Non-minimum Phase Plants Research Articles

Cost function methods of designing adaptive controllers for non-minimum phase plant

Three methods of designing adaptive controllers for non-minimum phase plant are presented. The methods minimize a cost function which is chosen to guarantee stability and for ease of application. Two of the methods use new results in parameter plane theory. The amount of computation required depends on the plant structure and will in many cases be more efficient than alternative methods.

プラントのむだ時間+ARモデルによる多入出力離散時間モデル規範形適応制御系の設計法とその応用

A new method for designing multivariable model reference adaptive control system is presented. In many adaptive control approaches, at least the following two assumptions regarding the plant have to be made. (1) The number of plant poles and zeros is known. (2) The plant is the minimum phase. The proposed method can avoid these restrictions by using the adaptive controller designed for an autoregressive model with dead time, based on Lyapunov’s direct method. Next, in order to illustrate the effectiveness of this model for the both minimum phase and non-minimum phase plants, the results of computer simulation are given. Finally, the method is successfully applied to the real plant testing the performance of refrigerant compressors.

むだ時間未知の非最小位相プラントに対する離散時間適応制御系の一設計法

むだ時間未知の非最小位相プラントに対する離散時間適応制御系の一設計法

Minimum Variance Control Harnessed for Non-Minimum-Phase Plants

Minimum variance control is applied to non-minimum phase plants augmented with adaptive compensators. The objective of the compensators is to achieve, asymptotically, a minimum phase property for the augmented plant. With this property, the minimum variance controller gives a stabilizing control signal.Results are developed for discrete-time, linear, stochastic plants for which the series and feedforward parallel moving average compensators have coefficients updated based on plant parameter estimates.The schemes perform well on simulations and were further supported by a global convergence theory.For tracking problems, preprocessing the desired trajectory may give improved performance. The design of the preprocessor can be achieved using a systematic approach.

On direct adaptive control of nonminimum-phase plants

Until recently direct adaptive control was limited to minimum-phase linear plants with unknown parameters. Two recent conceptual innovations, input matching and adjustable-model-reference adaptive control, are shown in this paper to provide justifiable direct adaptive control of minimum-phase and some nonminimum-phase plants. An initial, partially successful attempt at adaptive pole shifting arising from these efforts is also presented in order to spur further research of this important topic.

Blending of uncertain nonminimum-phase plants for elimination or reduction of nonminimum-phase property†

Abstract The benefits of feedback achievable in nonminimum-phase (nmp) systems are severely limited. However, if there are two parallel nmp branches whose outputs can be measured, then it may be possible to eliminate or reduce the nmp property with respect to some parts of the system, even if each of the two branches has uncertain parameters. It is always possible to do so for a finite, nonzero range of uncertainties for any complexity of pole-zero patterns of the branches. A design philosophy and methodology is presented for the general problem, permitting one to approach an optimum solution. under various constraints.

Parameter adaptive identification and control

A new parameter adaptive control scheme is outlined which essentially allows one to arbitrarily position all of the poles of an unknown, linear, scalar system of known dynamical order. The technique is based on identifying the parameters which characterize the dynamical behavior of the system in differential operator form and simultaneously implementing an adaptive observer which generates a feedback control signal which converges to the equivalent of an appropriate pole placing linear state variable control law. It is shown that the overall control configuration, consisting of a system identifier and a complementary adaptive observer, is globally stable provided only that the control input is sufficiently rich in frequency content. A study employing an unstable, nonminimum phase plant is presented to illustrate the technique.

Design of steady-state minimum variance controllers

A new technique to design optimal controllers is presented for plants described by rational transfer functions and additive disturbances with rational spectral densities. The objective is to minimize a weighted sum of the plant input and output steady-state variances subject to asymptotic stability of the closed-loop system. The technique is based on polynomial algebra. In fact, the design procedure is reduced to solving two linear polynomial equations whose unique solution directly yields the optimal controller transfer function as well as the minimized cost. This approach is simple, computationally attractive, and can handle unstable and/or nonminimum-phase plants with improper transfer functions. An integral part of the paper are effective computational algorithms, which include the spectral factorization, the solution of polynomial equations, and the evaluation of minimum cost.

