Pole Placement Algorithm Research Articles

Multirate Output Control for SISO Non-Minimum Phase Systems

The application of muhirate output control (MROC) to SISO non-minimum phase (NMP) systems exhibiting inverse response is considered in this paper. It is shown that the MROC improves considerably the control performance of such systems and the reasons for this are clarified. A detailed comparison between the MROC and linear time invariant (LTI) control structures (both continuous and discrete) like the PlO, IMC and observer/state feedback is carried out on a wide range of simple processes. The main advantage in the application of the MROC to NMP systems is that a drastic improvement in disturbance attenuation can be achieved while maintaining similar tracking capabilities. Sufficiently small sampling intervals yield an almost perfect disturbance rejection but degrades the robustness properties. This tradeoff is discussed in the paper and it is shown that an appropriate design of the MROC leads to good robustness properties with excellent performance incomparable to LTI control schemes. For the design of the MROC a tuning algorithm for optimal pole placement, based upon undershoot and settling time, is developed for two poles and one zero systems

Adaptive Control of a Two-Actuator Hydraulic System with Load Interaction

The paper is concerned with the problem of applying prescribed dynamic forces to a common structure, as in fatigue testing. The work reported investigates the use of self-tuning control in a two-channel force-control system acting upon a cantilever beam. An implicit pole-placement algorithm is developed on the basis of a linear model and its application in a nonlinear situation is tested and the results discussed. The effects of choosing different pole locations are investigated, and it is shown that minimum interaction between channels occurs when the poles are equal

Are the coefficients of a polynomial well-conditioned functions of its roots?

We show that the coefficients of a polynomial can be rather illconditioned functions of its given roots. In certain cases, however, the coefficients are well conditioned, e.g. if the roots lie symmetrically in a closed angular sector for an angle less than ? centered at the origin of the complex plane?. We introduce and study condition numbersB l(k) for the sensitivity of the polynomial coefficienta k to changes in the rootx l and develop an algorithm to compute the condition numbers and to decide whether a given set of roots will generate the polynomial coefficients in an ill way. This algorithm is an essential preliminary for certain numerical pole placement algorithms in linear control theory.

Parameter Convergence and Uniqueness in Nonminimal Parameterizations for Multivariable Adaptive Control

The issue of parameter convergence in multivariable adaptive control is addressed in a general framework. Parameter convergence is guaranteed if a certain design identity has a unique solution and if the inputs satisfy persistency of excitation conditions. The uniqueness of the solution of the design identity can be obtained, in general, by using parameterizations that, although nonminimal, are structured so as to guarantee uniqueness. This concept is illustrated with a direct adaptive pole placement algorithm, which is modified to guarantee uniqueness, and it is shown how the results can be used to establish stability and convergence properties of the algorithm.

Identification and control of a multizone crystal growth furnace

This paper presents an intelligent adaptive control system for the control of a solid-liquid interface of a crystal while it is growing via directional solidification inside a multizone transparent furnace. The task of the process controller is to establish a user-specified axial temperature profile and to maintain a desirable interface shape. Both single-input-single-output and multi-input-multi-output adaptive pole placement algorithms have been used to control the temperature. We also describe an intelligent measurement system to assess the shape of the crystal while it is growing inside a multizone transparent furnace. A color video imaging system observes the crystal in real time, and determines the position and the shape of the interface. This information is used to evaluate the crystal growth rate, and to analyze the effects of translational velocity and temperature profiles on the shape of the interface. Creation of this knowledge base is the first step to incorporate image processing into furnace control.

Adaptive Pole Placement Control Using Multiple Transputers

The paper details the implementation of an adaptive pole placement algorithm on a multiple transputer system. The controller makes use of the extended least squares parameter estimation algorithm and is controlled at the local level by a supervisor task which monitors the behaviour of the control system to ensure robust operation under a variety of environmental conditions. This enhances the integrity of the controller in real-time operations. The adaptive controller is also configured to be used as a node within a distributed control system such that a central network interface can configure a number of individual controllers within the distributed control network. The controller is demonstrated dealing with a plant with changing parameters and disturbances.

