Time-Varying Control for Optimal Disturbance Rejection and Robustness

This paper investigates the problem of adaptive disturbance rejection for a class of nonholonomic systems with unknown control coefficients which signs are known. A new dynamic high gain and new Lyapunov function are constructed, which successfully deals with the unknowns/uncertainties of the unknown control coefficients and the input-output polynomial growth rate. Inspired by related works on output feedback control of nonlinear systems, a new disturbance rejection controller is designed by backstepping techniques, high gain techniques, and an extended state observer. By appropriately selecting the design and auxiliary parameters, this controller ensures that both the original system state and their corresponding observer state converge to zero, while the estimation of the non-vanishing external disturbances converges to the actual values. In the simulation section, a numerical example and a bilinear mobile robot case are given to verify the effectiveness of the proposed control scheme.

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.

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

SUMMARY This paper investigates the problem of global disturbance rejection for switched nonlinear systems in strict-feedback form with unknown exosystem where the solvability of the disturbance rejection problem for subsystems is not assumed. First, a sufficient condition for the solvability of the global disturbance rejection problem is given. As an extension of the classic concept of internal model for non-switched systems, a new concept of switched internal model is proposed. Second, in order to solve the problem in question, a constructive adaptive control methodology is established on the basis of the multiple Lyapunov functions method, backstepping, and the changing supply functions technique. Finally, an example is provided to demonstrate the effectiveness of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.

An experimental and theoretical comparison is made of force control performance with different types of innerloop joint servoing techniques. The problem of disturbance rejection and sensitivity to plant dynamics variations (robustness) is addressed. Position, velocity, strain gauge derived joint torque, and current servos are designed and implemented on a specially instrumented industrial robot, and the end-effector force feedback performances achieved are compared. Joint strain derived torque servoing is found to provide the best overall robust force control performance. Experimental results of the robust hard-on-hard contact achieved with the novel force controller implementation based on joint torque sensing are provided. Conclusions are drawn on the force control performance achievable on a geared robot given the joint servoing technique. >

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.

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.

Input-output decoupling and disturbance rejection problems in structural analysis

The control of the field outlet temperature of a parabolic trough solar field (PTSF) is crucial for the safe and efficient operation of the solar power system but with the difficulties arising from the multiple disturbances and constraints imposed on the variables. To this end, this paper proposes a constraint optimal model-based disturbance predictive and rejection control method with a disturbance prediction part. In this method, the steady-state target sequence is dynamically corrected in the presence of constraints, the lumped disturbance, and its future dynamics predicted by the least-squares support vector machine. In addition, a maximum controlled allowable set is constructed in real time to transform an infinite number of constraint inequalities into finite ones with the integration of the corrected steady-state target sequence. On this basis, an equivalent quadratic programming constrained optimization problem is constructed and solved by the dual-mode control law. The simulation results demonstrate the setpoint tracking and disturbance rejection performance of our design under the premise of constraint satisfaction.

This paper studies the problem of disturbance attenuation and rejection for switched systems with nonlinear uncertainty and input saturation via composite anti-disturbance control technique, in which the exosystem-generated disturbance and H 2 -norm-bounded disturbance are considered. For switched systems, the switching law and input saturation increase the difficulty for the design of the disturbance observer and the composite control scheme. A switching disturbance observer is designed to obtain the estimation of the matched disturbance, and a novel switching composite controller is further constructed based on the estimated value. By proposing a state-dependent switching law and utilizing the multiple Lyapunov function technology, the criteria are presented to ensure the local asymptotic stability with an H ∞ performance level for the closed-loop system. Furthermore, two optimal algorithms of the design of the controller are put forward to maximize the estimation of the domain of attraction of the closed-loop and the upper bound on the H 2 -norm of the disturbance, respectively. The effectiveness of the proposed technique is illustrated via the numerical examples.

TRACKING METHODOLOGY WITH ZEROS VARIATION AND DISTURBANCE REJECTION APPLIED TO UNCERTAIN SYSTEMS

Independence of convergence rate of the wave tracking error on structures of feedforward controllers

We consider the problem of stabilization and disturbance rejection in discrete time systems with limited feedback information as it is commonly the case in Networked Control Systems. In a networked system, transmission of information is constrained by the network bandwidth and availability. Our goal is to decrease the rate at which a perturbed system needs to transmit feedback information to update its controller node while maintaining stability and disturbance rejection properties. A state-disturbance observation approach is presented and we show in this paper that asymptotic stability can be obtained in the presence of constant disturbances. Additionally, we provide conditions for inter-update performance for both, constant and piece-wise constant disturbances.

In this paper a discrete-time domain 2DOF design method is proposed for industrial stable processes with input time delay, based on a recently developed two-degree-of-freedom (2DOF) control structure. The setpoint tracking controller is analytically designed based on the H2 optimal control principle, and another controller for load disturbance rejection is derived by proposing the desired closed-loop complementary sensitivity function. Both controllers can be tuned independently to realize control optimization. Analytical expression of the setpoint response is given for quantitatively tuning the single adjustable parameter in the setpoint tracking controller. At the meantime, the tuning constraints of another adjustable parameter in the controller for disturbance rejection are derived by establishing the sufficient and necessary conditions for holding robust stability of the closed-loop system. Illustrative examples from the literature are used to show the effectiveness and merit of the proposed control method.