Stability Of Feedback Control System Research Articles

Regions of robust relative stability for PI controllers and LTI plants with unstructured multiplicative uncertainty: A second-order-based example

This example-oriented article addresses the computation of regions of all robustly relatively stabilizing Proportional-Integral (PI) controllers under various robust stability margins α for Linear Time-Invariant (LTI) plants with unstructured multiplicative uncertainty, where the plant model with multiplicative uncertainty is built on the basis of the second-order plant with three uncertain parameters. The applied graphical method, adopted from the authors’ previous work, is grounded in finding the contour that is linked to the pairs of P–I coefficients marginally fulfilling the condition of robust relative stability expressed using the H∞ norm. The illustrative example in the current article emphasizes that the technique itself for plotting the boundary contour of robust relative stability needs to be combined with the precondition of the nominally stable feedback control system and with the line for which the integral parameter equals zero in order to get the final robust relative stability regions. The calculations of the robust relative stability regions for various robust stability margins α are followed by the demonstration of the control behavior for two selected controllers applied to a set of members from the family of plants.

Controllability and stabilization of gravity-capillary surface water waves in a basin

<p style='text-indent:20px;'>The paper concerns the controllability and stabilization of surface water waves in a two-dimensional rectangular basin under the forces of gravity and surface tension. The surface waves are generated by a wave-maker placed at the left side-boundary and it is physical relevant to see whether the surface waves are controllable or can be stabilized using appropriate motion of the wave-maker. Due to the surface tension, an edge condition must be imposed at the contact point between the free surface and a solid boundary. Two types of wave-makers are considered: "flexible" or "rigid". It is shown that the surface waves are approximately controllable, but not exactly controllable, for both "flexible" and "rigid" wave-makers. In addition, under a static feedback to control a "rigid" wave-maker, the strong stability of feedback control system is obtained.</p><p style='text-indent:20px;'> </p><p style='text-indent:20px;'>Correction: The page numbers on each page of the PDF file have been corrected. We apologize for any inconvenience this may cause.</p>

Temporally Coupled Dynamical Movement Primitives in Cartesian Space

Control of robot orientation in Cartesian space implicates some difficulties, because the rotation group SO(3) is not contractible, and only globally contractible state spaces support continuous and globally asymptotically stable feedback control systems. In this paper, unit quaternions are used to represent orientations, and it is first shown that the unit quaternion set minus one single point is contractible. This is used to design a control system for temporally coupled dynamical movement primitives (DMPs) in Cartesian space. The functionality of the control system is verified experimentally on an industrial robot.

Designing a stable feedback control system for blind image deconvolution

Blind image deconvolution is one of the main low-level vision problems with wide applications. Many previous works manually design regularization to simultaneously estimate the latent sharp image and the blur kernel under maximum a posterior framework. However, it has been demonstrated that such joint estimation strategies may lead to the undesired trivial solution. In this paper, we present a novel perspective, using a stable feedback control system, to simulate the latent sharp image propagation. The controller of our system consists of regularization and guidance, which decide the sparsity and sharp features of latent image, respectively. Furthermore, the formational model of blind image is introduced into the feedback process to avoid the image restoration deviating from the stable point. The stability analysis of the system indicates the latent image propagation in blind deconvolution task can be efficiently estimated and controlled by cues and priors. Thus the kernel estimation used for image restoration becomes more precision. Experimental results show that our system is effective on image propagation, and can perform favorably against the state-of-the-art blind image deconvolution methods on different benchmark image sets and special blurred images.

