Global adaptive pole placement: Detailed analysis of a first-order system

This paper studies a deterministic adaptive pole positioning problem for a linear first-order system. The principal contribution is to specify an adaptive control law which secures global convergence. The key conditions required are that an externally available plant input be persistently exciting, and that an underbound (not necessarily tight) be known on the magnitude of the input coupling gain. The pattern of the solution to the problem can carry over to high-order systems.     

Global adaptive pole positioning

Adaptive pole positioning for linear time-invariant discrete-time systems is considered, under the constraint that the controller consists of an identifier, the gains in which do not go to zero, an observer, and a state feedback law (the latter two elements being viewed in transfer function form). A globally convergent algorithm is presented for achieving a prescribed set of closed-loop poles. Persistency of excitation of an external input is required, together with an underbound on the magnitude of the Sylvester resultant of the plant numerator and denominator polynomials, this in effect being an underbound on the product of a measure of pole-zero separation and a generalized gain.     

Efficient recursive adaptive pole placement algorithm

A recursive adaptive pole placement algorithm is presented. The stability and convergence of the algorithm are established respectively. Since a one-step iterative formulation in computing a controller's parameters is used, the on-line computation cost is greatly reduced with respected to the traditional algorithm. The algorithm with feed-forward can follow the arbitrarily bounded output. The algorithm is also extended to a multivariable case. Simulation examples show the efficiency and robustness of the algorithms.     

Robust pole placement direct adaptive control

A pole-placement direct adaptive control for not necessarily minimum-phase plants is presented, which is robust with respect to unmodeled dynamics and bounded disturbances. The robustness is achieved by using both a normalized least-squares algorithm with dead zone and appropriate nonlinear feedback. The resulting closed-loop system is shown to be globally stable subject to standard assumptions     

Limitations of robust adaptive pole placement control

In this paper we investigate the limitations of adaptive pole placement control of AR systems when an additive disturbance is present. The magnitude of the disturbance is dependent on past input and output values. It is shown that the control objective of robust stabilization restricts the set of systems one can deal with. We subsequently propose and analyze an adaptive algorithm which can be applied to convex, not necessarily bounded, subsets of the aforesaid set. In particular, it is shown that all signals in the control loop remain bounded     

多变量自适应极点配置对偶控制的研究

针对参数未知的多变量差分方程形式的系统,首先利用Kalman滤波器进行参数辨识,根据确定性等价原理对系统进行极点配置;然后利用极点配置得到的非对偶控制器作为标称输入,其对应的输出作为标称输出,进而根据双指标准则进行对偶控制器的设计;最后给出一个仿真实例,验证该算法的可行性和有效性.     

Singularity-free adaptive pole placement using periodic controllers

A globally convergent adaptive control scheme for nonminimum phase systems is presented. The approach is based on a particular periodic pole-placement controller. An ad-hoc parameter estimate correction procedure is used to prevent any possible singularities in the control law computation. Furthermore, a lower bound on the estimated model controllability is ensured. The a priori knowledge on the system is reduced to the process order     

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.     

Arbitrary adaptive pole placement for linear multivariable systems

This paper presents a methodology for adaptively assigning the closed-loop poles of either continuous or discrete time linear mnltivariable systems. The scheme is direct in nature in that no parametrized model of the unknown plant needs to be explicitely identified. Rather the control parameters, and an "equivalent" plant parameterization are simultaneously estimated from input-output data using linear parameter estimation procedures. Implementation of the scheme requires only knowledge of the system controllability indexes, and an upper bound on the observabilily index.     

Reduced order adaptive pole placement for multivariable systems

A method is suggested for adaptively assigning the closed-loop poles of a continuous time linear multivariable system. The resulting design significantly reduces the complexity in comparison to any other known multivariable scheme. For implementation one needs to know the order of the system and an upper bound on the observability index.     

