Multi-rate model predictive control to reject periodic disturbance with reduced ripple

Repetitive model predictive control applied to a simulated moving bed chromatography system

Repetitive control is one control algorithm based on the Internal Model Principle (Francis & Wonham, 1976) and has been widely implemented in various applications. A repetitive control based system has been shown to work well for tracking periodic reference commands or for rejecting periodic disturbances. Although the idea has been verified as early as 1981 (Inoue et al., 1981), a rigorous analysis and synthesis of repetitive controllers for continuous-time systems was not proposed until 1989, by Hara et al. (Hara et al., 1988). Tomizuka et al. (Tomizuka et al., 1989) addressed the analysis and synthesis of discrete-time repetitive controller, considering the fact that digital implementation of a repetitive controller is simpler and more straightforward. Since then, repetitive control has gained popularity in applications where periodic disturbances rejection or repetitive tracking are required, see (Wang et al., 2009; Cuiyan et al., 2004) and the references therein. These include controls of disk drive servo (Tomizuka et al., 1989; Guo, 1997; Moon et al., 1998), hydraulic closed-loop servo for material testing (Srinivasan & Shaw, 1993), vibration suppression (Hillerstrom, 1996), rejection of load disturbances in steel casting process (Manayathara et al., 1996), servo control for a positioning table (Yamada et al., 1999), X-Y table (Tung et al., 1993), noncircular turning process (Alter & Tsao, 1994), motor speed ripple reduction (Godler et al., 1995; Rodriguez et al., 2000), and eccentricity compensation (Garimella & Srinivasan, 1996). In literatures, repetitive controllers are synthesized and operate in time domain, which is in accordance with the fact that models or differential equations of physical systems are mostly derived using time as the independent variable. One of the key steps for designing a repetitive controller is to determine the period, or equivalently, the number of delay taps (q−1, q is the one step advance operator). This can usually be done by analyzing the periodic tracking or disturbance signal using techniques such as fast Fourier transform (FFT). To ensure effectiveness of the design, an underlying assumption is that the frequency constitutions of the periodic tracking or disturbance signal do not vary with respect to time, which corresponds to a stationary or time-invariant frequency spectrum of the signal. This assumption can be satisfied when the design objective is to track a prespecified periodic trajectory. However, it might be violated for disturbance rejection problems where the frequency constitutions of the disturbance are time-varying. For a motion system with rotary components such as gear-train, the disturbances due to gear

In recent years, wind turbines have been growing in size and became more lightweight and thus more flexible. Spatial variation in the wind speed results in asymmetrical blade loads, which include a periodic component increasing with growing wind turbine size. Asymmetrical blade loads can be reduced by individual blade pitch control in general and repetitive control can reduce especially the periodical parts of the loads. We investigate, how a repetitive control based individual blade pitch controller as extension to an existing collective pitch controller can reduce periodical loads resulting from unsteady non-uniform wind conditions under consideration of variable rotor speeds. As plant, we use a simulation model of a 3 MW wind turbine, developed by W2E Wind to Energy GmbH, and control it with a model predictive collective pitch controller. This controller is extended with the proposed repetitive individual pitch control scheme. This study shows, that the presented repetitive controller reduces especially the tower yaw moments by up to 65% and higher harmonics of the blade root moments by up to 30% at the cost of increased pitch activity. Hence, for the use of this controller one has to balance the load reduction of blades and tower with increased loads of the pitch actuators.

A repetitive control method is presented that is implemented in real-time for periodic wind disturbance rejection for linear systems with multiple inputs and multiple outputs and with both repetitive and non-repetitive disturbance components. The novel repetitive controller can reject the periodic wind disturbances for fixed-speed wind turbines and variable-speed wind turbines operating above-rated and we will demonstrate this on an experimental “smart” rotor test section. The “smart” rotor is a rotor where the blades are equipped with a number of control devices that locally change the lift profile on the blade, combined with appropriate sensors and controllers. The rotational speed of wind turbines operating above-rated will vary around a defined reference speed, therefore methods are given to robustify the repetitive controllers for a mismatch in the period. The design of the repetitive controller is formulated as a lifted linear stochastic output-feedback problem on which the mature techniques of discrete linear control may be applied. For real-time implementation, the computational complexity can be reduced by exploiting the structure in the lifted state-space matrices. With relatively slow changing periodic disturbances it is shown that this repetitive control method can significantly reduce the structural vibrations of the “smart” rotor test section. The cost of additional wear and tear of the “smart” actuators are kept small, because a smooth control action is generated as the controller mainly focuses on the reduction of periodic disturbances.

