Servomechanism Problem Research Articles

Robust Tracking and Disturbance Rejection for Decentralized Neutral Distributed-time-delay Systems

An important problem in control engineering is to design a controller to achieve robust asymptotic tracking of certain reference signals despite certain disturbance inputs. In the present work, this problem, which is known as the robust servomechanism problem, is considered for decentralized linear time-invariant (LTI) neutral systems with distributed time-delay. However, the system is also allowed to have discrete time-delays besides distributed time-delays. The reference signals and the disturbance input are assumed to satisfy a LTI neutral delay-differential equation with distributed and/or discrete time-delays. The necessary and sufficient conditions for the existence of a controller which solves this problem are derived. The structure of this controller (when it exists) is also presented.

An Analytical Design of Simplified Decoupling Smith Predictors for Multivariable Processes

In this study, the issues of complicated interactions between process variables were solved by decoupling techniques; in particular, simplified decoupling was used due to its simplicity and robustness. A new approach to solving decoupling realizability was developed by using the modified particle swarm optimization (PSO) algorithm. However, time delays still existed in the diagonal elements of the decoupled matrix, and they resulted in a more sophisticated controller design and sluggish responses in the outputs. To overcome the adverse effects of time delays, a Smith predictor, also known as a dead time compensator, is normally used. In this work, a Smith predictor structure in combination with simplified decoupling for multivariable processes was proposed in order to enhance system performances in terms of the servomechanism problem. The proportional integral or proportional integral derivative (PI/PID) controller tuning rules for several common industrial processes, such as first-order, second-order, and second-order with negative zero systems, were obtained. Many multivariable industrial processes were adopted to simulate the effectiveness of the proposed method in terms of the servomechanism problem and robust response.

Sinusoidal Servocompensator Implementations With Real-Time Requirements and Applications

This brief solves critical long-standing numerical stability issues for solutions to the sinusoidal robust servomechanism problem implemented as discrete-time linear time-invariant transfer functions; new closed-form results for direct form I and direct form II implementations now enable such forms to be used indefinitely in open-loop autonomous, or feedforward, configuration, and also provide difference equation initialization and servocompensator output parameter estimation methods that can be quickly calculated and used to enhance transient system performance and to assess harmonic control components. Simulation and real-time experimental results presented, respectively, exhibit expected concordance and robust effectiveness, and therefore highlight the method whereby such linear configurations can be pragmatically applied to further reduce computational implementation requirements relative to their mathematically intensive nonlinear time-varying counterparts.

Simple method of designing centralized PI controllers for multivariable systems based on SSGM

A method is given to design multivariable PI/PID controllers for stable and unstable multivariable systems. The method needs only the steady state gain matrix (SSGM). The method is based on the static decoupler design followed by SISO PI/PID controllers design and combining the resulted decoupler and the diagonal PI(D) controllers as the centralized controllers. The result of the present method is shown to be equivalent to the empirical method proposed by Davison EJ. Multivariable tuning regulators: the feed-forward and robust control of general servo-mechanism problem. IEEE Trans Autom Control 1976;21:35–41. Three simulation examples are given. The performance of the controllers is compared with that of the reported centralized controller based on the multivariable transfer function matrix.

Non‐parametric linear time‐invariant extensions of non‐invertible and backlash plant

SUMMARYA rigorous validation for the use of a set of linear time‐invariant models as a surrogate in the design of controllers for uncertain nonlinear systems, which are invertible as one‐to‐one operators, such as used in the nonlinear quantitative feedback theory (NLQFT) design methodology has been given by Baños and Bailey. This paper presents a similar validation but weakens the requirement on the invertibility of the nonlinear plant by application of Kakutani's fixed‐point theorem and an incremental gain constraint on the plant within its operational envelope. The set of linear time‐invariant models to be used for design is shown to be an extension (termed here the linear time‐invariant extension—LTIE) of the nonlinear plant restricted to the desired output operating space. A new non‐parametric approach to the modelling of the LTIE is proposed which is based on Fourier transforms of the plant I/O data and which accordingly may be based solely on experimental testing without the need for an explicit parametric plant model. This new approach thus extends the application of robust linear controller design methods (including those of NLQFT) to nonlinear plants with set‐valued (multi‐valued) inverses such as those containing backlash and also to plants for which explicit parametric models are difficult to obtain. The method is illustrated by application of the non‐parametric approach to an NLQFT tracking controller design for a mechanical backlashed servomechanism problem. Copyright © 2013 John Wiley & Sons, Ltd.

