Cancellation Of Zeros Research Articles

Multivariable controller for redundantly actuated systems: a numerical design approach for open-loop data

A numerical approach for the synthesis of multivariable controllers from plant input-output data is presented. The method is applicable whenever a system is open-loop stable, redundantly actuated, and when its transfer function matrix is of full rank for all s. The method has two major advantages. First, model-matching design is achieved without explicit open-loop zero cancellation. Second, explicit knowledge of an open-loop model is not needed for the design.

2-delay出力制御による零点消去条件と強安定化則

2-delay出力制御による零点消去条件と強安定化則

Cancellation of Discrete Time Unstable Zeros by Feedforward Control

This paper presents a design methodology for the cancellation of unstable zeros in linear discrete time systems with tracking control objectives. Unstable zeros are defined to be those zeros of the rational transfer function that occur outside the unit circle. Unstable zeros cannot be canceled by feedback without compromising stability. In light of this fact, a feedforward scheme is used. Future desired trajectory information is required because the feedforward scheme is noncausal. The amount of future desired trajectory information that is required depends upon the zero locations and design specifications. It is shown that for a known plant with no zeros on the unit circle one can obtain a frequency response arbitrarily close to 1. Robustness issues and simulation results are discussed.

Model Reference Adaptive Control for Non-Minimum Phase Multivariable System by 2-Delay Feedback

In the studies of model reference adaptive control (MRAC), controlled systems are confined to minimum phase systems. It makes the scope of application of MRAC too restrictive, for non-minimum phase discrete-time systems can often appear. In this paper, a design method of MRAC for non-minimum phase multivariable systems by utilizing 2-delay feedback, is proposed. In that method, the poles, zeros, and interactor matrices are relocated by 2-delay feedback, and no cancellation of zeros occurs. Stable model references adaptive control systems can be constructed even for non-minimum phase multivariable systems with unknown interactor matrices.

Model Reference Adaptive Control for Non-Minimum Phase System by 2-Delay Feedback

In most of the studies of model reference adaptive control (MRAC), the controlled systems are confined to minimum phase systems, since the MRAC techniques utilize the control laws involving cancellations of zeros of the systems. It makes the scope of application of MRAC too restrictive, for nonminimum phase discrete-time systems can often appear. In this paper, we propose a design method of model reference adaptive control systems for non-minimum phase systems by utilizing 2-delay input control. In our method, the poles and zeros of the controlled systems are relocated by the 2-delay feedback control laws with 2-delay sampling. Since no cancellation of zeros occurs, the stable model reference adaptive control systems can be constructed even if unstable zeros exist. Some simulation results for non-minimum phase systems also shown the effectiveness of the proposed method.

Singularity structure of a model quark propagator

A model Schwinger-Dyson equation for the fermion self-energy is solved for both spacelike and timelike momenta. The singularity structure of the quark propagator obtained as a solution of this equation is studied. It is found to be an entire function (except for an essential singularity at p 2 = −∞; timelike in our metric): a property that may be indicative of confinement. The absence of singularities is a non-trivial feature that arises only as a result of the cancellation of zeros in the numerator and denominator of the propagator.

空気圧サーボ系のδ演算子モデル規範形適応制御

There is much research on the application of model reference adaptive control (MRAC) to hydraulic or pneumatic control systems. The characteristics of pneumatic servo systems change remarkably according to changes in inertia load and supply pressure, etc. The MRAC is one of the most effective control methods for systems with such changing parameters. But it uses the plant zeros cancellation, so there occurs sometimes non-minimum phase unstable zeros problem for a rapid sampling system, as recently shown by Åström et al.The δ-Operator has been proposed to overcome the unstable zeros problem of the MRAC.This paper describes mainly the MRAC of a pneumatic servo with δ-Operator (δ-MRACS). The MRAC of a pneumatic servo with z-operator (z-MRACS) became unstable by the unstable zeros, but analog simulation and experiments with δ-Operator could overcome the unstable zeros. Moreover, experiments with δ-MRACS showed very good follow up characteristics for sudden large parameter changes of the plant, such as inertia load change, feedback gain change, etc. It was observed that the δ-MRACS follows up well with the reference input even though the estimated parameters do not converge to the true values.

Model Reference Adaptive Control for Non-Minimum Phase System by Periodic Feedback

Abstract In most of the studies of model reference adaptive control (MRAC), the controlled systems are confined to minimum phase systems, since the MRAC techniques utilize the control laws involving cancellations of zeros of the systems. In this paper, we propose a design method of model reference adaptive control systems for non-minimum phase systems. The poles and zeros of the controlled systems are relocated by the periodic feedback control laws with multirate sampling, and no cancellation of zeros occurs in our method. It is shown that even if the unstable zeros exist, the output error converges to zero asymptotically, while the control input remains uniformly bounded. Some simulation results for the non-minimum phase system, also show the effectiveness of the proposed method.

