Perfect and subperfect regulation in linear multivariable control systems

This paper is concerned with the synthesis of a high-gain feedback control, called perfect regulation (p.r.), for linear multivariable systems with external signals. The existence condition for p.r. is derived, in which the minimum phase property plays an essential role. The use of an observer is discussed for achieving p.r. under restricted state observation. Some asymptotically ideal feedback properties are demonstrated, such as the complete desensitization, the complete servo performance with decoupling and the complete disturbance rejection, which formulate the loop-tightness for multivariable systems. A design method for applying p.r. to non-minimum phase systems, called subperfect regulation (s.p.r.), is proposed based on the factorization of the plant transfer function matrix into the minimum phase part and the totally non-minimum phase part. It is a multivariable extension of a well-known design technique for scalar systems to overcome the difficulty of phase non-minimality. Computational procedures for p.r. and s.p.r. are discussed. An illustrative example is shown.     

Strong stabilization of MIMO systems via unimodular interpolation in H

In this paper, the strong stabilization problem of multivariable linear timeinvariant systems is considered. The problem is categorized into minimum and non-minimum phase systems. When the given system is minimum phase, the solution requires a stable inverse of a particular stable transfer function matrix; while for a non-minimum phase system, the solution requires an inner-outer factorization, whose outer part is unimodular in RH, and an interpolation in RH. The formulation of the two cases will be modified so that the conditions for the existence of stable inverse or unimodularity of the outer part are satisfied. When the system is strictly proper it is shown that the problem is more technically involved.     

基于互质分解法的内模控制系统的研究

本文针对内模控制在工业领域中应用的局限,结合现代频域理论的知识,提出了基于互质分解法的二自由度内模控制结构。仿真表明,此方法不仅对具有大时滞和非最小相位的对象有较好的控制效果,而且对干扰和模型失配具有较强的鲁棒性。     

相位的可辨识性及极大似然反褶积

本文所述系统有两个特点:输入为不可量测的随机信号;系统可以具有不稳定的零点或 者说系统可以是非最小相位的.文中研究了将一类输入信号与具有正确相位的脉冲响应从输 出信号中分开的条件,并对以状态空间模型为基础的极大似然反褶积方法进行了改进.利用 合成数据进行了仿真研究,仿真结果验证了非最小相位系统的可辨识性.     

Design of Robust Stabilization and Fault Diagnosis for an Auto-balancing Two-Wheeled Cart

This paper investigates robust fault diagnosis strategies for the auto-balancing of an ergonomically designed two-wheeled cart which is inherently unstable and has a non-minimum phase. To endow the rider with robust stabilization, the normalized coprime factorization for steering is employed for allowing maximum model uncertainties and the driving orientation is achieved with an electronic differential steering control. A model-based fault-detection filter is designed to detect sensor faults. The observer gain obtained by solving an algebraic Riccati equation in the normalized coprime factorization approach offers some design convenience associated with the fault diagnosis filter. In order to promptly alert the rider for safety purposes in the event of a malfunction, the decision-making process to identify a critical failure is also investigated. Finally, evaluation examples are given to illustrate the performance of the proposed robust fault diagnosis strategies.     

Iterative learning control with advanced output data for nonlinear non-minimum phase systems

This paper investigates iterative learning control of nonlinear discrete time non-minimum phase systems in tracking problems. The main objective of this paper is to find an input-to-output mapping in order to stabilize the non-minimum phase systems and to obtain an input update law for handling uncertain systems. In conventional approaches on the tracking of non-minimum phase systems, zero dynamics is stabilized from the system equations and the input is calculated from the state information. For the learning of uncertain systems, conventional approaches depend on the output-to-state and state-to-input mappings. In the proposed method, the inverse system is stabilized using the input-to-output mapping for nonlinear non-minimum phase systems. A new input update law is proposed based on the relative degree and the number of non-minimum phase zeros. This makes the overall proposed learning system have a simple structure as in the classical ILC.     