Decentralized Robust Servomechanism Problem for Large Flexible Space Structures Under Sensor and Actuator Failures

The decentralized robust servomechanism problem (DRSP) for colocated large flexible space structures (LFSS) under sensor and actuator failures is considered. A unified treatment of failures is enabled by introducing failure matrices. For colocated LFSS, stabilization, tracking of constant set points, and regulating against constant disturbances such that no “spillover effects” occur, can be simultaneously handled using a fault-accommodating decentralized tuning PID error-feedback controller. Necessary and sufficient conditions for solvability of the DRSP for colocated LFSS under sensor and actuator failures are derived in our analysis. In the case when each control agent is single-input/single-output, the decentralized fault-tolerant controller becomes particularly simple to implement. Steady-state output matrices for failed outputs are computed, and are found to be independent of controller gains.

Optimal Servomechanism Control of Plants With Fewer Inputs Than Outputs

AbstractThis paper deals with multivariable linear control in situations where the plant has fewer input channels than output channels. Our control approach is based on the classical robust servomechanism problem (RSP), in which exact asymptotic tracking and disturbance rejection are required despite uncertainty in the plant. We show that, for the class of systems dealt with here, it is possible to approximately satisfy the RSP specifications. More precisely, we construct a multivariable controller so that the asymptotic performance is optimal in the sense that the norm of the steady-state tracking error is minimized. The new scheme also exhibits some robustness, although not to the same extent as RSP controllers built for plants with at least as many inputs as outputs. We apply the new results to two classical industrial problems.

ROBUST TRACKING AND DISTURBANCE REJECTION FOR DECENTRALIZED NEUTRAL TIME-DELAY SYSTEMS

AbstractThe decentralized robust servomechanism problem, which is to design decentralized stabilizing controllers such that each decentralized output robustly tracks a given reference signal in the presence of certain disturbances, is considered for linear time-invariant time-delay systems of neutral type with discrete delays. The reference signals and the disturbance are assumed to satisfy a linear constant-coefficient delay-differential equation of neutral type with discrete delays. Necessary and sufficient conditions for the solvability of this problem are derived. The structure of the controller which solves this problem is also presented.

Control of uncertain systems by feedback linearization with neural networks augmentation. Part II. Controller validation by numerical simulation

The paper was conceived in two parts. Part I, previously published in this journal, highlighted the main steps of adaptive output feedback control for non-affine uncertain systems, having a known relative degree. The main paradigm of this approach was the feedback linearization (dynamic inversion) with neural network augmentation. Meanwhile, based on new contributions of the authors, a new paradigm, that of robust servomechanism problem solution, has been added to the controller architecture. The current Part II of the paper presents the validation of the controller hereby obtained by using the longitudinal channel of a hovering VTOL-type aircraft as mathematical model.

The Multivariable Servomechanism Problem for Positive LTI Systems $ $

In this technical note we study the servomechanism problem for positive open-loop stable LTI systems under constant tracking signals and constant disturbances. In particular, we show that in general the MIMO servomechanism problem for positive systems is not solvable, but is solvable for various classes of MIMO systems, and for the class of SISO systems in which the disturbances are small compared to the tracking signal. In particular, we give existence results as to what subclass of reference and disturbance signals can be considered, for the case when either the mathematical model of the plant is known or unknown, and we provide the controller structure that solves the problem for the case of measurable or unmeasurable disturbance signals.

On a Stabilization Problem of Nonlinear Programming Neural Networks

Intrinsically, Lagrange multipliers in nonlinear programming algorithms play a regulating role in the process of searching optimal solution of constrained optimization problems. Hence, they can be regarded as the counterpart of control input variables in control systems. From this perspective, it is demonstrated that constructing nonlinear programming neural networks may be formulated into solving servomechanism problems with unknown equilibrium point which coincides with optimal solution. In this paper, under second-order sufficient assumption of nonlinear programming problems, a dynamic output feedback control law analogous to that of nonlinear servomechanism problems is proposed to stabilize the corresponding nonlinear programming neural networks. Moreover, the asymptotical stability is shown by Lyapunov First Approximation Principle.

ROBUST TRACKING AND DISTURBANCE REJECTION FOR DECENTRALIZED TIME-DELAY SYSTEMS

The decentralized robust servomechanism problem, which is to design decentralized stabilizing controllers such that each decentralized output robustly tracks a given reference signal in the presence of certain disturbances, is considered for linear time-invariant time-delay systems of retarded type with discrete delays. The reference signals and the disturbances are assumed to satisfy a constant-coefficient linear delay-differential equation of retarded type with discrete delays. Necessary and sufficient conditions for the solvability of this problem are presented. The structure of the controller which solves this problem is also given.