A globally convergent pole placement indirect adaptive controller

A pole displacement indirect adaptive control algorithm is discussed for discrete-time linear deterministic plants with arbitrary zeros. The global convergence of the resulting closed-loop control system is achieved subject to the assumptions that the plant order and a nonzero lower bound on its degree of controllability are known. The problem of controllability of the plant model estimate is handled by using both a parameter correction and time-varying nonlinear feedback. A key property of the algorithm is that the plant estimate reaches a reasonable degree of controllability in a finite time, after which the parameter correction and the nonlinear feedback are no longer used     

Robust adaptive pole placement for linear time-varying systems

This paper studies the robustness properties of a basic adaptive control algorithm with respect to plant parameter variation as well as modeling errors and bounded disturbances. The algorithm consists of a projected gradient estimator and a pole assignment controller. A unified method of proof is presented for robust stability of both discrete and continuous-time adaptively controlled time-varying systems. The robust performance of an adaptive pole assignment controller is also discussed     

A parametrization for model reference adaptive pole placement

A new parametrization for a linear system is presented. This parametrization is the basis for two approaches to design an adaptive controller for pole placement. One approach is based on parameter estimation and requires sufficient excitation, while the other, the model reference adaptive pole placement, uses a reference model and an augmented error. It is shown that the two distinct approaches result in identical error terms.     

Direct pole placement adaptive tracking of non-minimum phase systems

In this paper, we propose a direct pole placement adaptive tracking scheme for non-minimum-phase, open-loop stable, linear plants with time delays. This controller utilizes the internal model principle to eliminate steady-state tracking error for signals with known distinct frequencies. The controller order depends only on the number of frequencies in the reference input, but not on the order of the plant. It is shown that with sufficiently small loop gain, the controller can guarantee stable closed loop, and asymptotic tracking.     

Direct adaptive pole placement for plants having purely deterministic disturbances

In this note, an extension of Elliott's direct adaptive pole-placement algorithm [1] for plants having purely deterministic disturbances consisting of sine waves and/or bias is given.     

Direct adaptive pole placement with application to nonminimum phase systems

This note presents the first direct adaptive control structure for nonminimum phase systems where controller parameter identification can be posed as a standard linear parameter estimation problem. In particular, a linear equation error model is formulated for estimating both the controller parameters and some additional auxiliary parameters. The key idea involves insertion of the Bezout polynomial identity into the polynomial design equation which arises in arbitrary pole placement.     

Direct model reference adaptive pole placement control withexponential weighting properties

A parameterization for a linear system is presented to design a direct model reference adaptive pole placement controller. This parameterized model is one of the structured nonminimal models. The exponentially weighted least-squares algorithm is employed to estimate the control parameters. The direct adaptive controller has the exponential weighting properties by the proposed method of selecting the characteristic polynomials of the sensitivity function filters in connection with the reference model     

Stable pole placement direct adaptive control for systems with arbitrary zeros

This paper extends a recently proposed adaptive regulation algorithm to the general case where a non–zero bounded reference signal is allowed. The desired control objectives are asymptotically satisfied in the sense that the estimated plant together with the adaptive controller yield a characteristic polynomial arbitrarily close to the desired one. Furthermore, in the case of a zero reference signal, the regulation objective is asymptotically achieved.     

A globally convergent adaptive pole placement algorithm without a persistency of excitation requirement

This paper presents an indirect adaptive control scheme for deterministic plants which are not necessarily minimum phase. Global convergence is established for the scheme in the sense that the closed-loop poles are asymptotically assigned for the given data sequence and the system input and output remain bounded for all time. A key feature of the scheme is that no persistency of excitation condition is required. The algorithm uses recursive least squares with variable forgetting factor, normalized regression vectors, and a matrix gain with constant trace.     

Robustness in partial pole placement

The robustness of state feedback solutions to the problem of partial pole placement obtained by a new projection procedure is examined. The projection procedure gives a reduced-order pole assignment problem. It is shown that the sensitivities of the assigned poles in the complete closed-loop system are bounded in terms of the sensitivities of the assigned reduced-order poles, and the sensitivities of the unaltered poles are bounded in terms of the sensitivities of the corresponding open-loop poles. If the assigned poles are well-separated from the unaltered poles, these bounds are expected to be tight. The projection procedure is described in [3], and techniques for finding robust (or insensitive) solutions to the reduced-order problem are given in [1], [2].