Adaptive pole placement control of a continuous fermentation process

The application of an adaptive pole placement control scheme for the control of real-life biotechnological processes is reported. The problem of simultaneous regulation and tracking of substrate concentration in a continuous fermentation plant is considered in view of recent adaptive control concepts. The process is described by a time-varying non-linear model obtained from mass-balance considerations, where the key process parameter is considered as a time-varying parameter. A discrete-time model is derived. The estimation of this key parameter is carried out using an adaptive filtering scheme. The estimated parameter is used in the explicit design of an adaptive filtering scheme. The estimated parameter is used in the explicit design of an adaptive pole placement algorithm. Good experimental results have been obtained in regulation and tracking, disturbance rejection and transient behaviour, showing the efficiency of this adaptive control scheme.

ART based adaptive pole placement for neurocontrollers

Indirect adaptive control of low order plants that are subjected to parametric variations arising from changes in operating environment requires real time dynamic system identification. In this paper, we propose a control scheme that utilizes a nearest neighbor search type of classifier capable of learning to dynamically identify these variations in plant parameters. The neural network architecture employed is based on the Adaptive Resonance Theory (ART-II) proposed by Carpenter and Grossberg (1987a, 1987b, 1987c, 1987d). An adaptive pole placement controller for a slow time varying linear second order system is implemented based upon this architecture to assess the performance of the network and the overall control scheme with the neural network in the control loop. The control strategy is based upon identification of changes in the time response characteristics of the system to standard test signals which are assessed by the network. A pole placement algorithm is utilized to relocate the poles of the overall closed loop system by altering the gains of the process controller to obtain desired system response. Experimental studies on a simulated system employing a Proportional Derivative controller are encouraging.

Estimation and control of a continuous alcoholic fermentation process

This paper deals with the problem of simultaneous regulation and tracking of substrate concentration in a continuous-flow fermentation plant. The process is described by a set of non-linear differential equations obtained from mass-balance considerations, from which a discrete-time model is derived. Due to an on-line measurement of the substrate, the estimation of the consumption rate, considered as a time varying parameter, is carried out using an adaptive filtering scheme. The reconstruction of the substrate noise-polluted concentration is also provided by this filtering scheme. An adaptive pole placement algorithm is then designed for regulation and tracking of the process. Good experimental results have been obtained, which show the efficiency of this adaptive control scheme in terms of disturbance rejection and transient behaviour.

Robustness of an adaptive pole placement algorithm in the presence of bounded disturbances and slow time variation of parameters

The robustness properties of a specific adaptive pole placement scheme in the presence of bounded disturbances and slow time variation of parameters are studied. It is shown that the least squares algorithm used in this scheme retains the global stability of the overall system in the presence of bounded disturbances of small magnitude and slow time variation of system parameters (within a compact set).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An Adaptive Autopilot for Inland Ships

The design of an adaptive autopilot for inland ships is discussed. An autopilot for inland ships has to control the rate of turn rather than the heading. Adaptive properties are desirable in order to reduce the cost of initial tuning and to maintain good performance under varying sailing conditions. As an adaptation scheme, indirect adaptive control is used. An extended Kaiman filter estimates the ship’s parameters. A pole-placement algorithm uses these estimates to tune a PI controller. The algorithms have been implemented in a VME-bus computer. Results of full-scale trials demonstrate the attractive performance of the adaptive autopilot.

Adaptive Pole-Placement Algorithm Based on Common Factor Elimination

This paper presents an indirect adaptive pole-placement algorithm for noiseless SISO systems. The control input consists of a feedback term and a self-excitation term. The latter is used to guarantee the global stability of the closed loop system. The former, the main part of this paper, is computed by eliminating the common factor included in the estimated parameters. A feature of the algorithm is that it is applicable to the plant whose order is not exactly known. However, a lower bound of the Sylvester resultant of plant polynomials is needed to estimate the order of the plant. Numerical examples are given to illustrate the effectiveness of the proposed algorithm.

On the stability of adaptive pole-placement controllers with a saturating actuator

The authors examine how existing pole-placement algorithms work in the case of a saturating input. The stability of such algorithms and the modifications needed to make them work in the case of saturation are examined. The net result is that the analysis of G.C. Goodwin and K.S. Sin (1984) can be slightly modified to prove the stability of adaptive pole-placement, but only for the case where the plant is stable. It is shown that, for unstable plants, it is possible to push the plant into a state from which it cannot be returned to the origin (with a saturating input). Thus, it is fairly easy to generate examples of instability in the adaptive control system that would not exist with unbounded control authority.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Stable eigenvalue placement by constrained optimization