Design of nonlinear H∞ controllers using describing functions with application to servomechanism

AbstractA systematic procedure for design of nonlinear H∞ controllers for amplitude‐dependent nonlinear plants is presented. The procedure is based on describing function concepts involving sinusoidal input describing function models of the nonlinear plant followed by application of an inverse describing function technique to arrive at nonlinear gains of the H∞ controller. The procedure is applied to a servomechanism problem to demonstrate the typical results that may be achieved. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Transient Response Improvement of the Robust Servomechanism Problem for Sinusoidal Signals

In this paper, the multi-input multi-output robust servomechanism problem for sinusoidal reference and/or disturbance signals having possibly unknown magnitude and/or phase components is examined. For the situation where such sinusoidal harmonic components are calibrated, for instance, via a priori tuning methods, simple initialization results are presented to reduce undesirable transient responses, and can be applied advantageously in a continuous-or discrete-time setting. Using this framework, additional optimization techniques then are developed and presented to minimize potentially undesirable tuning transients. Simulations are given using these new control design results when applied to a conventional hard disk drive system, where multiple harmonic disturbances may arise due to, for example, disk eccentricity or clamping effects. A comparison with another commonly-used harmonic cancellation method demonstrates and emphasizes the practical advantages and benefits that can be attained when using the proposed solution approach.

Application of the dynamic high‐gain scaling methodology to servocompensator design

AbstractThe error‐feedback servomechanism problem is addressed for a general class of strict‐feedback‐like systems. We provide two error‐feedback control designs based on our recent results on adaptive output‐feedback based on dynamic high‐gain scaling. One control design is of a dual high‐gain observer/controller structure, whereas the other control design utilizes a backstepping‐based controller in conjunction with a dynamic high‐gain scaling‐based observer. Owing to the particular robustness properties offered by a dynamic high‐gain scaling‐based controller and a backstepping‐based controller, the two designs require slightly different sets of assumptions on the system. Both design techniques allow the system to contain both unknown functions and uncertain appended input‐to‐state stable dynamics. Copyright © 2008 John Wiley & Sons, Ltd.

The servomechanism problem for unknown SISO positive LTI systems via tuning regulators and clamping

In this paper we consider the servomechanism problem for SISO positive LTI systems. In particular, we solve the robust servomechanism problem of nonnegative constant reference signals for stable SISO positive unknown LTI systems with constant nonnegative unmeasurable disturbances under strictly nonnegative control inputs, using a clamping tuning regulator.

On a Stabilization Problem of Nonlinear Programming Neural Networks

Intrinsically, Lagrange multipliers in Nonlinear Programming Theory play a regulating role in the process of searching the optima of constrained optimization problems. Hence, they may be regarded as control input variables as those in control systems. From this new perspective, it is showed that synthesizing nonlinear programming neural networks can be formulated to solve servomechanism problems. In this paper, under the second-order sufficient assumptions of nonlinear programming problems, a dynamic output feedback control law is proposed to stabilize the corresponding nonlinear programming neural networks. Moreover, their asymptotical stability is proved by the Lyapunov First Approximation Principle.

Output regulation of a class of linear systems with switched exosystems

In this article we investigate the output regulation (servomechanism) problem of linear systems with external inputs generated by switched linear systems. We use switching controllers and consider both the full information and the error feedback controllers under the assumption that there is a synchronization between exosystem and controller switching.

GLOBAL ROBUST SERVOMECHANISM OF A CLASS OF NONLINEAR SYSTEMS USING OUTPUT FEEDBACK

ABSTRACTThe robust servomechanism problem (alternatively, output regulation problem) of the class of nonlinear systems in lower triangular form has been extensively studied in recent years. The semi‐global solution was first given by either state feedback or output feedback. The global solution by state feedback was given very recently. However, the global solution by output feedback has long been an open problem. In this paper, we present a set of solvability conditions of the global robust servomechanism problem for this class of nonlinear systems by output feedback.

New developments in robust synthesis with antiwindup compensation.Flight control actuators applications

AbstractWe first summarize some results recently published by the authors on the application of classical robust servomechanism problem (RSP) to electrohydraulic servos. We present a solution consisting of three compensators: an integrator of the tracking error, a LQR stabilizing compensator and an antiwindup compensator. In this work we extend the analysis of the proposed solution by investigating the stability of the closed loop system with saturated control. We present here an approach to this problem based on the Lyapunov function method. The domain of attraction of the origin is obtained and it is shown that the system stability is ensured by simply choosing a particular compensator design which solves RSP. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)