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The implementation issues of digital controllers with finite word length (FWL) considerations are addressed. Both the shift and delta operator parameterisations of a general controller structure are considered. A unified formulation is adopted to derive a computationally tractable stability related measure that describes FWL closed-loop stability characteristics of different controller realisations. Within a given operator parameterisation, the optimal FWL controller realisation, which maximises the proposed stability related measure, is the solution of a nonlinear optimisation problem. The relationship between the z-operator and δ-operator controller parameterisations is analysed, and it is shown that the δ parameterisation has a better FWL closed-loop stability margin than the z-domain approach under a mild condition. A design example is included to verify the theoretical analysis and to illustrate the proposed optimisation procedure.
A plug-in digital repetitive learning (RC) controller is proposed to eliminate periodic tracking errors in constant-voltage constant-frequency (CVCF) pulse-width modulated (PWM) DC/AC converter systems. The design of the RC controller is systematically developed and the stability analysis of the overall system is discussed. The periodic errors are forced toward zero asymptotically and the total harmonics distortion (THD) of the output voltage is substantially reduced under parameter uncertainties and load disturbances. Simulation and experimental results are provided to illustrate the validity of the proposed scheme.
Nonlinear state feedback controllers are exhibited for locally stabilising linear discrete-time systems with both saturating actuators and additive disturbances when the output must track a certain time-varying reference level. The objective is to bring the steady-state error due to disturbances to zero, by using a saturated controller and a dead-zone function. The objective is two-fold: to determine both a stabilising controller and a region of the state space over which the stability of the resulting closed-loop system is ensured, when the controls are allowed to saturate.
The paper considers the problem of LQ regulator design for discrete-time systems with actuator failures. The problem is to design a reliable LQ state feedback regulator which can tolerate actuator failures, such that the cost of the system is guaranteed to be within a certain bound. The state feedback control design for guaranteed cost control is given in terms of solution to an algebraic Riccati equation. The resulting control system is reliable, in that it provides guaranteed asymptotic stability despite some actuator failures. A numerical example shows the effectiveness of the method.
A neural network (NN)-based adaptive control law is proposed for the tracking control of an n-link robot manipulator with unknown dynamic nonlinearities. Basis-function-like networks are employed to approximate the plant nonlinearities, and the bound on the NN reconstruction error is assumed to be unknown. The proposed NN-based adaptive control approach integrates the NN approach and an adaptive implementation of the discrete variable structure control, with a simple estimation mechanism for the upper bound on the NN reconstruction errors and an additional control input as a function of the estimate. Lyapunov stability theory is used to prove the uniform ultimate boundedness of the tracking error, and simulation results demonstrate the applicability of the proposed method to achieve desired performance.
Owing to its superior performance in high-speed signal processing/control, work on delta-operator based discrete time system implementations have attracted considerable attention. Stability and performance of such a system is closely related to the root distribution of its characteristic equation with respect to a certain `shifted' circle in the complex plane; the underlying sampling time determines its centre and radius. An algorithm that checks root distribution of a given polynomial with respect to this stability boundary is proposed. It is based on a scaled version of the well known Marden–Jury table that determines root distribution with respect to the unit circle in the complex plane; this is the stability boundary corresponding to discrete time systems that are implemented using the more conventional shift operator. The Marden–Jury table offers several additional advantages that are not all present in other available algorithms applicable to shift operator based polynomials. The proposed algorithm possesses all these properties, and the scaling scheme used ensures improved numerical accuracy and the existence of a limiting form.
