary high frequency measurement disturbances while operating the control loop close to the saturation. It is demonstrated that a derivative action should be avoided in this context, and how it can be replaced by other better performing structures. It is also shown how the effect of the high frequency disturbance may be further reduced by appropriate observer based feedback.

Logic-based switching adaptive stabilization of feedforward nonlinear systems

For a class of feedforward nonlinear systems, we systematically solve the global adaptive stabilization problem. The proposed adaptive stabilizer consists of a nested saturation feedback and a tuning mechanism, which is constituted by a set of switching logics and is used to adaptively tune the saturation levels in a switching manner. It is proved that under the proposed control, global asymptotic regulation of states is achieved. The class of systems can be of arbitrary dynamic order, the contained uncertain nonlinearities need not be explicitly bounded, and even the form of nonlinearities can also be unknown.

Symmetry Breaking of Periodic Orbits in Control Systems: A Harmonic Balance Approach

This work is concerned with linear control systems subjected to saturated feedback. A first harmonic approach is used to describe the existence of nonsymmetric periodic orbits in a three-dimensional control system. By taking a high-gain parametrization of the feedback control, the presence of nonsymmetric (first harmonic) periodic orbits is demonstrated for certain values of the parameter. Since it is also shown that nonsymmetric periodic orbits do not exist for small and large values of the parameter, evidences are found of the existence of symmetry breaking bifurcations.

First Harmonic Analysis of Linear Control Systems with High-Gain Saturating Feedback

A first harmonic approach (describing function method) is used in this work to study the behavior of linear control systems with a saturating high-gain linear feedback. It is shown that when the eigenvalues of the closed-loop system are located deeper in the left-half complex plane, several unstable periodic orbits shrink to the origin, thus leading to an unstable equilibrium point. This dynamical behavior is interpreted as the vanishing of the region of attraction of the origin when a saturating high-gain feedback is used.

FIRST HARMONIC ANALYSIS OF PLANAR LINEAR SYSTEMS WITH SINGLE SATURATED FEEDBACK

A first harmonic approach (describing function method) is used here to analyze the dependence of periodic orbits on the control parameters of planar linear systems with single saturated feedback. It is shown that, if the open-loop system has at least one unstable eigenvalue, periodic orbits converge monotonically to an unstable equilibrium point as the control gains go to infinity.

Optimal nonlinear, but continuous, feedback control of systems with saturating actuators

This paper presents a modification of the optimal saturating feedback control laws given by Frankena and Sivan (1979) and Ryan (1982 a) for asymptotically stable systems. Unlike their results, which involve bang-bang action and singular extremals, the modified control law is continuous. Specifically, the new control law is linear inside a cylinder set and saturated elsewhere. Using steady-state Hamilton-Jacobi-Bellman theory, this control law is shown to be optimal for a modified performance functional with a discontinuous integrand.

Volterra analysis of second- and third-order intermodulation of InGaAsP/InP laser diodes: theory and experiment

Analytical formulas for intermodulation- and harmonic-distortion products of a directly intensity-modulated laser diode are presented. The Volterra theory of nonlinear systems is applied to the single-mode rate equations of the modulated carrier and photon densities. This analysis takes gain saturation and noncoherent external optical feedback into account and provides expressions for the frequency-dependent intermodulation- and harmonic-distortion products. The single-mode analysis has been applied to a InGaAsP/InP Fabry-Perot laser diode, and the theoretical values of the second- and third-order intermodulation products at high modulation frequencies show good agreement with measurements. Thus, the formulas seem to provide a convenient and accurate means of predicting the laser-induced distortions in an analog optical transmission link over a wide frequency range.

Using nonlinear saturated feedback to control chaos: The Hénon map.

We used nonlinear saturated feedback to regulate the motion of chaotic dynamical systems. We studied the case of the H\'enon map by controlling both unstable equilibrium points and periodic orbits. A key issue addressed is that of the geometry of the saturated feedback.

Planar linear systems with single saturated feedback

We study planar linear systems with a linear or non-linear feedback global stabilizer subjected to saturation. The number of open-loop unstable eigenvalues characterizes the set of the equilibrium points and the shape of the asymptotic stability region (ASR). Some topological bifurcations on the shape of the ASR are described.

Class of globally stable saturated state feedback regulators

The aim is to find a feedback matrix F for a saturated stale feedback regulator, which guarantees its global asymptotic stability. We consider the discrete-time system with the constrained input described by xk+1 = Axk + Buk , where uk ∊ Ω R and matrix A is assumed to be critically stable, i.e. there exists some eigenvalues, lambda; i (A), such that |λ i (A)| = 1.

Two-tone suppression by a saturating feedback model of the cochlear partition

A model of a small strip of cochlear partition was computer simulated. The model is composed of two elements, approximations to the transfer functions of an inner hair cell (IHC) and an outer hair cell (OHC), respectively. The IHC element was insensitive to DC stimulation. Input was one or two sinusoids. One sinusoid, at the characteristic frequency (CF), was multiplied by the gain of the ‘cochlear amplifier’. A second sinusoid, representing a tone with much lower frequency, was not affected by the amplifier gain. This gain was determined by the OHC transfer function. In one form of the model (‘fixed-gain’), this gain was set at a fixed number determined from the furthest point reached on the OHC transfer function. This form of the model produced very realistic single-tone responses as well as showing ‘two-tone suppression’: that is, the IHC DC response produced by CF stimulation was reduced when the lower-frequency sinusoid, at suitable intensities, was added to the stimulus. When a DC component was added to the two-tone stimulus, the magnitude of this two-tone suppression was enhanced. In the second form of the model (‘variable-gain’), the cochlear-amplifier gain varied throughout the stimulus cycle. Its value was re-calculated at each instant, determined by the point on the OHC transfer function current at that particular instant. This form of the model showed two-tone suppression only when a DC component was added to the two-tone stimulus.

A note on the control of uncertain linear dynamical systems with constrained control input

A method is presented to design a stabilizing saturated state feedback controller for linear continuous-time systems with bounded uncertainty acting via the input channel.

On the stability of saturating nonlinear feedback systems

A saturating nonlinearity contained in a stable feedback system can be considered to lie within the sector [ \varepsilon,k ]. Thus all the well-known Popov-type stability criteria are applicable for the saturating nonlinear feedback system.

Synthesis of compensating servomechanism with backlash by incorporating non-linear saturable velocity feedback

Synthesis of compensating servomechanism with backlash by incorporating non-linear saturable velocity feedback

An Improved Square-Wave Oscillator Circuit

Inductively coupled square-wave transistor oscillators using a saturating output transformer subject the transistor to rather severe transient conditions and require an expensive transformer. The improved circuit, however, uses a separate saturating feedback transformer and a conventional output transformer. The described circuit has improved performance with less severe duty on the transistors, permits the use of inexpensive transformers, and allows the adaption to a variety of operating requirements.