Periodic Exogenous Signals Research Articles

Analyze and control on the membrane ethanol fermentation process with periodic exogenous signals

Bio-ethanol production by continuous fermentation reactor would generate self-oscillatory dynamics at high substrate concentrations, which exacerbates the control problem. Andronov-Hopf bifurcation analysis of the process model indicates that the self-oscillatory dynamics is caused by ethanol inhibition, and an ethanol selective membrane is assembled to the fermentation reactor for in-situ product removal (ISPR). The simulation results show that the membrane reactor eliminates the self-oscillatory dynamics effectively, but considering the operational cost for the membrane reactor is substantial, periodic operation and on/off control of the sweeping stream in the membrane separator is adopted, and it is interesting to find that when the ethanol content follow fine designed periodic trajectories, the corresponding control actions become regular and square waveform is formulated, which is beneficial from real-time operational perspective. This result could aid periodic operation and control of the fermentation reactor at high ethanol concentrations.

Harmonic internal models for structurally robust periodic output regulation

This note deals with the problem of output regulation for nonlinear systems in presence of periodic exogenous signals. We investigate the asymptotic properties of a controller given by an internal model designed by adding harmonics on the regulation error, and a static state feedback stabilizing the augmented system of the plant and of the internal model. The solution mimics internal model-based structures adopted for linear systems by showing the asymptotic properties that are guaranteed in the nonlinear case in presence of “generic” plant variations. Forwarding technique is adopted in the design of the stabilizer. We shed also light on the linear case by presenting a new easy-to-check condition under which the regulator equations admit a robust solution.

Sliding repetitive control with adaptive bound estimation for motion systems liable to periodic exogenous signals

Periodic exogenous signals often exist in motion systems, especially those involving one or more rotating elements. These periodic exogenous signals deteriorate the performance of motion systems, and these adverse effects cannot be practically eliminated by straightforwardly increasing feedback control gains due to sensor noise, actuator saturation, and unmodeled plant dynamics. This paper describes a sliding repetitive controller for motion systems subject to periodic exogenous signals. Moreover, an adaptive law for bound estimation is devised to ensure the presence of a sliding motion for both repetitive learning and disturbance observation. The tracking motion system of a disk drive is considered in practice, and a traditional repetitive controller is also implemented for performance comparisons with the proposed scheme. Experimental results are reported in this paper, showing the efficacy of the proposed scheme.

Unified Approach to Evaluation of Real and Complex Repetitive Controllers

Repetitive controllers (RCs) are known for their ability of controlling periodic exogenous signals, even if these signals have high harmonic content. Due to the variety of repetitive controllers proposed in the literature, which are significantly different from each other, a comparative evaluation in a collective way is analytically complex. This fact implies a greater difficulty to select the appropriate RC strategy when designing a control system, what makes most control system designers to not use this class of controllers. In order to solve this problem, the present paper develops a unified approach for representation of (real and complex) repetitive controllers, which is based on the use of multiple primitive repetitive cells in parallel. Through this approach the main characteristics of a repetitive controller, such as stability properties, dynamic response, set of harmonic components that are effectively compensated and computational burden, are easily identified. Furthermore, in order to validate the potential of the proposed unified approach, comparative studies of nk ±m RCs and nk+m RCs are performed. An experimental application based on a three-phase shunt active power filter is implemented to validate the theoretical evaluation presented in this paper.

A Simplified Method for Discrete-Time Repetitive Control Using Model-Less Finite Impulse Response Filter Inversion

Repetitive control (RC) achieves tracking and rejection of periodic exogenous signals by incorporating a model of a periodic signal in the feedback path. To improve the performance, an inverse plant response filter (IPRF) is used. To improve robustness, the periodic signal model is bandwidth-limited. This limitation is largely dependent on the accuracy of the IPRF. A new method is presented for synthesizing the IPRF for discrete-time RC. The method produces filters in a simpler and more consistent manner than existing best-practice methods available in the literature, as the only variable involved is the selection of a windowing function. It is also more efficient in terms of memory and computational complexity than existing methods. Experimental results for a nanopositioning stage show that the proposed method yields the same or better tracking performance compared to existing methods.

