On pole assignment in linear systems with incomplete state feedback

The following system is considered:dot{x}= Ax + Buy = Cxwherexis annvector describing the state of the system,uis anmvector of inputs to the system, andyis anlvector (l leq n) of output variables. It is shown that if rankC = l, and if (A,B) are controllable, then a linear feedback of the output variables u = K^*y, where K^*is a constant matrix, can always be found, so thatleigenvalues of the closed-loop system matrix A + BK^*C are arbitrarily close (but not necessarily equal) tolpreassigned values. (The preassigned values must be chosen so that any complex numbers appearing do so in complex conjugate pairs.) This generalizes an earlier result of Wonham [1]. An algorithm is described which enables K^*to be simply found, and examples of the algorithm applied to some simple systems are included.     

Robust partial pole assignment problem for high order control systems

In this paper, we consider the partial pole assignment problem (PPAP) for high order control systems. It is shown that solving the PPAP is essentially solving a pole assignment for a linear system of a much lower order, and the robust PPAP is then concerning the robust pole assignment problem for this linear system. Based on this theory, a rather simple algorithm for solving the robust PPAP is proposed, and numerical examples show that this algorithm does lead to comparable results with earlier algorithms, but at much lower computational cost.     

Projection and deflation method for partial pole assignment inlinear state feedback

Two projection methods are proposed for partial pole placement in linear control systems. These methods are of interest when the system is very large and only a few of its poles must be assigned. The first method is based on computing an orthonormal basis of the left invariant subspace associated with the eigenvalues to be assigned and then solving a small inverse eigenvalue problem resulting from projecting the initial problem into that subspace. The second method can be regarded as a variant of the Weilandt deflation technique used in eigenvalue methods     

Dominant pole and eigenstructure assignment for positive systems with state feedback

In this paper, the dominant pole assignment problem, the dominant eigenstructure assignment problem and the robust dominant pole assignment problem for linear time-invariant positive systems with state feedback are considered. The dominant pole assignment problem is formulated as a linear programming problem, and the dominant eigenstructure problem is formulated as a quasiconvex optimisation problem with linear constraints. The robust dominant pole assignment problem is formulated as a non-convex optimisation problem with non-linear constraints which is solved using particle swarm optimisation (PSO) with an efficient scheme which employs the dominant eigenstructure assignment technique to accelerate the convergence of the PSO procedure. Each of the three problems can be further constrained by requiring that the controller has a pre-specified structure, or the gain matrix have both elementwise upper and lower bounds. These constraints can be incorporated into the proposed scheme without increasing the complexity of the algorithms. Both the continuous-time case and the discrete-time case are treated in the paper.     

Limits of generalized state space systems under proportional and derivative feedback

In this paper we study the high-gain feedback classification problem for generalized state space systems. We solve this problem for proportional and derivative feedback transformations of regularizable systems, i.e., we give necessary and sufficient conditions for a regularizable system to be a limit of a given system under high-gain proportional and derivative feedback. We also derive a new complete set of invariants for proportional feedback equivalence and specify a set of necessary conditions for a system to be the limit of another system under these feedback transformations. The necessary conditions are sufficient for arbitrary state space systems and for controllable singular systems.     

Robust semiglobal stabilization of minimum-phase input-outputlinearizable systems via partial state and output feedback

In this paper we consider the problem of robust semiglobal stabilization and/or semiglobal practical stabilization of minimum-phase input-output linearizable systems. The results of this paper significantly extend the recent work of Teel and Praly (1993) on SISO (single-input/single-output) minimum-phase systems in several directions. Among these directions are the development of MIMO (multi-input/multi-output) theory and the relaxation of the restriction on the interaction between nonlinear zero dynamics and the state of the linearizable part of the system     

广义二阶动力学系统的鲁棒特征结构配置

考虑了具有摄动的广义二阶动力学系统的鲁棒特征结构配置问题, 提出了一种优化算法. 该算法的目标是使得特征结构配置的误差最小. 根据广义二阶动力学系统基于状态加微分反馈的参数化特征结构配置结果, 给出了优化指标的完全参数形式. 该算法不包含“返回”过程, 允许特征值在一定范围内参与优化, 能够给出鲁棒性较强的控制系统. 数值例子说明了算法的有效性.     

Exponential stabilization of linear systems with time-varying delayed state feedback via partial spectrum assignment

We consider the problem of controlling a linear system when the state is available with a known time-varying delay (delayed-state feedback control) or the actuator is affected by a delay. The solution proposed in this paper consists in partially assigning the spectrum of the closed-loop system to guarantee the exponential zero-state stability with a prescribed decay rate by means of a finite-dimensional control law. A non conservative bound on the maximum allowed delay for the prescribed decay rate is presented, which holds for both cases of constant and time-varying delays. An advantage over recent and similar approaches is that differentiability or continuity of the delay function is not required. We compare the performance of our approach, in terms of delay bound and input signal, with another recent approach.     

Robust pole assignment for systems with parameters

In this paper we investigate issues related to the control of linear multivariate systems which contain structured, parametric-type uncertainties. The objective is to construct parameter-independent proper compensators that provide ‘robust control’. Specifically, we consider the question of robust pole assignment. Systems are described by matrix fraction representations which involve a structured parametric form of uncertainty. We suggest conditions for robust pole assignability and demonstrate how to construct the required proper compensators. For the problem considered, we show that the class of systems which satisfy these conditions is quite large and we include results on generic solvability. The method is demonstrated by a physical example.     

Robust pole assignment

This paper presents new theorems on the theory of interval matrix inequalities and the theory of polynomials with interval roots, and applies them to the problem of robust pole-placement. We formulate optimization problems and derive convergent iterative algorithms which allow the designer to find controllers that place closed-loop poles within desired intervals for plants with unknown-but-bounded parameter uncertainties. The algorithms are computationally reasonable and provide a useful addition to currently existing control CAD tools.     

Augmented gradient flows for on-line robust pole assignment via state and output feedback

This paper is concerned with robust pole assignment in synthesis of linear control systems via state and output feedbacks. First, both the pole assignment and robustness requirements are appropriately formulated as two optimization problems. Then, gradient flow models are developed for the on-line computation of feedback gain matrices that result in robust pole assignment by solving these two optimization problems. A technique is introduced to facilitate the real-time matrix inverse involved for realizing the gradient flow models. The resulting augmented gradient flows have desired convergence properties. Simulation results are included to show the effectiveness of the proposed approach.