Design of a repetitive controller as a feed-forward disturbance observer

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

Dynamic voltage restorer (DVR) has been demonstrated to be a very effective mechanism to deal with key voltage-quality disturbances. Although the dynamic response requirement for voltage sag could be satisfied with a feedforward control strategy, the steady-state requirement and zero-error tracking need an advanced feedback control strategy. This paper proposes a fast repetitive controller based feedback control strategy for DVR system. In the control system, the feedforward control loop could meet the dynamic requirement; the repetitive controller based feedback control loop could realize zero steady-state error tracking for fundamental voltage and harmonic components. The fast repetitive controller: 1) could eliminate all odd signals (including fundamental component); 2) could be simply implemented in digital signal processors just with a time delay loop; 3) has fast dynamic response when compared with traditional repetitive controller as its delay time is reduced to half of traditional's. This paper also chooses the small gain theorem for control system analysis and parameters design. The simulation on MATLAB/simulink also demonstrates the validity and superiority of proposed control strategy.

A novel design strategy for iterative learning and repetitive controllers of systems with a high modal density: Theoretical background

Traditional DFT harmonic detection algorithm and repetitive control both have certain inherent delay, which seriously affects the dynamic performance of active power filter (APF). To quicken the dynamic response performance, as well as reduce the calculation amount and memory space occupied by the algorithm, characteristics of load harmonics in synchronous rotation coordinates are analyzed and an improved DFT algorithm with six-fold computing frequency is proposed. Secondly, a quasi-internal model with six-fold base control frequency in synchronous rotation coordinates is established. Detailed design of novel repetitive control (RC) and system stability check are carried out. Kinds of experiments are conducted to validate the feasibility and effectiveness of proposed methods.

Disturbances that come from multiple originating domains, e.g., time, position, or commutation-angle domain, are often encountered in practice due to the increasing complexity of mechatronic systems. The aim of this paper is to present a generalized approach that enables asymptotic rejection of multi-dimensional disturbances which are periodic in the different originating domains, e.g., if speed changes, then spatially-periodic disturbances manifest themselves differently in the time domain. A multi-dimensional Gaussian process (GP) based internal model is employed in conjunction with a traditional repetitive control (RC) setting using non-equidistant observations, allowing to learn a multidimensional buffer for RC. A case study with a spatio-temporal disturbance confirms the benefit of this method.

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.

Repetitive control can be effective in improving current quality when used with grid-connected inverters. Mathematically, a repetitive controller is equivalent to a parallel combination of resonant controllers with high gain at the fundamental frequency and its harmonics, and accordingly good disturbance rejection can be achieved at these frequencies. To ensure stability, a low-pass filter needs to be incorporated within the repetitive controller to attenuate the high frequency resonant peaks of the controller gain (above the system's cross-over frequency), without significantly affecting the low frequency resonant peaks corresponding to significant grid harmonics that need to be rejected. The paper therefore argues that it is desirable that the system and the inverter's output filter should have a high bandwidth - higher than the most significant grid harmonics - which may be counter intuitive. The high bandwidth requirement dictates a high PWM switching frequency, which becomes challenging in high power systems as the maximum achievable switching frequency of power electronic devices reduces as their power rating increases. This limitation can be overcome in low voltage systems by using an interleaved inverter topology in which the power is shared between several 2-level half-bridge inverter legs connected in parallel. In addition to using low power devices capable of high switching frequency, the value of the LC output filter capacitance can be relatively very small thanks to the ripple cancellation feature of the interleaved inverter. Both of these features mean that the bandwidth of an interleaved inverter can be much higher than that achievable using a classical 2-level inverter with an LCL output filter. The paper discusses the design and practical implementation of a repetitive controller for an interleaved inverter with 6 half-bridge legs per phase. Simulation and experimental results are also presented to demonstrate the effectiveness of the proposed controller in improving the THD of the output current of the inverter.

