Robust Disturbance Rejection for Left-Invertible Linear Systems With Nonlinear-Uncertain Structure

The problem of robust disturbance rejection for left invertible linear systems, with nonlinear uncertain structure and with measurable and nonmeasurable disturbances, is studied and solved for the first time. The necessary and sufficient conditions for the problem to have a solution, via an independent of the uncertainties static feedback law, are established. The general explicit expression of the feedback matrix is derived. The feedback invariant poles are determined. Sufficient conditions for robust disturbance rejection with simultaneous robust stability, are established.

Simple algebraic criteria are derived for the solvability of the combined problem of I/O Decoupling and Disturbance Rejection (DDR) for general neutral multi-delay systems with measurable and nonmeasurable disturbances, via proportional measurable disturbance feedback and measurement output feedback. Additionally, the necessary and sufficient conditions, for the problem to admit a realizable solution, are established and the general analytical expression of the realizable controller matrices solving the problem are determined.

The problem of robust exact model matching is studied for the case of SISO discrete-time linear systems with nonlinear uncertain structure. The problem is solved using finite precision dynamic output feedback controllers. The controller is restricted to be independent from the uncertainties. Necessary and sufficient conditions for the problem to have a solution are established. The general solution for the controller parameters is derived. Moreover, sufficient conditions for robust exact model matching with simultaneous robust asymptotic stability are derived

This paper deals with the problem of robust tracking and disturbance rejection for a linear time-invariant system where the uncertainty of the system is represented in a structured form and the output to be controlled may be different from the measurement output. First, the problem is considered in a rather classical setting in that the required property of tracking and disturbance rejection can be attained as long as the resulting closed-loop system remains stable. Conditions for solvability of the problem are given and two algorithms are presented for designing controllers having the robust tracking and disturbance rejection property. Second, the problem of robust output regulation with robust stability is formulated as one of finding a controller such that the resulting closed-loop system satisfies an additional requirement of robust stability and thus the output regulation property can be maintained for all perturbations of uncertain parameters within a prescribed set. A procedure based on a high gain observer approach is proposed to solve this problem.

This paper focuses on the problems of robust stabilization and disturbance rejection for a class of positive systems with time-varying delays and actuator saturation. First, a convex hull representation is used to describe the saturation characteristics. By constructing an appropriate copositive type Lyapunov functional, we give sufficient conditions for the existence of a state feedback controller such that the closed-loop system is positive and asymptotically stable at the origin of the state space with a domain of attraction. Then, the disturbance rejection performance analysis in the presence of actuator saturation is developed viaL1-gain. The design method is also extended to investigate the problem ofL1-gain analysis for uncertain positive systems with time-varying delays and actuator saturation. Finally, three examples are provided to demonstrate the effectiveness of the proposed method.

The contribution addresses the problem of robust trajectory tracking control and disturbance rejection for a non contact, high-precision Lorentz force planar motion stage of linear DC brushless type. The control problem is accomplished by using a composite control law including a simple computed torque type controller together with an extended Luenberger type of state and disturbance observer also known as extended state or generalized proportional integral observer (GESO/GPIO). We provide stability proofs and estimation error bounds of the GESO/GPIO related to the choice of the eigenvalues of the observer estimation error dynamics. Finally, we assess the performance of the proposed controller on the basis of a recently developed motion stage model that comprises a realistic disturbance modeling and thus is capable of reflecting the major challenges for control.

The problem of robust asymptotic disturbance rejection for systems involving parametric uncertainties is studied. A design method is proposed that is based on polynomial techniques. Various uncertainty structures are considered including single and multiple parameters as well as affine, polynomic and even non-polynomic cases. Both unmeasurable and measurable disturbances are considered. If the disturbance is not directly measurable, one must employ the standard internal model principle (controller denominator should contain the dynamics of the disturbance). When a direct measurement of the disturbance is available, however, a feedforward can be added that avoids the need to apply the principle. Therefore, a simpler controller (with two-degrees-of-freedom but of lower order) may be used. In addition, such a controller has no prespecified factors and hence it is more likely to be found robustly stabilizing. Transfer functions of the controller result from the solution of a couple of linear equations in polynomials with coefficients depending on the plant parameters. The first of the equations, that provides a robustly stabilizing feedback, is now frequently discussed in control literature. The second one: is the central theme of this paper. It gives rise to the feedforward part of the controller that guarantees the desired robust performance. Due to specific symmetry in appearance of the uncertain parameters, the feedforward equation is easier to handle. If the disturbance is not measurable or if, for some reason, its measurement is refused, the feedforward equation becomes trivial: a purely feedback controller results from a single equation-the modified feedback one.

