Robust partial pole assignment problem for high order control systems

A computational approach is proposed to solve the minimum norm and/or robust pole assignment problem for linear periodic discrete-time systems. The proposed approach uses a periodic Sylvester equation based parametrization of the periodic pole assignment problem and exploits the non-uniqueness of the problem by imposing conditions on the norm of the resulting periodic state feedback and/or on the condition numbers of the periodic eigenvector matrices of the closed-loop system. The solution method relies on using gradient search methods on suitably defined cost functions. Explicit expression of the gradients of cost functions are derived and the efficient evaluation of the cost functions and gradients is discussed. Numerical examples illustrate the effectiveness of the proposed approach.

This paper considers pole assignment and robust pole assignment problems for discrete-time linear periodic systems by using linear periodic state feedback. The monodromy matrix of the closed-loop system is represented in a special form. By combining this special form with our recent result on solutions to a class of generalized Sylvester matrix equations, a complete parametric approach for pole assignment via periodic state feedback is proposed. The free parameters existing in the solutions to pole assignment are further used to achieve robustness performances. The robust pole assignment problem is converted into a nonconvex optimization problem. Numerical examples illustrate the effectiveness of the proposed approaches.

This short paper deals with the problem of pole assignment with incomplete state observation. It is shown that if the system is controllable and observable, and if n \leq r + m - 1 , an almost arbitrary set of distinct closed-loop poles is assignable by gain output feedback, where n, r , and m are the numbers of state variables, inputs and outputs, respectively. This result improves considerably the ones obtained so far about this problem. Different from the conventional approach using the characteristic equation, an approach based on the properties of the eigenspaces of the closed-loop dynamics is used in this short paper, which gives a new light on the various problems in the linear system theory. It is also shown, as a direct consequence of this result, that the minimum order of the dynamic compensator required for almost arbitrary pole assignment of overall closed-loop system is not greater than n - m - r + 1 .

The problem of pole assignment in linear multivariable systems by means of unity rank output feedback is studied in this paper. It is shown that when the number of specified poles is equal to the number of inputs or outputs of the system, exact pole assignment can be achieved and the feedback matrix is calculated from a set of simple linear equations. When the number of specified poles exceeds this value, the pole assignment problem becomes non-linear. Three different formulations of the problem are considered and three numerical techniques are described for the calculation of the feedback matrix. Numerical examples are given for illustration.

This paper introduces a mathematical formula for calculating the eigenvalue differential sensitivities of the closed-loop state matrix with respect to a disturbance matrix when the closed-loop system is subjected to an additive structured perturbation. The robust pole assignment problem is then formulated as an optimization task in which the differential sensitivities of the closed-loop poles are minimized. The case of “multi-perturbations” can be considered naturally in our problem formulation. The gradient of the objective function to be minimized is then derived which permits the minimization to be proceeded effectively. Numerical examples are then employed to illustrate the design technique.

It is shown that the problem of pole assignment by gain output feedback in linear time-invariant multivariable systems may be reduced to an algebraic optimisation problem, using the concept of virtual model following. The method requires no transformation of the open-loop system to a canonical form. A number of related problems involving combinations of pole placement with a secondary design objective are also discussed.

This paper highlights the importance of the co-efficient matrix of the numerator transfer function matrix in pole placement and stabilization assessment of multivariable control systems. The problem of pole assignment with non-unity-rank output feedback, obtained as the sum of unity rank output feedback in two stages, is discussed. The design equations of Seraji [5] formulated in terms of the appropriately partitioned co-efficient matrix of the system numerator transfer function matrix. The pole placement and stabilization assessment procedures are illustrated with numerical examples.

Partial eigenvalue assignment with time delay in high order system using the receptance

The pole assignment problem for distributed parameter systems governed by analytic semigroups is discussed. Introducing unbounded feedback operators, we can solve the problem under a weaker restriction on the separation of the open-loop and the closed-loop poles. These types of feedback systems inherit the spectrum determined growth assumption of the open-loop systems. We first present a characteristic equation whose roots are the poles of the closed-loop system. Next we give a feedback element which realizes the desired pole assignment of the closed-loop system. We show an interesting result that an infinite number of the open-loop poles can be uniformly moved by means of a suitable linear feedback. We apply the results -to a heat system and a flexible structure for the cases of distributed controls and boundary controls.

Robust pole assignment in systems subject to structured perturbations

ABSTRACTThe paper considers the pole assignment and the stabilisation problem under the practically essential constraint, that the designed controllers have to be causal, because only in that case they will be realisable in real time. It is shown that in case of a strictly proper process, when the set of solutions of the pole assignment or stabilisation problem is not empty, then it always contains a non-empty subset of non-causal controllers. Moreover, according to the set of causal controllers, we have one of the three situations: (1) the set is empty, (2) the set has actually one element and (3) there exists a subset of causal solutions. The paper provides complete solutions for both problems in the form of instructions for building the corresponding sets of causal controllers. Drawing on examples of a double integrator with delay, the procedures are illustrated.

Pole assignment for linear systems by periodic output feedback

A multi-step method for partial quadratic pole assignment problem with time delay

In this paper, from the point of view reducing the system calculation cost, a digital channelized receiver is proposed. The decimation factor of the proposed digital channelized receiver with low calculation cost is equal to the number of signal channels, which is acquired by changing the input signal of the embedded instantaneous frequency measurement receiver. Due to the increase of the system decimation factor, the data to be processed are decreased and the system processing speed is improved indirectly. In this paper, the architecture and working principle of the proposed digital channelized receiver with low calculation cost is firstly given; secondly, the overlapping channel division method used in the digital channelized receiver with low calculation cost is put forward. Meanwhile, the channel arbitration method of the unmodulated or modulated signal in the case of overlapping channel division is analyzed. Then, the frequency measurement principle of the embedded instantaneous frequency measurement receiver is deduced in detail. Through the use of the overlapping channel division method, the proposed digital channelized receiver with low calculation cost is able to avoid the existence of blind spots between channels and increases the interception probabilities of the input signals. And, the proposed digital channelized receiver can distinguish two signals coming simultaneously to the same channel by using the overlapping channel division method. In addition, the channel of the input signal truly residing can be simply determined by using the channel arbitration in the case of overlapping channel division and according to the output frequency of the embedded instantaneous frequency measurement receiver. Finally, the related simulation results verify the correctness and feasibility of the theories and method involved in this paper.

We consider the problem of robust pole assignment for a linear time invariant plant with state feedback subject to time delay in the control input. For systems with a known time delay, we offer a parametric formula for the feedback gain matrix that will assign a desired set of closed-loop eigenvalues to the time-delay system. Secondly we consider systems subject to small input time delays and introduce an unconstrained optimisation algorithm for the computation of a state feedback matrix to deliver the desired pole placement in a manner that minimises the sensitivity of the eigenvalues to input time delays. The performance of the algorithm is compared against an alternative robust pole placement method from the recent literature and found to give significantly reduced time delay sensitivity.