非最小相位系统的扩展Laguerre基函数迭代学习控制

针对非最小相位系统的跟踪问题,提出了一种新的基函数迭代学习控制算法.该算法利用新型的非因果Laguerre扩展基函数逼近系统逆传递函数,设计最优迭代学习律使系统输入收敛到系统的稳定逆,保证了控制性能.算法不依赖于系统的先验模型,仅需以基函数信号作为系统输入进行模型辨识,减少了模型不确定性的影响.通过对单连杆柔性机械臂这样的典型非最小相位系统跟踪问题的仿真,验证了该方法的良好效果.     

Optimal tracking performance of communication-constrained systems under energy constraints

This paper investigates the optimal tracking performance of systems by considering packet dropouts, additive white Gaussian noise(AWGN), and coding under energy constraints. The optimal tracking performance of communication-constrained systems is obtained by spectral decomposition and partial factorization. The results show that the optimal tracking performance of the system is related to intrinsic properties such as non-minimum phase zeros and unstable poles. What's more, encoding, data loss rate, and AWGN are also able to affect the performance of the system. Finally, the correctness of the results is verified by specific examples.     

Fractional-order unstable pole-zero cancellation in linear feedback systems

As a very well-known classical fact, non-minimum phase zeros of the process put some limitations on the performance of the feedback system. The source of these limitations is that non-minimum phase zeros cannot be cancelled by unstable poles of the controller since such a cancellation leads to internal instability. The aim of this paper is to propose a method for fractional-order cancellation of non-minimum phase zeros of the process and studying its properties. It is specially shown that the proposed cancellation strategy increases the phase and gain margin without leading to internal instability. Since the systems with higher gain and phase margin are easier to control, the proposed method can be used to arrive at more effective controls, which is also verified by the simulation results.     

基于非线性PID的非最小相位系统控制

提出一种新型非线性PID控制器简单结构，利用非线性PID控制器的非线性特性，抑制非最小相位系统的右半平面零点所造成的负调问题，克服非最小相位系统的超凋、负调和调整时间之间的矛盾。数值仿真结果表明，由非线性PID控制器构成的非最小相位系统具有良好的动静态性能、高的控制精度和较强的鲁棒性。数值结果说明方法有效，算法简单，易于实时实现。     

Experimentally validated continuous-time repetitive control of non-minimum phase plants with a prescribed degree of stability

This paper considers the application of continuous-time repetitive control to non-minimum phase plants in a continuous-time model predictive control setting. In particular, it is shown how some critical performance problems associated with repetitive control of such plants can be avoided by use of predictive control with a prescribed degree of stability. The results developed are first illustrated by simulation studies and then through experimental tests on a non-minimum phase electro-mechanical system.     

QFT design for uncertain non-minimum phase and unstable plants revisited

Design method for uncertain non-minimum phase and unstable plants in the quantitative feedback theory (QFT) developed by Horowitz and Sidi is revisited in this paper. It is illustrated that the existing method may not work since some design rules have not been clearly specified by several examples including non-minimum phase plants and unstable plants. Then stability of a new nominal plant is carefully examined and analysed, and an improved design method is presented. The result in this paper provides mathematical justification of the QFT design procedure for nonminimum phase and unstable plants in Horowitz and Sidi (1978) and Horowitz (1992).     

非最小相位系统的基函数型自适应迭代学习控制

针对重复运行的未知非最小相位系统的轨迹跟踪问题, 结合时域稳定逆特点, 提出了一种新的基函数型自适应迭代学习控制(Basis function based adaptive iterative learning control, BFAILC)算法. 该算法在迭代控制过程中应用自适应迭代学习辨识算法估计基函数模型, 采用伪逆型学习律逼近系统的稳定逆, 保证了迭代学习控制的收敛性和鲁棒性. 以傅里叶基函数为例, 通过在非最小相位系统上的控制仿真, 验证了算法的有效性.     