Indirect adaptive pole-assignment controllers with direct implementations

A new strategy involving the cancellation of system poles and controller zeros is proposed for the indirect adaptive pole-assignment controllers. The resulting controllers can be implemented without solving simultaneous equations. A new method of eliminating the offset due to reference input without an explicit integrator is also proposed. The new strategies can be applied to pole assignment controllers of both general-feedback structure and error-driven structure. The results obtained from the simulations and trials on a stirred tank process verify that the controllers work well.

Adaptive Control of a Non-minimum Phase System Tracking a Periodic Reference Output

A number of techniques now exist for designing adaptive control systems when the unknown plant is linear and time-invariant. However, in most cases studied to date it has been assumed that the plant is stably invertible. This assumption is used to establish the key property of the boundedness of the system input and output. This paper presents a discrete-time adaptive control algorithm applicable to non-minimum phase plants when the reference output is periodic. The control algorithm causes the plant output to track the periodic reference output. The idea of the scheme is based on the pole placement technique. The controller does not give rise to the cancellation of process zeros. This implies that the algorithm can be applied to non-minimum phase plants. Global convergence and boundedness of the plant input and output are proved under the persistent excitation condition. A computer simulation example illustrating the performance of the algorithm is given. The effectiveness of the scheme is confirmed by applying it to a laboratory scale thermal system.

A fast ARMA transversal RLS filter algorithm

A fast pole-zero (ARMA) transversal RLS (recursive least squares) algorithm is derived, using a geometric formulation and the concept of projection onto a vector subspace to derive a recursive solution. The algorithm estimates a parameter vector that contains both numerator and denominator coefficients of an unknown system transfer function, i.e. models an ARMA (pole-zero) process. The algorithm has a transversal filter structure, but is distinguished from previous multichannel transversal algorithms, wherein each input channel is constrained to have the same order; here the pole and zero orders can be independently and arbitrarily specified. The derivation of the algorithm uses permutation matrices similar to those in the ARMA fast Kalman algorithm, but achieves a significant reduction in computations when compared to that algorithm. It is shown that when the pole and zero orders of the ARMA process are correctly specified, the algorithm generates an extremely good estimate. Furthermore, if the poles and zeros are overspecified, it is shown that a spectral match is still achieved by mutual cancellation of superfluous poles and zeros.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Model reference adaptive control using the delta operator

Reference is made to a recent paper by G.C. Goodwin, R. Lozano Leal, D.Q. Mayne, and R.H. Middleton (Automatica, vol.22, p.199-207, 1986), where it is shown that a cancellation of nonminimum-phase zeros appearing in discrete-time model reference adaptive control (MRAC) at a fast sampling rate can be easily avoided if the model to be identified is expressed in terms of the delta operator. A new proof of stability of the MRAC is given using the delta operator which, in contrast to the proof given in the above paper, does not require an assumption that a system consisting of a model determined by estimated parameters and a control law based on certainty equivalence principle is exponentially stable. A simple parameterization is proposed for the discrete-time MRAC using the delta operator which allows application of the usual (i.e. without dead zone) estimation algorithms. >

Simplified parameter adaptive control

AbstractA simple parameter adaptive controller design methodology is introduced in which steady‐state servo tracking properties provide the major control objective. This is achieved without cancellation of process zeros and hence the underlying design can be applied to non‐minimum phase systems. As with other self‐tuning algorithms, the design (user specified) polynomials of the proposed algorithm define the performance capabilities of the resulting controller. However, with the appropriate definition of these polynomials, the synthesis technique can be shown to admit different adaptive control strategies, e.g. self‐tuning PID and self‐tuning pole‐placement controllers. The algorithm can therefore be thought of as an embodiment of other self‐tuning design techniques. The performances of some of the resulting controllers are illustrated using simulation examples and the on‐line application to an experimental apparatus.

Noninvertible Digital Transfer Functions Arising From Minimum Phase Analog Process Models

Current approaches to discrete model reference adaptive control (MRAC) [1–6] require the inverse of the discretized process model to achieve the desired model following. The objective of this paper is to illustrate that the step-invariant transformation of a minimum phase, physical analog process model (based upon a machine tool position controller) leads to a nonminimum phase discrete-time model and thus precludes the possibility of obtaining a stable inverse for the discrete-time process model. This example illustrates the shortcomings of applying discrete MRAC to higher-order processes and indicates the need for alternative MRAC approaches which do not require the adaptive cancellation of process zeros.