This paper presents a reduced order discrete extended state observer (RODESO) based repetitive controller (RC) with application to a piezoelectric actuator (PEA) based nano-positioning system. The RODESO-based RC proposed in this paper is capable of rejecting both periodic and aperiodic disturbances. Moreover, RODESO can be tuned using only two parameters and the model free approach of RODESO-based RC makes it an ideal solution to overcome the challenges of piezoelectric actuator control. Various types of periodic and aperiodic disturbances are used in the simulation to demonstrate the disturbance rejection capability of the proposed algorithm. The comparison studies demonstrate that the RODESO-based RC has superior performance over the phase lead RC.

Repetitive dynamic matrix control for systems with periodic specifications

The tracking/rejection of periodic signals constitutes a wide field of research in the control theory and applications area and Repetitive Control has proven to be an efficient way to face this topic; however, in some applications the period of the signal to be tracked/rejected changes in time or is uncertain, which causes and important performance degradation in the standard repetitive controller. This thesis presents some contributions to the open topic of repetitive control working under varying frequency conditions. These contributions can be organized as follows: One approach that overcomes the problem of working under time varying frequency conditions is the adaptation of the controller sampling period, nevertheless, the system framework changes from Linear Time Invariant to Linear Time-Varying and the closed-loop stability can be compromised. This work presents two different methodologies aimed at analysing the system stability under these conditions. The first one uses a Linear Matrix Inequality (LMI) gridding approach which provides necessary conditions to accomplish a sufficient condition for the closed-loop Bounded Input Bounded Output stability of the system. The second one applies robust control techniques in order to analyse the stability and yields sufficient stability conditions. Both methodologies yield a frequency variation interval for which the system stability can be assured. Although several approaches exist for the stability analysis of general time-varying sampling period controllers few of them allow an integrated controller design which assures closed-loop stability under such conditions. In this thesis two design methodologies are presented, which assure stability of the repetitive control system working under varying sampling period for a given frequency variation interval: a mu-synthesis technique and a pre-compensation strategy. On a second branch, High Order Repetitive Control (HORC) is mainly used to improve the repetitive control performance robustness under disturbance/reference signals with varying or uncertain frequency. Unlike standard repetitive control, the HORC involves a weighted sum of several signal periods. With a proper selection of the associated weights, this high order function offers a characteristic frequency response in which the high gain peaks located at harmonic frequencies are extended to a wider region around the harmonics. Furthermore, the use of an odd-harmonic internal model will make the system more appropriate for applications where signals have only odd-harmonic components, as in power electronics systems. Thus an Odd-harmonic High Order Repetitive Controller suitable for applications involving odd-harmonic type signals with varying/uncertain frequency is presented. The open loop stability of internal models used in HORC and the one presented here is analysed. Additionally, as a consequence of this analysis, an Anti-Windup (AW) scheme for repetitive control is proposed. This AW proposal is based on the idea of having a small steady state tracking error and fast recovery once the system goes out of saturation. The experimental validation of these proposals has been performed in two different applications: the Roto-magnet plant and the active power filter application. The Roto-magnet plant is an experimental didactic plant used as a tool for analysing and understanding the nature of the periodic disturbances, as well as to study the different control techniques used to tackle this problem. This plant has been adopted as experimental test bench for rotational machines. On the other hand, shunt active power filters have been widely used as a way to overcome power quality problems caused by nonlinear and reactive loads. These power electronics devices are designed with the goal of obtaining a power factor close to 1 and achieving current harmonics and reactive power compensation.

