Improved disturbance rejection with online adaptive pole-zero compensation on a Φ-shaped PZT active suspension

In feedback control systems, the anti-resonant zeros cannot be arbitrarily placed, hence degrading tracking performance as well as input disturbance and noise rejection capabilities due to reduced gain at the frequencies of the zeros. In this paper, an online adaptive inverse control with saturation (OAICS) algorithm is proposed for compensating the minimum phase resonant poles and anti-resonant zeros of a PZT active suspension using measured position error signal. Experimental results on a Φ-shaped PZT active suspension using laser Doppler vibrometer (LDV) shows the proposed OAICS is effective in cancelling the first two dominant minimum phase pole-zero pairs to achieve high servo bandwidth and low sensitivity servo system with small overshoot during set-point tracking.     

Digital inverse model control using Generalised holds with extensions to the adaptive case

In this paper, a digital implementation of an inverse-model based control scheme is proposed using Generalised Sampling and Hold Functions. The implementation of the controller using this kind of holds allows overcoming the difficulties related to the presence of unstable zeros in the continuous-time model and the usual appearance of unstable discretisation zeros in the discrete model when a ZOH is applied. The Generalised Sampling and Hold Functions allows obtaining a discrete model of the plant with all its zeros stable which allows realizing an exact inverse model of the plant in comparison to the use of a classical ZOH which only allows, in general, an approximate inversion of the plant. The proposed approach is then extended to the adaptive case where the stability and tracking properties of the general scheme are fully proved. Simulation examples showing the scope and application of the method are also presented.     

Approximate output tracking for nonlinear non-minimum phase systems with an application to flight control

An unstable zero-dynamics is a known obstruction to inducing exact asymptotic tracking for an open set of output trajectories with internal stability. This paper proposes a procedure for achieving approximate tracking for a nonlinear system whose linearization possesses real right-half plane zeros. The method is guaranteed to remove the right-half plane zeros while the other zeros remain in their previous location; moreover, it provides information on the class of signals for which good approximate tracking can be obtained. With other methods, the right-half plane zeros are eliminated but the final location of the remaining zeros is not known a priori. The design procedure is illustrated on a trajectory control problem of an aircraft in rapid manoeuvres. Simulations illustrate the computations involved and show that precise lateral and longitudinal manoeuvres can be performed, even in the presence of uncertainties.     

模型参考自适应控制系统的两种简化方案

基于波波夫超稳定理论进行模型参考自适应控制系统设计,分别采用参考模型极点和零点做滤波器,设计出了两种不用线性补偿器的简化模型参考自适应控制方案,避免了分解系统的繁琐工作,仿真验证本方案能实现渐进跟踪,且控制效果令人满意     

Characterization and compensation of discrete-time non-minimum-phase systems for precision tracking control

The objective of this study is to characterize the unstable zeros of discrete-time non-minimum-phase systems and to compensate the gain and phase errors induced by unstable zeros for tracking control. These two objectives are attempted via examining the frequency response of unstable zeros. The gain error and phase shift induced by unstable zeros are first presented. It is well known that they are undesirable and cannot be cancelled directly via the method of pole-zero cancellation. Through investigating the characteristics of unstable zeros, a systematic approach is then given to compensate the gain and phase errors induced by unstable zeros. Using this approach, both a simple tracking control method and a precision tracking control method are proposed. The design procedure is presented and the design formulae are given. Simulation results are presented to illustrate the effectiveness of the proposed methods.     

Adaptive control of a class of discrete-time MIMO nonlinear systems with uncertain couplings

In this article, adaptive control is investigated for a class of discrete-time multi-input-multi-output nonlinear systems in block-triangular form with uncertain couplings of delayed states among subsystems. Future states prediction is carried out to facilitate adaptive control design and auxiliary outputs are introduced to develop a novel compensation mechanism for the uncertain nonlinear couplings. By using Lyapunov method and ordering signals growth rate, it is rigorously proved that all the signals in the whole closed-loop systems are globally bounded and the output tracking errors asymptotically converge to zeros. The effectiveness of the proposed control is demonstrated in the simulation study.     

Feedforward digital tracking controllers for motion control applications

This paper reviews digital tracking control algorithms for motion control applications. In tracking control, the control objective is to steer the control object along the time-varying desired output. Two design approaches are presented for the case where the desired signal is known in advance, i.e. previewable. One approach is based on the mathematical inverse of a closed-loop system consisting of a controlled plant and a feedback controller. If the mathematical inverse is asymptotically stable, i.e. the closed-loop system does not possess zeros outside the unit circle (unstable zeros), it is an ideal feedforward controller for achieving perfect tracking under the preview assumption. For closed-loop systems with unstable zeros, a cancellation technique for the phase shift induced by unstable zeros is introduced. Another approach is based on linear quadratic optimal control and is known as finite optimal preview control. In this approach, the feedback controller and feedforward controller are determined simultaneously by minimizing a quadratic performance index which involves a tracking error term and a term related to the control effort. Applications of these tracking control algorithms to mechanical systems control are described.     

