Repetitive controller for time-delay systems based on disturbance observer

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

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.

In complex industrial situations, modern permanent magnet synchronous motor (PMSM) servo drive system always face different kinds of disturbances, especially constant or slowly-varying disturbances (load disturbances) and periodic disturbances (torque ripples). Conventional disturbance rejection techniques, e.g., the extended state observer based control (ES-OBC) and the disturbance observer based control (DOBC), can only reject asymptotically single kind of disturbances (constant or slowly-varying disturbances). To this end, it is essential to extend the conventional disturbance rejection approach for multiple disturbances. Inspired by the internal model principle (IMP), appropriately embedding the model of disturbances into the design of disturbance observer, a composite disturbance observer based control is proposed for PMSM with multiple disturbances. The proposed disturbance observer (named as IMESO), consisting of the internal model principle (IMP) and the extended state observer (ESO), can reject multiple disturbances asymptotically. Thus, a composite control law consisting of proportional feedback and disturbance feedforward compensation is developed to control the speed loop. The proposed method is effective to reject the intricate multiple external disturbances and unmodeled dynamics. Simulations and experiments both verify the effectiveness of the proposed method.

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.

The quality of the final prints in electronic-shaft paper-folding machinesseriously influenced by the mechanical periodic disturbance. This paper takes the periodic shock-disturbance and sinusoidal disturbance in the electronic-shaft paper-folding machineas as the research objects. Disturbance observer is designed based on Propotional Integral Diffrential (PID) control algorithm. Firstly this paper establishes a model of the system with MTALAB system identification tools in the process of establishing the control system. Secondly,the paper inverses this established model. In order to approximate the mode and guarantee the stability of the inversed model, zero-phase error-tracking controller (ZPETC) has been designed to remove the instable zero-point of the original model. Finally, the paper constructs the disturbance observer of the established reversed model based on PID control algorithm. The simulation on experimental platform shows that the resistivity of paper-folding machine to the external disturbance has been improved impressively and the proposed PID algorithm disturbance observer has been proved can be used in periodic disturbance suppression in the electronic-shaft paper-folding machine.

This paper proposes a sliding-mode control (SMC) scheme based on the internal model principle (IMP) for robust reference tracking and disturbance rejection. The conventional linear IMP-based controller is known for its capability of perfect tracking and disturbance rejection with an internal model of exogenous signals, while the traditional SMC controller is robust to system perturbations and exogenous signals with unknown dynamics. The proposed SMC design combines the best features of these two fundamentally different but effective methods. Furthermore, with the help of the SMC, an initial state of the internal model is determined independently of system perturbations in order that transient performance is greatly improved compared with that of the linear IMP-based controller. In addition, by properly assigning the initial state of the internal model, a sliding-control law is derived to ensure the existence of a sliding mode during an entire response. This global sliding motion yields excellent robustness of the entire system from the very beginning of a system response. Experimental results show the feasibility of the proposed scheme.

This paper proposes a frequency separation type current control system for a grid-connected single-phase five-level inverter. The proposed control system realizes high tracking performance and high disturbance suppression performance. To obtain high tracking performance to the sinusoidal reference signal, a repetitive controller is applied to the current controller. The current controller with a repetitive controller is capable of tracking to fundamental frequency, without the steady-state error. The disturbance observer using a notch filter (notch type disturbance observer) is used to obtain the high disturbance suppression performance. Using the notch type disturbance observer, the frequency components except for the fundamental frequency are suppressed. The proposed control system is configured by combining the current controller with a repetitive controller and a PI controller, and adding a notch type disturbance observer. Numerical simulation results and experimental results confirm that the proposed control system effectively reduces the output current distortion. The THD of the output current is reduced by 15.5 % when using the proposed control system.

From the structure point of view, a repetitive controller (RC) is considerably similar to a disturbance observer. By adding a correction term to the traditional RC and considering the disturbances as states, the repetitive controller can be designed in the same way as a disturbance observer. This paper presents therefore a new simple way of tuning a repetitive controller. Simulations show that, when compared with the traditional RC, the proposed RC configuration can achieve greater stability margin. As opposed to the traditional plug-in RC, the new RC structure studied in this paper is also shown to be robust against variations in the inner loop delays if it is used in a cascaded configuration. The immunity to plant parameter variations is another added benefit of the proposed controller.

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.

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

In the paper, a digital repetitive control scheme is proposed for the single-phase inverters to achieve the high-quality sinusoidal output voltages and the minimum total harmonics distortion. In the proposed control scheme, the repetitive controller is plugged into the stable state feedback controlled single-phase inverter system. The repetitive controller is designed to eliminate the periodic disturbance and track the periodic or dc reference signal with zero tracking error. The design method of the controller is described systematically, besides the stability of system is analysed. Simulation results illustrate the availability of the proposed scheme.

Repetitive control is a renowned method for managing periodic disturbances and references in control systems. Despite its effectiveness, performance issues arise when confronting disturbances like polynomial or sinusoidal signals. To enhance its capability, we introduce an extended state repetitive observer by incorporating internal models of periodic, sinusoidal, and polynomial signals into a novel observer framework. This design empowers the observer to adeptly reject and track both periodic and combined sinusoidal+polynomial signals. Beyond addressing the limitations of traditional repetitive control, our observer offers precise disturbance estimation for further analysis and feedback implementation. The observer’s performance is demonstrated through experimental validation within a control setup across various scenarios, focusing on its ability to reject periodic disturbances and track periodic signals effectively.

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

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.

Robust internal model control based on a novel generalized extended state observer and its application on a two-inertia system