A pole placement algorithm is proposed which uses constrained nonlinear optimization techniques on a finite-dimensional model of a linear n degree of freedom system. Low-order feedback control is assumed where r poles may be assigned; r being the rank of the sensor coefficient matrix. It is shown that by combining feedback-control-theory methods with optimization techniques, one can ensure the stability characteristics of a system, and simultaneously improve its transient response

An algorithm for the multiinput eigenvalue assignment problem

A very simple and inexpensive algorithm is presented for pole placement in the multiinput case. The algorithm consists of orthogonal reduction to a Block-Hessenberg form and a simple linear recursion. It yields a matrix F such that A+BF has any specified set of eigenvalues whenever the system is controllable. It is extremely easy to program on a computer. The algorithm is not a robust pole-placement algorithm but appears to give comparable results in most well-conditioned cases at a fraction of the cost. It is a direct (noniterative) algorithm and no eigenvalues or singular values are computed. The algorithm does not need any complex arithmetic, even when complex conjugate eigenvalues need to be assigned. >

Adaptive control for systems with bounded disturbances

The authors present an identification algorithm that can be used to design globally stable indirect adaptive controllers for minimum- and nonminimum-phase systems subject to bounded disturbances. The parameter estimation scheme is a least-squares algorithm with dead zone. The dead zone is such that the estimates converge and make it possible to define projected estimates having the same convergence properties as the original estimates. In the minimum-phase case, the projection facility can be used to ensure that the leading coefficient projected estimate is greater than or equal to the true leading coefficient in absolute value. The projection procedure can also be used to avoid pole-zero cancellations in an adaptive pole-placement algorithm.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Stability analysis of Elliott's direct adaptive pole placement

The stability of Elliott's direct adaptive pole placement algorithm is examined without the persistency of excitation assumption. The conditions for the sequence of estimated parameters that are sufficient for the plant input and the plant output to be bounded are given. It is also shown that the modifications proposed in many papers for ensuring the global stability of the indirect adaptive pole placement algorithm can be also applied to the direct one if an auxiliary estimation algorithm for identifying the plant parameters is applied.

Generalization of ILQ Method for the Design of Optimal Servo Systems

Recently, a new design method of optimal servo systems, called “ILQ Method”, has been developed by applying the pole placement method. This paper treats its generalization for relaxation of a restriction imposed on the system in its original version. By a natural extension of the selection method of design parameters as well as the pole placement algorithm, the restriction can be relaxed significantly. Under a relaxed condition, the design parameters can be chosen so as to specify each output response in a certain class, and in addition, the optimal gain achieving such specified output responses can be expressed explicitly in terms of the system matrices and the design parameters. Some numerical examples are also illustrated to show the validity of the design method.

Phonetic discrimination experiments with a spatiotemporal recognition network: [formula omitted]. Siemens Corporate Research and Support, Inc. 105 College Road East, Princeton, NJ 08540-6668 USA

Indirect adaptive control of low order plants that are subjected to parametric variations arising from changes in operating environment requires real time dynamic system identification. In this paper, we propose a control scheme that utilizes a nearest neighbor search type of classifier capable of learning to dynamically identify these variations in plant parameters. The neural network architecture employed is based on the Adaptive Resonance Theory (ART-II) proposed by Carpenter and Grossberg (1987a, 1987b, 1987c, 1987d). An adaptive pole placement controller for a slow time varying linear second order system is implemented based upon this architecture to assess the performance of the network and the overall control scheme with the neural network in the control loop. The control strategy is based upon identification of changes in the time response characteristics of the system to standard test signals which are assessed by the network. A pole placement algorithm is utilized to relocate the poles of the overall closed loop system by altering the gains of the process controller to obtain desired system response. Experimental studies on a simulated system employing a Proportional Derivative controller are encouraging.

Application of explicit criterion minimization in adaptive control

The explicit criterion minimization (ECM) algorithm for adaptive control is investigated. From an engineering point of view, a boundedness condition based on the incremental quantity of controller parameters, Δρ, is employed in the present study. It is found that successful operation is achieved by using control amplitude constraints rather than switching between an ECM and a pole-placement algorithm, as suggested by Trulsson. To reduce the effect of disturbances, an integral term is added to the controller. With these modifications the ECM algorithm is found to perform satisfactorily. The effect of different orders of the system model and controller is discussed for a varying dead-time control system. The application of ECM on the tuning parameters of a proportional-integral-derivative (PID) controller is also presented in the paper. The ECM algorithm was also evaluated by applying this algorithm in the experiment of a pilot scale coupled-tank liquid level control system.