A Survey of Repetitive Control for Nonlinear Systems

In aerospace engineering and industry, control tasks are often of a periodic nature, while repetitive control is especially suitable for tracking and rejection of periodic exogenous signals. Because of limited research effort on nonlinear systems, we give a survey of repetitive control for nonlinear systems in this paper. First, a brief introduction of repetitive control is presented. Then, after giving a brief overview of repetitive control for linear systems, this paper summarizes design methods and existing problems of repetitive control for nonlinear systems in detail. Lastly, relationships between repetitive control and other control schemes are analyzed to recognize repetitive control from different aspects more insightfully.

Internal Model Control of Lightly Damped Systems Subject to Periodic Exogenous Signals

This paper presents an internal model control (IMC) design for lightly-damped systems subject to periodic exogenous signals. For such systems, the conventional design of the so-called IMC filter in the IMC structure can result in oscillatory behavior even when the closed-loop transfer function is designed to be well damped. To circumvent this problem, several band-pass filters are incorporated into the IMC filter based on knowledge of the frequencies of the plant's resonance modes and exogenous signals. The track-following system of an optical disk drive is employed to illustrate the design of the proposed IMC filter. Experimental results confirm the effectiveness of the proposed design.

Switched linear model predictive controllers for periodic exogenous signals

This article develops switched linear controllers for periodic exogenous signals using the framework of a continuous-time model predictive control. In this framework, the control signal is generated by an algorithm that uses receding horizon control principle with an on-line optimisation scheme that permits inclusion of operational constraints. Unlike traditional repetitive controllers, applying this method in the form of switched linear controllers ensures bumpless transfer from one controller to another. Simulation studies are included to demonstrate the efficacy of the design with or without hard constraints.

Control of a class of nonlinear systems subject to periodic exogenous signals

This paper examines the control of single-input feedback linearizable nonlinear systems that are either subject to periodic disturbances or tracking periodic reference trajectories with known periods. The key concept is the combination of differential geometric techniques with the internal model principle resulting in a nonlinear repetitive control strategy. A formulation is presented for the case of input-state linearizable and input-output linearizable systems in continuous time. The potential benefits of the nonlinear repetitive controller are given. It is shown that while the standard nonlinear control techniques can be made robust to disturbances, the nonlinear repetitive technique is more robust to specific types of disturbances in that it does not require knowledge of the disturbance magnitude and does not need high gains to accomplish robustness. An experiment on the active vibration isolation of a single degree of freedom magnetic levitation testbed shows the effectiveness of the approach.

Discrete-Time Linear Periodic Systems: Stabilization and Zero Error Regulation

With reference to discrete-time linear periodic systems, two classical problems of control theory are tackled in this paper: output stabilization and zeroerror regulation. The first problem is solved in two ways, involving a suitably periodic pole placement technique and the theory of the difference periodic Riccati equation. Moreover, a consistent definitions of zeros of periodic system and of 'periodic integrators' allow to define a control structure capable of robustly zeroing the error produced by periodic exogenous signals.

Repetitive control system: a new type servo system for periodic exogenous signals

A control scheme called repetitive control is proposed, in which the controlled variables follow periodic reference commands. A high-accuracy asymptotic tracking property is achieved by implementing a model that generates the periodic signals of period L into the closed-loop system. Sufficient conditions for the stability of repetitive control systems and modified repetitive control systems are derived by applying the small-gain theorem and the stability theorem for time-lag systems. Synthesis algorithms are presented by both the state-space approach and the factorization approach. In the former approach, the technique of the Kalman filter and perfect regulation is utilized, while coprime factorization over the matrix ring of proper stable rational functions and the solution of the Hankel norm approximation are used in the latter one. >