Linear Closed-loop System Research Articles

Dynamical anti-reset windup method for discrete-time saturating systems

This paper presents a dynamical anti-reset windup method for multivariable discrete-time saturating control systems. With the intention of maintaining the behavior of unsaturated linear systems as far as possible, an additional dynamical compensator is determined explicitly for the saturating system. Due to the additional compensator, the state positioning problem of saturated systems is completely resolved. The proposed method guarantees total stability of resulting systems, and asymptotic stability in the absence of exogeneous inputs can be addressed easily. The resulting dynamics of the compensated controller reflects the linear closed-loop system. The proposed method is applicable to any open-loop stable plants with saturating actuators and linear controllers. Simulation examples are included to illustrate the effectiveness of the proposed method.

Fuzzy model based controller for an inverted pendulum

A new fuzzy logic controller which can guarantee closed-loop stability, without resorting to a common Lyapunov function, and produce desirable transient performance for nonlinear systems is proposed. Application results in a linear closed-loop system of configurable poles. This controller has been successfully applied to an inverted pendulum.

A velocity algorithm for the implementation of gain-scheduled controllers

A new method is proposed to implement gain-scheduled controllers for nonlinear plants. Given a family of linear feedback controllers designed for linearizations of a nonlinear plant about constant operating points, a nonlinear gain-scheduled controller is derived that preserves the input-output properties of the linear closed loop systems locally, about each equilibrium point. The key procedures in the proposed method are to provide integral action at the inputs to the plant and differentiate some of the measured outputs before they are fed back to the scheduled controller. For a fairly general class of systems, the nonlinear gain-scheduled controllers are easy to obtain, and their structure is similar to that of the original linear controllers.

Asymptotic linearization and stabilization for a class of nonlinear systems

This paper presents a nonlinear output feedback which asymptotically linearizes the class of nonlinear, continuous-time, affine in the control systems having relative degree equal to the state space dimension. Moreover, we show that any set of eigenvalues can be assigned for the asymptotic closed-loop linear system. The controller is based on a nonlinear observer, presented in a previous paper, and on the linearizing state feedback proposed by Isidori and computed in the estimated state. The main result obtained is equivalent to the separation theorem in the linear case.

An algebraic characterization of fixed modes in a decentralized control (a simplified existence proof)

Algebraic characterizations for the existence of fixed modes in a linear closed-loop system with linear decentralized feedback controls are now well known. A simplified approach to the existence proof is presented here

Robust frequency design of linear stationary systems in aeroautoelastics

Robust frequency design of linear closed-loop stationary aeroelastic systems (LCLSAES) is considered with the help of doubly coprime fractional representations, linear affine manifolds, and the matrix Corona problem as well as with or without the help of the separation principle. The numerical algorithm is produced by using the finite Lagrange-Sylvester interpolation formulas. An example is given.

Sensitivity of closed-loop eigenvalues and robustness

Analytical results are obtained in a present investigation of the way in which full state feedback controller and estimator eigenvalues in a closed-loop linear control system affect these eigenvalues' sensitivity with respect to uncertain plant parameters. A controller eigenvalue lying near an estimator eigenvalue yields large eigenvalue sensitivity, which should be reduced through the separation of controller eigenvalues from estimator eigenvalues.

Fixed Modes and Modes Not Attainable Under Structurally Constrained Output Feedback

Abstract Closed-loop linear systems under structurally output feedback are considered. Fixed modes of multiplicity h are exactly defined. Furthermore, the notion of modes not attainable by admissible output feedback is introduced. Based on algebraic properties of the closed-loop system determinant and its minors, algebraic characterizations both of fixed modes including their multiplicities and of modes not attainable under structurally constrained output feedback are derived.

Direct adaptive tuning of robust controllers with guaranteed stability properties

We address the following problem: given a fixed regulator that insures closed-loop stability for a partially known plant, design a mechanism to adaptively tune the controller parameters in order to improve performance. Our main concern is to insure that global L ∞-stability of the overall system is preserved. The proposed parameter update law includes a signal normalization [1] and a σ-modification [2]. The condition for global L ∞-stability relates the margin of stability of the closed-loop linear system, the speed of adaptation and the size of the residual set for the tracking error.

A Computerized Research Microdensitometer for Spectrographic Data Analysis

A research grade microdensitometer has been modified and updated with a linear optical encoder to monitor and control accurately photographic plate position and digitized read out of density data. This measurement system is fully interfaced to a Data General time-shared computer network. Plate position is controlled to within ±0.0001 in. (0.0025 mm) via a closed-loop computer, stepper motor, and incremental linear optical encoder system. Plate movement and density sampling are under computer control with resulting data stored on disc memory for later analysis. Program techniques, including error analysis, have been developed to determine unknown wavelengths to within ±0.006 Å from spectral dispersion data fit to third-order polynomials. Analytical implications, especially relating to sequential multi-element analysis, are discussed. The completed instrument may be applied to a variety of spectroscopic and nonspectroscopic problems.

Application of the theory of branching of solutions of nonlinear equations in the estimation of pole perturbance of linear closed-loop systems

When the state and input matrices of a multivariable linear time-invariant system are perturbed, the problem of the estimation of pole perturbance of closed-loop system is considered by making use of the theory of branching of solutions for nonlinear equations.

