Pole assignment using proportional-plus-integral output feedback control

The design of proportional-plus-integral compensators for linear multivariable systems is considered, using an output feedback control law. An algorithm is developed based on results obtained elsewhere (Munro and Novin-Hirbod 1979). It is shown that cyclicity of the augmented system matrix is not needed with this approach. It is also demonstrated that the integral part of the compensator should be of full-rank for an arbitrary set of non-zero eigenvalues to be assignable.     

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.     

Robust control of uncertain systems with polynomial nonlinearity by output feedback

The problem of global robust stabilization by output feedback is investigated for two classes of uncertain systems with polynomial nonlinearity—one is with controllable/observable linearization and the other is not. The uncertainties in the systems are assumed to be dominated by both lower‐ and higher‐order nonlinearities multiplying by an output‐dependent growth rate. There are two ingredients in this study. One is to exploit the idea of how to handle polynomial growth conditions via homogeneity and domination without introducing an observer gain updated law. The other is the development of a recursive design algorithm for the construction of reduced‐order observers, which is not only interesting in its own right but also has a valid counterpart, capable of dealing with strongly nonlinear systems, even lack of uniform observability and smooth stabilizability. Copyright © 2008 John Wiley & Sons, Ltd.     

Insensitive and robust control design via output feedback eigenstructure assignment

Insensitive and robust control design using output‐feedback eigenstructure assignment for linear multivariable systems is considered in this paper. A parametric expression of closed‐loop eigenvectors and generalized eigenvectors is developed. It can cope with the case where the closed‐loop eigenvalues are multiple and/or the same as the open‐loop ones so that the system to be designed can be uncontrollable and/or unobservable. The controller designed via output‐feedback eigenstructure assignment is expressed by proposed parameter vectors. The freedom provided by output‐feedback eigenstructure assignment is used to optimize some performance functions which are used to measure the sensitivity of the closed‐loop matrix and the robustness of the closed‐loop system. Copyright © 2000 John Wiley & Sons, Ltd.     

Descent algorithms for optimal periodic output feedback control

Periodic output feedback is investigated in the context of linear-quadratic regulation for finite-dimensional time-invariant linear systems. Discrete output samples are multiplied by a periodic gain function to generate a continuous feedback control. The optimal solution is obtained in two steps by separating the continuous-time from the discrete-time structure. First, the optimal pole placement problem under periodic output feedback is solved explicitly under the assumption that the behavior at the sample times has been specified in terms of a gain matrix G. Then the minimum value, which depends on G, is substituted into the overall objective. This results in a finite-dimensional nonlinear programming problem over all admissible gain matrices G. The solution defines the optimal periodic output feedback control via the formulas of the optimal pole placement problem. A steepest descent and a direct iterative method for solving this problem are formulated and compared. Numerical examples show that the performance using periodic output feedback is almost equivalent to that using optimal continuous-state feedback     

Robust output feedback control of polynomial growth nonlinear systems with measurement uncertainty

Even in the presence of uncertainty in both state and output equations, we prove that global asymptotic stabilization is still possible by output feedback for a family of uncertain nonlinear systems dominated by a triangular system with a polynomial output‐dependent growth rate. In contrast to the linear growth requirement in the recent work the nonlinear perturbations in this paper are allowed to satisfy a linear growth condition with a polynomial output‐dependent rate. To handle simultaneously the polynomial nonlinearities and unknown parameter in the system output, we propose a high‐gain estimator with a dynamic gain that is updated online through a Riccati‐type dynamic equation. Then, an estimator‐based controller is designed by a recursive algorithm that makes it possible to assign the controller gains step by step. The globally stabilizing output‐feedback controller developed in this paper is robust with respect to uncertainties in the system dynamics and output equations.     

On optimal output feedback

Control of linear systems through the use of constant output feedback is considered. Conditions obtained by Levine and Athans [1] that must be satisfied by constant feedback gains in order to be optimal are developed here using an alternate and mechanically simpler approach.     

Simultaneous linear-quadratic optimal control design via static output feedback

In this paper, the problem of designing a fixed static output feedback control law which minimizes an upper bound on linear quadratic (LQ) performance measures for r distinct MIMO plants is addressed using linear matrix inequality (LMI) technique. An iterative LMI algorithm is proposed to obtain the solution. Examples are used to demonstrate its effectiveness. Copyright ©1999 John Wiley & Sons, Ltd.     

Parametric control of quasi-linear second-order systems with partitioned eigenstructure assignment by output feedback

In this paper, a parametric design approach for stabilizing a quasi-linear second-order system with partitioned eigenstructure assignment(PESA) is investigated through output feedback control. The PESA approach is established by partitioning the desired eigenvalue matrix into two parts to separate the associated right and left eigenvectors into a subset of the generalized eigenvectors simultaneously. A parametric controller is established by solving two second-order generalized Sylvester matrix ...     

Eigenvalue-generalized eigenvector assignment by output feedback

This note generalizes the previous results of the closed-loop eigenstructure assignment via output feedback in linear multivariable systems. Necessary and sufficient conditions for the closed-loop eigenstructure assignment by output feedback are presented. Some known results on entire eigenstructure assignment are deduced from this result.     