In this paper, a new grid current control strategy based on internal model control and repetitive control is designed. The performance characteristic and operation principle are analyzed according to the basic principle of internal model control and the dynamic mathematical model of three-phase photovoltaic grid-connected inverters. Because the harmonic current caused by the dead-time effect and the periodic disturbance of the grid can not be eliminated by internal model control, a composite control strategy with internal model control and repetitive control is proposed in the paper. Internal model control can simplify the controller’s parameters and ensure the dynamic quality of the system. Repetitive control is able to restrain the dead-time effect and the periodic disturbance of the grid. It can also reduce the total harmonic distortion of the grid-connected current. The simulation results show that the proposed control strategy has good dynamic and steady-state performance and can restrain the periodic disturbance as well.KeywordsThree-phase grid-connected invertersInternal model controlRepetitive controlDead-time effect

It is well known that the speed control system, even though which is constructed with an excellent control method, has an unexpected steady speed error when it is suffered by a periodical load disturbance. As the method of eliminating the speed fluctuation caused by such kind of disturbance, a repetitive control is the most effective. But the repetitive control method is only adoptive for a constant speed control system.In this paper, a novel control system designing method which is effective to both the constant speed control system and variable speed driving system is shown. The fact that a periodical disturbance depends on time function and also rotational angle is utilized to design the control system. From the result, the numerical modeling of the controlled object is derived in the rotational angle function domain. For the obtained numerical model, an extended state variable equation based on the original system is presented by using the control technique named “Error System Technique”. And then the optimal feedback gains are decided by solving the optimal regulator problem for the extended state equation. Therefore, a stability of the system is ensured.The proposed control method is applied to DC motor variable speed control system and the experimental setup is constructed. Finally, the effectiveness of the proposed method is confirmed by the result of simulations and experiments.

Periodic deformations of organs which are due to respiratory movements may be critical disturbances for surgeons manipulating robotic control systems during laparoscopic interventions or tele-surgery. Indeed, the surgeon has to manually compensate for these motions if accurate gestures are needed, like, e.g., during suturing. This paper proposes a repetitive model predictive control scheme for driving a surgical robot towards the reference trajectory defined by the surgeon, while tracking periodic disturbances of known periods on the output. A new cost function is developed for an unconstrained generalized predictive control scheme based on a repetitive multiple input-output model of the robot. Contributions of the controller output to reference tracking and to disturbance rejection are split and computed separately; then, filtering of repetitive disturbances and tracking of the reference trajectory can be independently weighted by the controller while simultaneously running on the plant. The proposed control scheme is validated through simulations and experimental results shown in a surgical robotics application.

Implementation of Plug-in Type Repetitive Controller for Position-based Periodic Control Systems

The modified repetitive control system is a type of servomechanism for periodic reference inputs. That is, the modified repetitive control system follows the periodic reference input with a small steady state error, even if a periodic disturbance or uncertainty exists in the plant. Using previously proposed modified repetitive controllers, even if the plant does not include time-delay, transfer functions from the periodic reference input to the output and from the disturbance to the output have infmite numbers of poles. To specify the input-output and the disturbance attenuation characteristic easily, Yamada et al. proposed the concept of a simple repetitive control system such that the controller works as a modified repetitive controller and transfer functions from the periodic reference input to the output and from the disturbance to the output have fmite numbers of poles. In addition, Yamada et al. clarified the parameterization of all stabilizing simple repetitive controllers. Recently, the p...

This paper presents design and implementation of model predictive control with repetitive control for periodic signal tracking and constraint handling of fast sampled-data systems. An internal model based discrete time repetitive control law is integrated with the model predictive controller and the original problem is then transformed to a quadratic programming problem to deal with the given constraints. This heavy computational control was implemented on a piezo-actuated system at a 10 kHz sampling rate. The experimental results demonstrate the feasibility and effectiveness of the proposed approach for asymptotic error tracking of periodic reference profiles with constraint handling.

Multi-rate Modeling and Economic Model Predictive Control of the Electric Arc Furnace

Effects of Non-Periodic Disturbances on Repetitive Control Systems