Robust Nonlinear Control of BLDC Motor in Quadcopter Applications

This paper describes the development of a nonlinear closed loop motor control system for a quadcopter micro-unmanned aerial vehicle (micro-UAV) platform. Research groups have analyzed the performance of brushless direct current (BLDC) motors with nonlinear effects in various applications, focusing on areas such as friction’s effect on position. This paper analyzes the nonlinear effects of BLDC motors on speed when these motors are used in quadcopter flying robots. Notably, to account for nonlinear torque from the aerodynamic forces on a quadcopter rotor, a Control Lyapunov Function (CLF) approach is used in designing a stable feedback control system. The paper also explains the custom model and simulation of the system built in MATLAB/Simulink used to demonstrate and quantify the successful performance of the design. KEYWORDS: Control Lyapunov Function; Micro-Unmanned Aerial Vehicle; Aerial Robotics; Quadcopters; Nonlinear Motor Control

BIBO stabilization of feedback control systems with time dependent delays

This paper investigates the bounded input bounded output (BIBO) stability in a class of control system of nonlinear differential equations with time-delay. The proofs are based on our studies on the boundedness of the solutions of a general class of nonlinear Volterra integral equations.

Structural Instability and Minimal Realizations

In this note, we consider the structural stability of an unstable plant, feedback stabilized by a controller. It is shown that infinitesimal parameter perturbations in the plant transfer matrix can destabilize the stable feedback control system obtained from a minimal realization of the ¿nominal plant.¿ The remedy for such structural instability consists in using a minimal realization in which the dimension of the ¿antistable part¿ is maximized over the uncertain parameter values. This requires knowledge of the ¿correct class¿ of parametrizations to which the nominal plant transfer matrix belongs.

Modelling of quantum networks of feedback QED systems in interacting Fock space

The present article is concerned with the study of quantum electrodynamics (QED) in interacting Fock space and a generalised approach of modelling quantum feedback systems of the optical QED cavities. The dynamical behaviour and the state space representation in stochastic field of the optical QED system provide the basis for developing quantum feedback QED control system. This study is also motivated by the design of quantum networks of any number of optical QED baths connected in parallel. Nyquist stability of the feedback control system in the interacting Fock space using two-mode beam splitter device at the input and a single-mode fractional beam splitter device at the output of the cavity has been analysed. The degree of stability of the quantum feedback control system of the cavity QED is studied by measuring gain margin and phase margin of the system in terms of parameters of the beam splitter.

A Lie Algebraic Approach to Design of Stable Feedback Control Systems with Varying Sampling Rate

This paper addresses the design of a controller family that, given a continuous-time linear plant sampled at a varying rate, asymptotically stabilizes the closed loop. Under the assumption of having a finite and known set of allowable sampling intervals, the problem is formulated as that of stabilizing a discrete-time switched system (DTSS). The solution approach consists in choosing the controller parameters in order for the Lie algebra generated by the closed-loop DTSS-matrices to be solvable, as this property guarantees the existence of a common Lyapunov function for the control system. The results can be applied to design digital controllers sharing resources, as it is the case of networked control systems, where the need of adapting the rate of task scheduling may originate significant sampling time variations.

Application of an anti-windup multivariable continuous-time generalised predictive control to a temperature control of an aluminium plate

This paper is concerned with a design problem of a Multivariable Continuous-time Anti-windup Generalised Predictive Control (MCAGPC) using coprime factorisation and Youla-Kucera parameterisation for an aluminium plate thermal process with input constraints. Based on the proposed design scheme, using a stable predictive controller, a stability condition of closed-loop system with input constraints is derived. As a result, a strongly stable feedback control system based on predictive control technique is obtained. The effectiveness of the proposed design scheme is confirmed by a simulation to a constrainted temperature control of an aluminium plate thermal process.

Stabilization of Feedback Control Systems with Infinite Delays

Based on variation of parameter formula, by making use of delay integral inequality and combining with the eigenvalue assignment technique, a new approach for designing state feedback controller with nonlinear perturbation is presented. Using this approach, the bounded-input and bounded-output (BIBO) stability of infinite delay control system is also discussed. The results are compared with other previous results by a example.