SummaryIn this article, the decentralized repetitive tracking controller design for fractional‐order large‐scale Takagi–Sugeno fuzzy system with time delays is developed. We mainly focus on the design of a decentralized repetitive tracking controller based on the Lyapunov stability theory, by which the addressed large‐scale system asymptotically stabilized with performance index. Further, the repetitive control with quantized signal is developed to ensure the good tracking performance with the presence of interconnected model and external disturbances. Specifically, a logarithmic quantizer is used to quantify the control signal which can reduce the data transmission rate in the network. Finally, a numerical example is presented to verify the effectiveness of the proposed controller design technique.

This paper studies a repetitive controller design scheme for a bridgeless single-ended primary inductor converter (SEPIC) power factor correction (PFC) converter to mitigate input current distortions. A small signal modeling of the converter is performed by a fifth-order model. Since the fifth-order model is complex to be applied in designing a current controller, the model is approximated to a third-order model. Using the third-order model, the repetitive controller is designed to reduce the input current distortion. Then, the stability of the repetitive controller is verified with an error transfer function. The proposed controller performance is validated by simulation, and the experiment results show that the input current total harmonic distortion (THD) is improved by applying the proposed controller for an 800 W bridgeless SEPIC PFC converter prototype.

This paper describes the design and implementation of a repetitive controller (RC) for tracking periodic trajectories in aerial robots, such as unmanned aerial vehicles (UAVs). The RC is ideally suited for situations where the robot is required to execute a defined flight pattern, over and over again in a periodic fashion. Applications include precision agriculture, and search and rescue, where the desired trajectory is often periodic in time and known a priori. Compared to iterative learning control (ILC), RC is a feedback-based approach which can be plugged into an existing feedback control loop to improve the tracking of period trajectories. Herein, a plug-in type RC is applied to a micro aerial robot, and a systematic approach is presented for designing the control system. The plug-in nature of the design also allows users to enable/disable the controller on the fly. The proposed RC is also compared to existing approaches, including no-reset ILC, which have recently been applied to control aerial robots. The effectiveness of the RC is demonstrated on a custom-designed experimental micro aerial robot. Tracking of circle, square, and figure-eight trajectories are shown in both simulations and experiments. In these cases, the RC reduces the average tracking error by over 58% compared to a well-tuned PID controller, and simulations that compare to no-reset ILC show that the performance of RC is less sensitive to changes in the reference trajectory.

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.

A novel continuous time repetitive control design is presented for time-delay systems with periodic references and disturbances. Taking profit of the system model and an appropriate time-delay, an inner positive feedback loop is constructed to establish an internal model for periodic signals, and a simple proportional control is utilised in the outer feedback loop to stabilise the closed-loop system. Thus, the tracking capability can be guaranteed according to internal model principle. In addition, to compensate for the effect of external periodic disturbances, a disturbance observer using the system model and a model-based compensator is introduced inside the proposed internal model such that the tracking and disturbance rejection can be achieved simultaneously. Sufficient stability conditions and the robustness analysis under modelling uncertainties are all studied. Only two parameters are needed to be chosen by the designer. Numerical examples and practical experiments on a motor control system are included to illustrate the feasibility and simplicity of the proposed methods.

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 converts the design of robust repetitive controller into a standard problem. In order to handle the large delay in the internal model structure of repetitive controller, a new framework, which utilizes Structured Singular Values method (μ synthesis) for solution, is proposed. It is shown that the μ value of the new framework is a tight upper bound of the μ value of the standard problem. Under this framework, the conditions of robust stability and robust performance can be incorporated and analyzed. The designed repetitive controller preserves a special low-order filter structure for efficient real-time implementation. The robust performance can be achieved not only to the periodic signals of the fundamental frequency and its harmonics as the existing repetitive controller did, but also to asynchronous periodic and non-periodic signals by choosing appropriate performance weighting function. The design procedure is more systematic and less conservative than conventional methods. A robust repetitive controller designed using this method is implemented on a hydraulic servo for noncircular cutting. Experimental results are presented to illustrate the control system synthesis procedure and performance.

Effects of Non-Periodic Disturbances on Repetitive Control Systems