Virtual Reference Feedback Tuning for non-minimum phase plants

Model reference control design methods fail when the plant has one or more non-minimum phase zeros that are not included in the reference model, leading possibly to an unstable closed loop. This is a very serious problem for data-based control design methods, where the plant is typically unknown. In this paper, we extend the Virtual Reference Feedback Tuning method to non-minimum phase plants. This extension is based on the idea proposed in Lecchini and Gevers (2002) for Iterative Feedback Tuning. We present a simple two-step procedure that can cope with the situation where the unknown plant may or may not have non-minimum phase zeros.     

非线性非最小相位系统的控制研究综述

非线性非最小相位系统是指具有不稳定零动态或内部动态的非线性系统, 其本身固有的非最小相位特性限制了许多常规非线性控制方法(如反推控制、反馈线性化、滑模控制等)的直接应用. 因此, 非最小相位系统的控制比最小相位系统要困难得多, 是控制理论与工程应用中具有挑战性的课题之一. 本文综述了目前非线性非最小相位系统的研究成果, 着重介绍了非最小相位系统的成因、特性、 理想内模求解等问题, 并对其镇定、轨迹跟踪及路径跟踪等控制方法进行了分析比较. 最后, 讨论了非线性非最小相位系统研究领域中尚存在的问题, 并对其未来发展方向进行了展望.     

Regulation performance limitation of networked time-delay systems with incomplete information

In this paper, the regulation performance limitation of networked time-delay systems is studied. The communication network is mainly affected by parameters such as packet dropouts, encoding-decoding, interference signal, and channel noises. Non-minimum phase zeros, unstable poles, and time delay are all considered for a given plant. The corresponding regulation performance expression is derived using coprime factorization and spectral decomposition techniques in the frequency domain. The results indicate that the regulation performance of the system is related to the inherent characteristics of the given plant, including non-minimum phase zeros, unstable poles, and time delay. Additionally, network communication parameters such as white Gaussian noise, packet dropouts, encoding-decoding, and external interference signals all affect the regulation performance of networked time-delay systems. Finally, some simulation examples are provided to demonstrate the effectiveness of the theory.     

Weakly and strongly non-minimum phase systems: properties and limitations

In this paper, a new classification of non-minimum phase systems based on stabilisability of the internal dynamics is introduced. According to this classification, the non-minimum phase systems are categorised as follows: (1) weakly non-minimum systems, for which a finite value of minimum norm of the regulation error can be obtained, and (2) strongly non-minimum phase systems for which this minimum norm of the regulation becomes infinite due to the presence of both transient and steady-state errors while for the weakly non-minimum phase systems there is no steady-state regulation error. It is worth mentioning that based on this new classification a level of non-minimum phase-ness can be further defined for any given desired trajectory. Furthermore, some numerical simulations are carried out to show consistency with theoretical analysis.     

垂直/短距起降飞机的轨迹跟踪控制器设计

针对垂直/短距起降飞行器在悬停状态下滚转力矩与横侧向推力存在强耦合、系统具有非最小相位特性的问题,本文设计了轨迹跟踪控制器.首先利用坐标变换和输入输出线性化将系统分解成最小相位子系统和非最小相位子系统.对非最小相位子系统,采用稳态系统中心的方法求解理想内部动态,并跟踪系统理想内模设计了LQR控制器,使得内部动态有界;对最小相位子系统设计了高增益控制器使得外部动态渐进稳定.仿真结果表明本文设计的控制器对给定轨迹和飞行器机动轨迹都有较好的跟踪效果,验证了控制器的有效性.     

Improving an adaptive controller for non-minimum phase plants

This study improves an adaptive controller for linear discrete-time plants in two aspects: (1) a new adaptation law is proposed to reduce the residual and the parameter errors; (2) a new method is proposed to modify the parameter estimates if the estimated model is not controllable. The second improvement is required when the plant is non-minimum phase. It obtains a controllable model from available parameter estimates while minimizing the modification offset. These features enhance closed-loop tracking performance of the adaptive controller when it is applied to non-minimum phase plants.