Pole assignment by output feedback: A solution for 2 × 2 plants

The problem of pole assignment by static output feedback is solved in this paper for 2 × 2 plants. It is shown that the problem solvability is equivalent to the solvability of some quadratic equation and the latter can be checked through the affine transformation of quadratic functions. All solutions are given in a parametric form if a solution exists. An example is provided to illustrate the method.     

Pole assignment with output feedback

For pole assignment with output feedback, appropriate partitioning of the coefficient matrix of the system numerator transfer function matrix leads to simplified design equations to solve for the vectors of the unity rank output feedback matrix. This concept is applied to derive the pole placement equations for the proportional-derivative output feedback dynamic compensator. The simplicity of the design procedure is illustrated with a numerical example.     

Pole assignment for linear time-invariant systems by periodic memoryless output feedback

It is well known that the poles of a linear time-invariant controllable and observable system can be assigned arbitrarily by state feedback. When only the output is available, pole assignment is still possible by means of dynamic output feedback. In this paper the potential of time-varying memoryless output feedback is considered. It is shown that, up to some technical conditions, it is indeed possible to allocate the poles of a linear time-invariant discrete-time system by memoryless output feedback with periodic gains. The period of the gains is (n + 1) with n the order of the system. The power of the design technique is proved to be comparable to what can be achieved by the classical dynamic feedback approach.     

A necessary condition for pole assignment by constant output feedback

In this paper we shall investigate the pole assignment problem by constant output feedback using transfer function techniques. In particular, a necessary condition is given for the existence of constant output feedback which assigns the eigenvalues of closed-loop system to any desired positions.     

Pole assignment for uncertain systems in a specified disk by output feedback

In this paper the problem of pole assignment in a disk by output feedback for continuous-or discrete-time uncertain systems is addressed. A necessary and sufficient condition for quadratic d stabilizability by output feedback is presented. This condition is expressed in terms of two parameter-dependent Riccati equations whose solutions satisfy two extra conditions. An output d stabilization algorithm is derived and a controller formula given.     

On pole assignment of linear systems by gain output feedback

In this paper, the Geometric Approach is used to derive in a straightforward way a sufficient condition for pole assignability by gain output feedback. This result leads to a pole assignment procedure which reduces to solving a system of min (n - m, n - p) polynomial equations where n is the number of states, m the number of inputs, p the number of outputs. In the case where m + p > n, this system clearly appears to be linear. The degrees of freedom related to the pole assignment problem are expressed in terms of (right or left) eigenvectors.     

Set-point-related indirect iterative learning control for multi-input multi-output systems

A form of iterative learning control (ILC) is used to update the set-point for the local controller. It is referred to as set-point-related (SPR) indirect ILC. SPR indirect ILC has shown excellent performance: as a supervision module for the local controller, ILC can improve the tracking performance of the closed-loop system along the batch direction. In this study, an ILC-based P-type controller is proposed for multi-input multi-output (MIMO) linear batch processes, where a P-type controller is used to design the control signal directly and an ILC module is used to update the set-point for the P-type controller. Under the proposed ILC-based P-type controller, the closed-loop system can be transformed to a 2-dimensional (2D) Roesser s system. Based on the 2D system framework, a sufficient condition for asymptotic stability of the closed-loop system is derived in this paper. In terms of the average tracking error (ATE), the closed-loop control performance under the proposed algorithm can be improved from batch to batch, even though there are repetitive disturbances. A numerical example is used to validate the proposed results.     

Nonlinear disturbance observer-based control for multi-input multi-output nonlinear systems subject to mismatching condition

For a multi-input multi-output (MIMO) nonlinear system, the existing disturbance observer-based control (DOBC) only provides solutions to those whose disturbance relative degree (DRD) is higher than or equal to its input relative degree. By designing a novel disturbance compensation gain matrix, a generalised nonlinear DOBC method is proposed in this article to solve the disturbance attenuation problem of the MIMO nonlinear system with arbitrary DRD. It is shown that the disturbances are able to be removed from the output channels by the proposed method with appropriately chosen control parameters. The property of nominal performance recovery, which is the major merit of the DOBCs, is retained with the proposed method. The feasibility and effectiveness of the proposed method are demonstrated by simulation studies of both the numerical and application examples.     

A self-tuning fuzzy controller for a class of multi-input multi-output nonlinear systems

This paper presents a systematic design procedure of a multivariable fuzzy controller for a general Multi-Input Multi-Output (MIMO) nonlinear system with an input-output monotonic relationship or a piecewise monotonic relationship for each input-output pair. Firstly, the system is modeled as a Fuzzy Basis Function Network (FBFN) and its Relative Gain Array (RGA) is calculated based on the obtained fuzzy model. The proposed multivariable fuzzy controller is constructed with two orthogonal fuzzy control engines. The horizontal fuzzy control engine for each system input-output pair has a hierarchical structure to update the control parameters online and compensate for unknown system variations. The perpendicular fuzzy control engine is designed based on the system RGA to eliminate the multivariable interaction effect. The resultant closed-loop fuzzy control system is proved to be passive stable as long as the augmented open-loop system is input-output passive. Two sets of simulation examples demonstrate that the proposed fuzzy control strategy can be a promising way in controlling multivariable nonlinear systems with unknown system uncertainties and time-varying parameters.     

Pole assignment of multivariable systems using proportional-derivative state feedback

In this article, the parametric solution to the pole assignment problem for multivariable linear time-invariant systems controlled by proportional-derivative (PD) state feedback is developed. The new expressions for the PD gain controllers are derived which describe the available degrees of freedom offered by PD state feedback. The freedom provided by PD state gain matrices is utilised to obtain closed-loop systems with robust and small gain matrices. Two computational algorithms are introduced, and their effectiveness is demonstrated by two simulation examples.     