Conditions for Robustness and Nonrobustness of the Stability of Feedback Systems with Respect to Small Delays in the Feedback Loop

It has been observed that for many stable feedback control systems, the introduction of arbitrarily small time delays into the loop causes instability. In this paper we present a systematic frequency domain treatment of this phenomenon for distributed parameter systems. We consider the class of all matrix-valued transfer functions which are bounded on some right half-plane and which have a limit at $ + \infty $ along the real axis. Such transfer functions are called regular. Under the assumption that a regular transfer function is stabilized by unity output feedback, we give sufficient conditions for the robustness and for the nonrobustness of the stability with respect to small time delays in the loop. These conditions are given in terms of the high-frequency behavior of the open-loop system. Moreover, we discuss robustness of stability with respect to small delays for feedback systems with dynamic compensators. In particular, we show that if a plant with infinitely many poles in the closed right half-plane is stabilized by a controller, then the stability is not robust with respect to delays. We show that the instability created by small delays is itself robust to small delays. Three examples are given to illustrate these results.

Stability of Feedback Systems with Uncertain Dynamics

The application of functional analytic methods to the stability of feedback control systems with nonlinear, imprecise or unknown models is discussed. A method is proposed to find the appropiate center and radius parameters of the Conicity Stability Criterion. A technique is also presented to deal with unmodelled plants and to obtain its functional gain in an empirical way from energy measures.

Stability of feedback systems with uncertain dynamics

The application of functional analytic methods to the stability of feedback control systems with nonlinear, imprecise or unknown models is discussed. A method is proposed to find the appropiate center and radius parameters of the Conicity Stability Criterion. A technique is also presented to deal with unmodelled plants and to obtain its functional gain in an empirical way from energy measures.

補償器の付加による受動的冗長化

This paper brings up a new problem on reliable stabilization with passive redundancy.This paper considers the situations where a stable feedback control system is operational, and aims at supplementing this system with a new compensator to obtain a total system which is reliably stable with passive redundancy.A type of supplementary compensators is presented, which corresponds to a new type of resulting total control systems. The reliable stabilizability condition by such a supplementary compensator is equivalent to the strong stabilizability condition of the operational compensator.

Robustness margin calculation with dynamic and real parametric uncertainty

The problem of robust stability in feedback control systems with real uncertain parameters and unmodeled dynamics is considered. A robust margin r/sub m/ is defined, and an algorithm to calculate r/sub m/ and the closely related multivariable stability margin k/sub m/ is developed. How robust performance for real parametric uncertainty can be handled in this framework is also shown. The result essentially provides a method to check whether or not the infinity norm of a closed-loop transfer matrix is less than a specified level over a bounded set of real parametric variations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Optimal control of substrate concentrations in bioreactors with separated sensors

Many of the sophisticated sensors desirable for monitoring bioreactors cannot be placed in the bioreactor either because they are not steam sterilizable or because they require nonphysiological operating conditions. Such sensors can be used if they are separated from the bioreactor. Separation of the sensor from the bioreactor causes a time lag in data acquisition. This results in several complexities in the development of an appropriate and stable feedback control system based on a separated sensor. This paper analyzes the optimal control of a bioreactor with a separated sensor without a time lag and analyzes the feedback control (but not necessarily the optimal control) with a time lag. Simulation results indicate that this type of analysis could be extended to more general bioreactor operating conditions.

Linear dynamic output feedback: Invariants and stability

A full invariant under linear dynamic output feedback is derived. Some of its applications to the design of internally stable feedback control systems are considered.

Bounded input bounded-output stability of linear time-varying feedback systems

The bounded-input bounded-output stability of feedback control systems with time-varying gain is studied, and both continuous and sampled-data feedback systems are considered. It is shown that if the total gain deviation from a constant is finite, and if the feedback system with that constant gain is stable, then the output of the time-varying feedback system due to any bounded input is bounded; furthermore, the response of the time-varying system tends to that of the constant gain system. Similar results, somewhat weaker, are obtained for the time-varying sampled-data feedback system.

A stability criterion for nonlinear feedback systems

A frequency domain criterion is formulated to prove global asymptotic stability of feedback control system with more than one nonlinear element. The input-output characteristics of the nonlinearities are confined to sectors of the input-output planes. Sufficient conditions for global asymptotic stability are derived in terms of a number of inequalities equal to the number of nonlinear elements.