Single-loop feedback-stabilization of linear multivariable dynamical plants

This paper derives the necessary and sufficient conditions for a multivariable plant P( s) with asymptotically stable hidden modes to be stabilizable by means of singleloop feedback employing an asymptotically stable controller and feedback sensor. These conditions are completely general and therefore encompass unstable, nonminimum-phase plants as well. For single-input-output plants with zero gain at infinite frequency the conditions reduce to the sole requirement that no plant zeros on the nonnegative real axis of the complex s-plane lie to the left of an odd number of real plant poles, multiple poles counted according to their multiplicities. It has also been possible to derive simple necessary and sufficient conditions for a closed-loop transfer function T( s) to be realizable by asymptotically stable compensation around a prescribed single-input-output plant P( s). It is expected that this latter result can be suitably generalized to the multivariable case. In a real sense, this paper constitutes a continuation of some earlier unpublished work [8] by the first author.

Wiener‐Hopf methods for unstable, nonminimum phase processes

AbstractIt is shown that existing methods for design of optimal regulators by the Wiener‐Hopf procedure must be modified in order to be applicable to unstable and/or nonminimum phase plant or disturbance transfer functions, such as are frequently encountered in the chemical industry. Solutions are developed for three cases: I. stable, but possibly nonminimum phase, plant and disturbance transfer functions; II. minimum phase, but possibly unstable, plant with no restrictions on the disturbance transfer functions; and III. prestabilized, with a proper modification to retain the original control effort inequality constraints, but possibly nonminimum phase plant and disturbance transfer functions. Case III gives the general solution for regulation of linear, time‐invariant, lumped‐parameter systems. When prestabilization is not necessary, it reduces to case I. Where applicable, solutions by the method of case II frequently involve less algebra than in case III.

Approximate parameter invariance with nonlinear feedback

The principle of invariance, first discussed by Kulebakin [2] for systems subject to external disturbances, is extended to the problem of building systems that are insensitive to plant-parameter variations. Through the use of nonlinear signal comparators and plant models, several classes of systems that are relatively insensitive to large parameter variations have been devised. These feedback configurations implicitly identify major parameter changes and modulate the plant drive to compensate for these changes. The control of nonminimum phase plants and systems with noisy output transducers may be improved with these schemes.

Comparison of linear feedback systems with self-oscillating adaptive systems

This paper compares the adaptive and disturbance attenuation properties of the linear feedback system with those of the self-oscillating-adaptive system (SOAS). The purpose is to permit the designer to decide, in any specific problem, which of the two systems is preferable. In minimum-phase plants, the system sensitivity to feedback transducer noise is used as the basis for comparison. In nonminimum phase plants an additional consideration is the sheer realizability of system specifications. Due to the absence of a rational, quantitative design procedure for the SOAS, it was first necessary to develop one. This is presented for the single loop SOAS using a bistable element, and without limit cycle identifier and gain changer. The procedure may be easily applied to other kinds of nonlinear elements. The relative superiority of the linear system and the SOAS depends on the following factors: ratio of extreme output plant must deliver to maximum acceptable limit cycle amplitude, the severity of the disturbance attenuation problem, the actual extremes of parameter variations and acceptable tolerances, and the magnitude and frequency distribution of feedback transducer noise. In some problems the critical factor is the response of the SOAS nonlinear element to high-frequency noise. The problem areas in which the SOAS is superior may be increased if a minor loop is added around the nonlinear element. The possible advantages of adding a limit-cycle identifier and a gain changer to the SOAS are also considered.

Stability Considerations in the Synthesis of Time-Varying Feedback Systems

In a recent paper <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> the synthesis technique proposed by Guillemin for liniear stationary systems <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> was extended for nonstationary feedback systems. It is to be expected, however, that stability problems may arise when applying the method for unstable or nonminimum phase plants, as it does in the time-invariant case. In this investigation it is shown that stability of the system can be assured by imposing constraints in the open-loop differential equation. These constraints are seen to be analogous to those of the time-invariant case.

Plant adaptive systems versus ordinary feedback systems

The limitations in classical feedback that might justify the more complex plant or process adaptive systems are studied. Some of the limitations cited in the adaptive literature apply only to the classical single-degree-of-freedom configuration and not to the classical two-degree-of-freedom structures. Model and conditional feedback configurations are not superior to ordinary two-degree-of-freedom configurations. Time invariant (classical) compensation is adequate for coping with the sensitivity and disturbance problem in lightly damped and drifting plant poles. Two significant limitations in ordinary linear feedback systems that may justify the adaptive approach are: a) Their susceptibility to feedback transducer noise when the plant by itself does not have the loop gain area required for the desired sensitivity properties of the system; b) The limited sensitivity reduction achievable in nonminimum phase and unstable plants. The first of these may be eased by a multiple-loop design and the second by a parallel plant design. However, it has not been shown how the adaptive systems overcome the limitations of ordinary feedback systems.