执行器有故障的多输入单输出系统的自适应输出反馈控制

对一类控制增益符号未知且执行器有故障的输出反馈多输入单输出非线性系统,提出了一种后推容错控制方案.该方案在系统状态不可量测的情况下,利用Nussbaum函数处理符号未知的常数增益,并通过构造K-滤波器来估计了系统不可量测的状态.在容错控制器设计过程中,引入变能量函数来处理利用虚拟控制律所无法抵消的部分.与现有研宄成果相比,放宽了未知增益需要上下界均为已知的假设条件.最后,通过选取合适的李雅普诺夫函数,证明了闭环系统所有信号半全局一致终结有界,且跟踪误差收敛到原点的一个小邻域内.仿真结果表明了所提控制方法的有效性.     

An algorithm to compute state feedback matrices for multi-input deadbeat control

An algorithm for the computation of a state feedback controller shifting all eigenvalues of the closed loop system to the origin is presented. The available freedom in multi-input systems is used to reduce the norm of the feedback matrix. The algorithm places one or more eigenvalues in each step using partial feedback laws of minimal norm. This results in an overall feedback matrix whose norm is close to its minimum value in most cases.     

Generalized pole placement via static output feedback: A methodology based on projections

This paper presents an algorithm for solving static output feedback pole placement problems of the following rather general form: given n subsets of the complex plane, find a static output feedback that places in each of these subsets a pole of the closed-loop system. The algorithm presented is iterative in nature and is based on alternating projection ideas. Each iteration of the algorithm involves a Schur matrix decomposition, a standard least-squares problem and a combinatorial least-squares problem. While the algorithm is not guaranteed to always find a solution, computational results are presented demonstrating the effectiveness of the algorithm.     

Gain-scheduled static output feedback controller synthesis for discrete-time LPV systems

This study is concerned with the problem of gain-scheduled static output feedback H_∞ controller synthesis for discrete-time linear parameter varying systems. The scheduling parameters, which may affect all the system matrices, and their deviations are supposed to lie in a known hyper-rectangle. A design procedure is presented in terms of sequentially solving three parameter-dependent linear matrix inequality (LMI) optimisation problems. The parameter-dependent LMIs are solved through finite-dimensional LMI relaxations exploiting homogeneous polynomial matrices of arbitrary degree. One of the advantages of the new method lies in its less conservatism which is theoretically shown in comparison with some available approaches. By an iterative scheme, the performance of the method can be improved. Numerical examples reveal the effectiveness of the new method.     

Global output feedback control for uncertain nonlinear feedforward systems

This paper considers a class of uncertain nonlinear feedforward systems with unknown constant growth rate, output polynomial function growth rate and system input function growth rate. Under the most general growth rate condition, only one dynamic gain is used to compensate simultaneously these three types of growth rates, an output feedback controller is constructed to guarantee the boundedness of closed-loop system states and the convergence of original system states.     

Pole assignment for systems over rings

A very simple proof of the pole assignment theorem for systems over a principal ideal domain (and other rings) is given. Furthermore, an algorithm is presented. Extensions are also indicated.     

Adaptive hierarchical control for output feedback systems

In this paper, we address the problem of adaptive hierarchical control for a class of so-called uncertain output feedback systems. The proposed approach is to design an adaptive output interface dynamic by estimating the uncertainties. With the interface connected to the uncertain nonlinear system and a linear abstract system, the system could track approximately the abstraction. Finally, two examples are presented to illustrate our approach.     

多输出非线性系统在数据截断协议下的 时滞多采样率输出反馈镇定

本文研究一类多输出非线性系统基于一类数据截断协议的时滞多采样率输出反馈控制. 所考虑的非线性 系统的输出以异步方式进行采集, 通过网络传输到输出反馈控制端后立即用于构造输出反馈控制器. 当控制输入 信号可用时, 立即用来更新被控制系统. 这样, 就存在两种传输时滞, 一种是非线性系统输出端到输出反馈控制器端 的传输时滞, 另一种是输出反馈控制器端到非线性系统输入端的传输时滞. 从而被控系统的更新和输出反馈控制 器的更新不在同一个时间区间. 利用区间分解, 可以在同一个区间考虑被控系统和输出反馈控制器并分析闭环系 统的稳定性. 最后, 一个算例用来验证所提方法的有效性.     

Static output feedback based fault accommodation design for continuous-time dynamic systems

This article addresses the integrated fault estimation (FE) and accommodation problem for continuous-time dynamic systems. First, using a specific system decomposition, we propose a new multi-objective reduced-order FE observer (RFEO), whose application range is wider than the existing adaptive and sliding mode ones. FE performances are further enhanced by introducing slack variables to reduce the conservatism generated by the direct design method. Finally, with the help of both system decomposition and slack variable techniques, a static output feedback fault tolerant controller (SOFFTC) design, whose sufficient condition is given in terms of linear matrix inequalities, is proposed to guarantee the stability of the closed-loop system in the presence of faults. Moreover, the RFEO and the SOFFTC are designed separately, so that their design parameters can be calculated easily. Simulation results of an aircraft application are presented to illustrate our contributions.     

实现输出反馈极点配置的数值方法

本文讨论了用数值方法实现输出反馈极点配置的问题.求解反馈阵的矩阵方程被等效成非线性向量方程,用牛顿迭代法可求得反馈阵.本文推导了牛顿迭代法所需的导数公式,并给出有关算例.还可将非线性向量方程化作性能指标,用寻优的方法求得所需的输出反馈阵.