Simultaneous (C, A, B)-pairs for Infinite-Dimensional Systems

A robust controller, facilitating yaw aircraft manoeuvres without affecting the respective roll modes, is designed for the case of uncertain air density, aircraft's mass and inertia. To handle the issue the robust input output decoupling technique is applied to the lateral motion dynamics of the aircraft. The condition under which the problem is solvable via state feedback appears to be generically true. The general form of the robust static decoupling controllers, as well as the general form of the resulting decoupled closed loop system, are derived. The conditions for robust decoupling with simultaneous robust stability are also established in terms of the lateral stability derivatives.

This paper focuses on the simultaneous robust stability and robust performance problem from the view point of a Quantitative Feedback Theory (QFT) design. We develop closed-form algorithms for computing QFT bounds for this problem class. These bounds are necessary for the QFT's nominal loop shaping.

This paper is concerned with the problem of disturbance rejection in an adaptive controller design. A new adaptive control algorithm is derived to obtain the complete measurable disturbance rejection both in dynamic and static states for a class of non-minimum phase MIMO systems by reassigning the system zeros to the stable region

In this paper the robust asymptotic tracking and disturbance rejection problem is studied for linear periodic discrete-time systems, and for general classes of disturbance functions and reference signals, consisting in free responses of periodic processes. The necessary and sufficient conditions for the existence of a solution, which involve the periodic notion of invariant zero, are found. A constructive design procedure of the periodic compensator is given; it is based on the internal model principle.

Static output feedback considers an optimal low-order feedback matrix which directly connects the sensors to the control inputs. This work demonstrates the numerical techniques needed to compute the analytical gradient of the optimal feedback matrix with respect to design variables, which may then be used for gradient-based optimization. The derivatives are demonstrated for aeroservoelastic optimization under a series of closed- loop gust load alleviation constraints, considering a continuous stochastic gust load applied to a transport vehicle configuration, among other design constraints such as utter and maneuver loads. The optimal trade-o s between passive load alleviation and active load alleviation for static output feedback are compared with those from full-state feedback, which may be considered an upper-bound for effective sensor-based control.

ABSTRACTIn this paper, the static output feedback stabilisation of discrete event dynamic systems (DEDSs) is investigated via the semi-tensor product (STP) of matrices. Firstly, the dynamics of DEDSs modelled by deterministic Moore-type finite automata are converted into an matrix expression in the STP frame. Secondly, necessary and sufficient conditions for the existence of a static output feedback control pattern, stabilising the controlled discrete event dynamic systems to some equilibrium point, are given, and constructive algorithms to seek the static output feedback control pattern including an effective specific solution algorithm and an analytic solution algorithm are proposed. Thirdly, the equilibrium-based static output feedback stabilisation of DEDSs is extended to the set-based static output feedback stabilisation and necessary and sufficient conditions and constructive algorithms to seek the corresponding control pattern are provided. Finally, some examples are presented to illustrate the effectiveness of the proposed approach.

In this paper, we study the problems of robustness and disturbance rejection in a general setting, whereby the signal space in which the inputs and outputs reside is not necessarily L 2 . It is well known that, if the signal space is taken as L 2 , then both optimal robustness design and optimal disturbance rejection can be formulated as H ∞ -norm minimization problems. Three distinct 'Aizerman' type of conjectures regarding the stability of nonlinear feedback systems are formulated, each of which happens to be true in the special case when the underlying signal space is L 2 . It is shown that, in a general setting, only one of the three Aizerman-type conjectures is true, namely: If a feedback system is stable for all linear, possibly time-varying feedback elements belonging to a specified sector, then the feedback system remains stable for all nonlinear, possibly time-varying feedback elements belonging to the same sector. It is shown that the remaining two conjectures are equivalent to each other, and necessary and sufficient conditions for each of the two conjectures to hold are derived. Next, it is shown that, in general, the problems of optimal disturbance rejection and optimal robustness design are quite distinct. In the special case where the signal space is L 2 and the corresponding Banach algebra of causal stable LTI systems is H ∞ , both problems coincide. But in general, the problem of optimal disturbance rejection is that of minimizing the norm of the weighted sensitivity matrix, whereas the problem of optimal robustness design is that of minimizing something like the spectral radius of the weighted complementary sensitivity matrix.