On blocking zeros

A new set of zeros, the blocking zeros, for linear time-invariant multivariable systems is described. The motivation for focusing attention of the blocking zeros is that they serve to characterize the essential feature that the error transfer function matrix of an asymptotic tracking control system must possess.     

多输入输出反馈系统虚轴的零点对跟踪问题的约束

反馈系统的设计会受到闭环系统特性的制约. 本文给出了反馈控制系统接近虚轴或虚轴上的稳定零点对跟踪误差的时间域积分约束. 这一时间域积分约束是任何一个线性时不变系统为保证其闭环系统的稳定性, 其跟踪误差必须满足的. 接近虚轴或虚轴上的稳定零的存在表明跟踪误差与调节时间之间存在某种折中. 对固定的调节时间, 本文给出了在虚轴上存在零点情形下, 其跟踪误差的无穷范数下界的一个有效估计. 此估计表明, 零点的绝对值越小, 其无穷范数的下界越大. 这些约束由一个例子加以解释.     

Limitations on maximal tracking accuracy

This paper studies optimal tracking performance issues pertaining to finite-dimensional, linear, time-invariant feedback control systems. The problem under consideration amounts to determining the minimal tracking error between the output and reference signals of a feedback system, attainable by all possible stabilizing compensators. An integral square error criterion is used as a measure for the tracking error, and explicit expressions are derived for this minimal tracking error with respect to step reference signals. It is shown that plant nonminimum phase zeros have a negative effect on a feedback system's ability to reduce the tracking error, and that in a multivariable system this effect results in a way depending on not only the zero locations, but also the zero directions. It is also shown that if unity feedback structure is used for tracking purposes, plant nonminimum phase zeros and unstable poles can together play a particularly detrimental role in the achievable tracking performance, especially when the zeros and poles are nearby and their directions are closely aligned. On the other hand, if a two parameter controller structure is used, the achievable tracking performance depends only on the plant nonminimum phase zeros     

Compensation of uncertain continuous systems by using the internal model control principle

In this paper the design of compensators for uncertain continuous plants is investigated. The standard derived compensators are based on the application of the internal model control (IMC) method. The required a priori knowledge on the plant is rather weak, namely, an upper bound of the plant relative order, the numbers of the strictly unstable and critically unstable plant poles being integrators and upper and lower bounds of the amplitude-versus-frequency plot over the low frequency band in the case of minimum-phase open-loop systems. If the open-loop system has unstable zeros and/or poles then the above bounds are required to be known for a modified magnitude plot which substitutes the unstable zeros (poles) by stable poles (zeros) which are their complex-conjugate reflections on the left-hand plane. An absolute upper bound of the open-loop phase plot is obtained on a finite frequency interval which allows the closed-loop system to guarantee a prescribed relative stability in many practical situations. The method is dependent on the alternative design of phase lead/lag classical compensators and to indirect adaptive control situations where the adaptive identifier is used for the parametrization of the adaptive controller.     

A parameter adaptive control structure for linear multivariable systems

This paper presents an adaptive control structure which can be used to assign all poles and zeros of a continuous-time linear multivariable system represented by an (m times m) strictly proper transfer matrixT(s), providedT(s)has no right-half plane zeros. The controller parameters can be directly estimated from input-output data. The paper also serves to point out the type of a priori information necessary for multivariable adaptive controller design. This information is a natural extension of that required in the scalar case.     

Imperfect model reference adaptive control: deadbeat output error approach

It is well known that while the perfect model matching condition (i.e. unstable plant zeros must be zeros of the reference model) is not met, the model reference adaptive control cannot easily be implemented. In adaptive control systems, since the plant is assumed to be unknown previously, it is a difficult task to choose an adequate reference model such that the perfect model matching condition is guaranteed in every adaptive step. In this paper, a new design algorithm for model reference adaptive control systems is proposed to synthesize an adaptive controller such that the error between the reference model output and the plant output can vanish in a deadbeat manner. In this situation, the stringent matching condition can be relaxed in every adaptive step, so our design algorithm is also suitable for unstable or non-minimum phase systems. Several simulation results are presented to illustrate the good behaviour of our design algorithm.     