Sensitivity functions for linear dynamic systems†

Gradient matrices are formulated for open-loop and closed-loop linear dynamic multivariable systems. The incremental motions of the poles, the zeros, and the coefficients of the numerator and denominator transfer function polynomials are determined as a function of the variation in the elements of the open-loop system matrices.

Algebraic characterization of fixed modes in decentralized control

Algebraic characterizations are presented for the existence of fixed modes of a linear closed-loop system with decentralized feedback control. The class of controllers for which fixed modes are present is extended beyond that currently known.

Representations of jointly stationary stochastic feedback processes†

Abstract Stable constant linear closed-loop systems relating an input vector u to an output vector u and vice versa produce a jointly stationary (y, u)-procoss. On the other hand it is often natural to split up a stationary vector random process z into component vectors yand u, and to examine the closed-loop relations between y and u. This paper presents a number of new results on the spectral factorization and the closed-loop representation of a jointly stationary vector (y, u)-proccss. Conditions are derived on the closed-loop models for the joint process model to bo oE minimal degree, stable and minimum-phase. Relations between different joint process models producing the same spectrum φyu(z)are established.

Parameter Estimation in Systems with Time Delay and Closed Loop Systems

A study of the mean square performance criterion is presented for the identification of open loop discrete time systems with unknown time delay, as well as for discrete time systems with linear feedback. The reasons of a multiextremal nature of the performance criterion are discussed in the estimation of unknown time delay. An original technique is suggested of transforming the criterion into a unimodal function. Estimability conditions are defined for the transfer function parameters of the object or of the regulator in linear closed loop systems, as well as in non-linear Hammerstein systems with feedback in their linear parts. A computer simulation was performed, and mathematical models were built for the control of high pressure pumped pipelines.

Identifiability conditions for Continuous Time Linear Closed Loop Systems

Necessary and sufficient conditions are given for the identifiability of open loop transfer functions for linear continuous time systems operating in closed loop. It is shown that provided certain structural properties are assumed, it is necessary and sufficient that the joint input-output spectral density be block diagonal when evaluated at infinity. With finite data, the spectral density cannot be exactly determined. However, it is shown in the paper, that the errors in the recovered open loop transfer functions will be small provided the estimated spectral density is approximately block diagonal when evaluated at infinity. This latter result leads to a practical test for identifiability of closed loop systems using finite data.

Expanding subinterval random search for system identification and control

A random search technique defined sequentially over an expanding subinterval has the property of locating the global minimum of a sequence of instantaneous performance measures as well as their sum. Therefore, such a technique is mostly suitable as a search technique to identify a set of unknown system parameters by minimizing a mean-square error type criterion on or equivalently to locate sequentially the optimal control coefficients of a feedback stochastic process with unknown dynamics by minimizing a performance criterion defined over the whole process. Several identification schemes based on this search technique have been developed for unknown nondynamic, nonlinear dynamic, open-loop linear dynamic, and closed-loop linear dynamic stochastic systems, respectively, and are discussed in this paper. The results of the investigation are compared with the results obtained by the author using stochastic approximation schemes. The comparison results are overwhelmingly in favor of the random search algorithm in terms of speed of convergence, globality of the search, etc. The major contribution of the method is that it yields unbiased estimates for dynamic feedback systems which utilize the identification information for state estimation and control, without the use of perturbation inputs required by the stochastic approximation method. The results used for the comparison of the two methods in this paper, have been obtained through simulations of four case studies like the chemical process of the pyrolysis of benzene, the linearized model of the booster stage of a space-vehicle, etc. Therefore, in addition the paper presents a new parameter identification method for feasibility studies which is important for the practicing engineer.

Direct synthesis of discrete-time feedback systems by equivalence transformations of polynomial matrices

It is shown that the synthesis of closed-loop linear multivariable discrete-time systems can be directly effected by performing equivalence transformations on appropriate polynomial matrices. These polynomial matrices are the Smith canonical forms of the closed-loop characteristic matrices of such systems subject to the constraints imposed by the fundamental theorem of linear state-variable feedback.

Sensitivity analysis in. multilinear systems†

The primary objective of this study is to examine tho sensitivity properties of a multilinear plant embedded in a feedback structure. As a prelude tho existing linear theory ia summarized and extended. Tho bilinear case is then treatod in detail. Extrapolation to the multilinear ease has been carried out by Porter and DeSantis (1974 a). New results includo the following : (i) the use of causality structure as a component of sensitivity analysis in closed-loop linear and non-linear systems, (ii) the establishment of terminal equivalence conditions for multilinear plants and multilinear compensators, (iii) the development of a sensitivity operator in the multilinear setting including existence conditions, (iv) extensions of linear results to largo parameter perturbations.

Closed-loop Analysis of Manual Flare and Landing

An approach to analyzing the manual flare and landing of an airplane is described here. The basis of this approach is a mathematical model of the flare maneuver which is derived from manual landings of both real and simulated aircraft. This flare model, in turn, lends itself to a linear closed-loop system description of the combined pilot/vehicle. Furthermore, simple Laplace transform methods can be used to map flare performance as functions of the flare maneuver. Having this link between flare maneuver and landing performance, we can estimate the pilot's ease in achieving desired levels of landing performance. Examples of this approach will be given using the results of a STOL airplane approach and landing simulation.