船舶航向非线性H∞逆优化输出反馈控制

为抑制船舶航向非线性优化控制中模型参数摄动和由状态观测器引入的不确定观测误差,提出了一种非线性H∞逆优化控制算法.首先,基于无源理论设计观测器以实现海浪滤波,该观测器无需海浪扰动的方差信息从而减少了观测器参数数量.然后,考虑模型参数摄动对观测误差的影响,给出了描述系统局部(全局)性态的局部(全局)H∞优化性能指标.在以广义黎卡提方程(GARE)对局部优化问题的求解的基础上,应用逆优化方法将全局H∞优化问题转化为构造闭环系统的Lyapunov函数问题,得到同时满足两种指标的优化控制器,并证明了稳定性.仿真结果证明了该算法的有效性.     

A gradient flow approach to decentralised output feedback optimal control

This paper visits the quadratic optimal control problem of decentralised control systems via static output feedback. A gradient flow approach is introduced as a tool to compute the optimal output feedback gain. Several nice properties are revealed concerning the convergence of the gain matrix along the trajectory of an ordinary differential equation obtained from the gradient of objective cost, i.e. the objective cost is decreasing along this trajectory. If the equilibrium points are isolated, the convergence can be guaranteed. A simulation example is given to illustrate the effectiveness of this approach.     

Eigenstructure assignment by output feedback and residue analysis

This note deals with the use of feedback to approximate the closed-loop eigenstructure of a system to a prescribed set of values. A new method is proposed to reduce the controller complexity, based on eigenvalue sensitivity concepts. A flight control example is presented as an application.     

Pole assignment using dynamic output feedback compensators

The design of dynamic output feedback compensators for the pole assignment of linear time-invariant multivariable systems is considered. A systematic procedure is developed for the synthesis of the transfer function matrix of the compensator. A certain number of poles can be arbitrarily assigned by the proposed compensator. Moreover, in order to assign more poles using a compensator of the same order as before, a new approximate assignment approach based on the least-square-error algorithm is proposed. A numerical example is given to demonstrate the effectiveness of the proposed approaches.     

Eigenvalue/eigenvector assignment using output feedback

The problem of pole-assignment in a linear time-invariant multivariable system using output feedback is considered. New sufficient conditions are derived to assign an almost arbitrary set of min(n,m+r- 1)distinct eigenvalues, wheren, m, andrare the number of states, inputs, and outputs, respectively. The analysis also highlights the freedom in selection of closed-loop eigenvectors which can be used for response shaping.     

Relatively optimal control and its linear implementation

Motivated by the fact that determining a feedback solution for the optimal control problem under constraints is a hard task we introduce the concept of relative optimality, roughly optimality for a specific (nominal) plant initial condition. We consider a generic discrete-time finite-horizon constrained optimal control problem for linear systems, and we seek for a state feedback (possibly dynamic) controller. As a fundamental requirement, we do not admit preactions or controller-state initialization based on the plant initial state and we assume our controller to be time-invariant. In particular, we do not consider controllers simply achieved by the feedforward and tracking of the optimal trajectory. A relatively optimal control is a stabilizing controller such that, if initialized at its zero state, produces the optimal (constrained) trajectory for the nominal initial condition of the plant. We show that one of such controllers is linear, dead-beat, and its order is equal to the length of the horizon minus the plant order, thus, of complexity which is known a priori. Some additional features such as the assignment of the compensator poles to achieve strong stabilization are proposed. We show that, by means of the proposed approach, we can face several problems such as optimal point-to-point operations, optimal impulse response and optimal tracking.     

LQG optimal scalar static output feedback

An eigenproblem-based technique is given for computing the stabilizing scalar static output feedback gain that minimizes the standard linear quadratic performance index in the presence of a Gaussian white-noise disturbance. The method adapts recent work on eigenproblem-based computation of _∞-norms.     

Generic eigenvalue assignment by memoryless real output feedback

By extensive use of methods from algebraic geometry, X. Wang proved that arbitrary pole placement by static output feedback is generically possible for strictly proper plants with n states, m inputs, and p outputs, if n < mp. Here we show the same result using no more of algebraic geometry than the definition of genericity.     

Exact pole assignment by output feedback Part 2

We continue the study in Fletcher and Magni (1987) concerning controllable and observable linear time-invariant multivariable control systems in which the number of inputs plus the number of outputs exceeds the number of states. In this paper we shall prove that exact assignment of distinct poles by means of a real output feedback is always possible if the set of poles to be assigned consists entirely of complex conjugate pairs of non-real numbers. We examine the problem of assigning these eigenvalues in complex conjugate pairs by means of the algorithm described in the first paper. We reduce the problem to the case in which just one of the observability and controllability indices of the system is larger than 2, and further detailed analysis then disposes of this case.     

Exact pole assignment by output feedback Part 3

This part concludes a series of three papers concerning controllable and observable linear time-invariant multivariable control systems in which the number of outputs plus the number of inputs exceeds the number of states. Following from the second paper (Fletcher 1987) it remains to consider the assignment by real output feedback of a set of distinct eigenvalues consisting of a mixture of real numbers and complex conjugate pairs of non-real numbers. We examine the possibility that in the algorithm described in the first paper (Fletcher and Magni 1987) all the real eigenvalues can be assigned before any of the complex conjugate pairs. If this is possible then the argument of Fletcher (1987) can be used to complete the assignment. It is only from the failure of this possibility that the pathological cases detailed in the first paper can arise.