Adaptive visual tracking using the prioritized Q-learning algorithm: MDP-based parameter learning approach

This paper introduces an adaptive visual tracking method that combines the adaptive appearance model and the optimization capability of the Markov decision process. Most tracking algorithms are limited due to variations in object appearance from changes in illumination, viewing angle, object scale, and object shape. This paper is motivated by the fact that tracking performance degradation is caused not only by changes in object appearance but also by the inflexible controls of tracker parameters. To the best of our knowledge, optimization of tracker parameters has not been thoroughly investigated, even though it critically influences tracking performance. The challenge is to equip an adaptive tracking algorithm with an optimization capability for a more flexible and robust appearance model. In this paper, the Markov decision process, which has been applied successfully in many dynamic systems, is employed to optimize an adaptive appearance model-based tracking algorithm. The adaptive visual tracking is formulated as a Markov decision process based dynamic parameter optimization problem with uncertain and incomplete information. The high computation requirements of the Markov decision process formulation are solved by the proposed prioritized Q-learning approach. We carried out extensive experiments using realistic video sets, and achieved very encouraging and competitive results.     

Optimal tracking performance of MIMO discrete‐time systems with communication constraints

The optimal tracking problem for multiple‐input multiple‐output linear‐time‐invariant discrete‐time systems with communication constraints in the feedback path is studied in this paper. The tracking performance is measured by the energy of the error signal between the output of the plant and the reference signal. The objective is to obtain an optimal tracking performance, attainable by all possible stabilizing compensators. It is shown that the optimal tracking performance consists of two parts, one depends on the nonminimum phase zeros and zero direction of the given plant, as well as the reference input signal direction, and the other depends on the nonminimum phase zeros, unstable poles, and pole direction of the given plant, as well as the bandwidth and additive white Gaussian noise of the communication channel. It is also shown that, if the constraint of the communication channel does not exist, the optimal tracking performance reduces to the existing tracking performance of the control system without communication constraints. A typical example is given to illustrate the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

Finite-time behavior of inner systems

In this paper, we investigate how nonminimum phase characteristics of a dynamical system affect its controllability and tracking properties. For the class of linear time-invariant dynamical systems, these characteristics are determined by transmission zeros of the inner factor of the system transfer function. The relation between nonminimum phase zeros and Hankel singular values of inner systems is studied and it is shown how the singular value structure of a suitably defined operator provides relevant insight about system invertibility and achievable tracking performance. The results are used to solve various tracking problems both on finite as well as on infinite time horizons. A typical receding horizon control scheme is considered and new conditions are derived to guarantee stabilizability of a receding horizon controller.     

Performance limitations in the robust servomechanism problem for discrete-time LTI systems

Fundamental limitations for error tracking/regulation are obtained for the robust servomechanism problem (RSP) for a sampled system. In studying this problem, the cheap control problem for a multi-input/multi-output discrete time system is considered, and explicit expressions are obtained for the limiting steady state solution of its associated algebraic Riccati equation (ARE), as the weight on the control energy tends to zero. Application of these results is then made to obtain explicit expressions for the limiting performance costs associated with error tracking/regulation in the RSP. These limitations can be characterized by the system order, the dimension of the outputs, the number of the system's transmission zeros and the location of the system's nonminimum phase transmission zeros.     

Performance limitations in the robust servomechanism problem for discrete time periodic systems

Fundamental limitations for error tracking/regulation are obtained for the robust servomechanism problem (RSP) for discrete time periodic systems. In studying this problem, the RSP for a multi-input/multi-output discrete time system is considered; application of these results is then made to the “periodic system robust servomechanism problem”, and explicit expressions for the limiting costs for error tracking regulation are obtained. These limitations can be characterized completely by the number and location of the non-minimum phase transmission zeros of the system's associated lifted system, together with a term which depends on the order of the system, the number of inputs, the number of transmission zeros and the system's period.     

适用于含公共零点SIMO信道的盲均衡算法

在含公共零点单输入多输出(SIMO)模型的基础上,提出一种针对含公共零点的SIMO信道的直接无限冲击响应(IIR)盲均衡算法。该算法利用IIR预测均衡算法对输入信号进行初始均衡和对均衡结果进行相偏纠正,通过最小均方误差准则提高算法在高斯白噪声环境中的适应性,克服IIR预测算法中的相位偏转问题与IIR预测算法对信噪比敏感的缺点。仿真实验结果表明,该算法对IIR信道及含公共零点信道都具有较好的均衡效果。     

Improvement of stability of zeros in discrete-time multivariable systems using fractional-order hold

This paper is concerned with the stability of zeros of the discrete-time multivariable systems composed of a fractional-order hold (FROH), a continuous -time plant and a sampler in cascade. The properties of the limiting zeros are studied and a condition for obtaining stable zeros for sufficiently small sampling periods is derived. An approximate fractional-order hold (AFROH) is proposed as an implementation of FROH. It is shown that the AFROH as well as the FROH can locate the zeros of discrete-time multivariable systems inside the stable region and improve stability properties when the zero-order hold (ZOH) cannot. Experimental results of adaptive control with AFROH demonstrate a significant improvement of control performance compared with the use of a ZOH.