Compensation for unknown nonlinearities and parameter optimization in a modified repetitive-control system

Compensation in Repetitive Control System for Aperiodic Disturbances and Input Dead Zone

In this paper, a robust H∞ control problem is considered for an uncertain singular system. An active disturbance rejection method called equivalent input disturbance (EID) is used to reduce the influence of exogenous disturbances and uncertainties on the system. At the first, there exists an EID, which can produces the same effect on the system as disturbances and uncertainties do in the control channel according to the EID concept. Then, an EID estimator is constructed to estimate the influence of EID on the system. Finally, based on Lyapunov stability theory, a static output feedback‐based robust H∞ controller combined with EID estimate is designed, guaranteeing that closed‐loop system is admissible (regular, impulse‐free, and stable) with a prescribed H∞ performance level. Compared with traditional H∞ control method, H∞ control based on EID method improve the control performance of the system. A numerical example demonstrates the validity of the method.

This article presents a proportional integral derivative (PID) control system for lower-limb rehabilitation robot that not only features satisfactory control performance for the pedal angle but also provides a function for pedal torque estimation. Nonlinear state feedback simplifies the stability analysis and control system design. The stability condition of the closed-loop system is derived based on a Lyapunov function. The PID controller ensures that the pedal angle tracks the reference trajectory. The equivalent input disturbance (EID) method in the control system was compared with the disturbance observer (DOB) and extended state observer (ESO) methods in terms of pedal torque estimation performance. The simulation results indicated that the EID method achieved a root mean square error of 0.37 N·m with 47.6% and 51.8% improvements over the DOB and ESO methods.

In this paper, the problem of attitude tracking control for a class of vertical take-off landing (VTOL) aircraft in the presence of uncertain disturbances is addressed. The active disturbance rejection control (ADRC) method is utilized to address uncertain disturbances, while the radial basis function (RBF) neural network is considered for handling unknown nonlinear dynamics. By incorporating a modified tracking differentiator, a nonlinear state error feedback controller, and an extended state observer, the disturbance observation problem in the aircraft system is solved. These disturbances, seen as a combined disturbance in the aircraft system, are counteracted through the extended state observer. Furthermore, the unknown nonlinear dynamics within the aircraft system are approximated using the RBF neural network. Subsequently, the paper suggests adaptive ADRC strategies based on neural network and formulates adaptive control laws to estimate unknown parameters. The Lyapunov stability theory proves the effectiveness of the proposed control strategies. The simulation results show that the attitude tracking control problem of VTOL aircraft can be achieved under the proposed control strategies and adaptive control laws.

To regulate uncertainties in system dynamics and external disturbances, a robust controller is proposed for a plant with time-varying uncertainty. The design is based on the concept of extended state observer (ESO) with repetitive controller (RC). In real time estimation and mitigation of the total effect of various uncertainties, ESO based RC is particularly effective against a wide range of parameter variations, model uncertainties, and large disturbances. With only two tuning parameters, the controller provides a simple and user friendly solution to complex engineering problems in practice. The comparison results verified the effectiveness of the ESO based RC over state observer (SO) based RC.

This paper considers the problem of tracking a periodic signal for a plant with an input dead zone in the actuator. The nonlinearity greatly degrades control performance. To solve this problem, we incorporate an equivalent-input-disturbance (EID) compensator into a repetitive control system (RCS), resulting in a new system configuration. We combine the linear-matrixinequality technique with singular-value decomposition to analyze the stability of the system and to devise a design method. Unlike other methods, this one does not require any information about the dead zone. Simulation results demonstrate its effectiveness.

This study investigates the challenge of repetitive control in a type of linear uncertain system with exogenous disturbances. The uncertain systems with state and state derivative uncertainties. To preserve the uncertain properties of these systems, this class is not directly transformed into a general linear uncertain system. Therefore, it is challenging and complicated to study the control issues of these systems. In this study, a novel approach that combines the system and differential states into a new state is presented; this approach transforms an uncertain system into a linear singular system and is effective for handling uncertainty. The repetitive control problem of the linear singular system with disturbances is addressed from two perspectives. First, the traditional modified repetitive control system is enhanced by introducing an error compensator to improve system tracking performance. Second, to enhance disturbance rejection, a novel modified equivalent‐input‐disturbance (EID) approach is introduced for the first time. Unlike the traditional EID method, the modified method directly compensates for the disturbance estimation error to enhance the accuracy of disturbance estimation and achieve optimal disturbance‐rejection performance in the system. The required and sufficient requirements for the stability of a closed‐loop system are provided. And the controller design algorithm is presented based on these conditions. Finally, the presented method is compared with other control methods, demonstrating its effectiveness and superiority.

Adaptive disturbance rejection neural output feedback control of hydraulic manipulator systems

Time-varying multiplicative/additive faults compensation in both actuators and sensors simultaneously for nonlinear systems via robust sliding mode control scheme

This paper presents a novel design method for discrete-time repetitive control systems (RCS) based on two-dimensional (2D) discrete-time model. Firstly, the 2D model of an RCS is established by considering both the control action and the learning action in RCS. Then, through constructing a 2D state feedback controller, the design problem of the RCS is converted to the design problem of a 2D system. Then, using 2D system theory and linear matrix inequality (LMI) method, stability criterion is derived for the system without and with uncertainties, respectively. Parameters of the system can be determined by solving the LMI of the stability criterion. Finally, numerical simulations validate the effectiveness of the proposed method.

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 shows that design of a robustly stable repetitive control system is equivalent to that of a feedback control system for an uncertain linear time-invariant system satisfying the well-known robust performance condition. Once a feedback controller is designed to satisfy the robust performance condition, the feedback controller and the repetitive controller using the performance weighting function robustly stabilizes the repetitive control system. It is also shown that we can obtain a steady-state tracking error described in a simple form without time-delay element if the robust stability condition is satisfied for the repetitive control system. Moreover, using this result, a sufficient condition is provided, which ensures that the least upper bound of the steady-state tracking error generated by the repetitive control system is less than or equal to the least upper bound of the steady-state tracking error only by the feedback system

In this paper, the adaptive control problem is addressed for active vehicle suspension systems with the unknown nonlinearity as well as the unknown time-varying input delay. A dynamic gain control frame is proposed to suppress vehicle vibration and maintain the required suspension performance. Firstly, a dynamic gain extended state observer (ESO) is constructed to obtain the unknown velocity information and nonlinearity for the implementation of the control scheme. Moreover, a robust control method with a dynamic gain control term and a time delay compensation term is designed to mitigate the effect of unknown input time delay and uncertainty on system stability. By resorting to the Lyapunov-Krasovkii stability theory, the ultimate uniform boundedness of all signals in the closed-loop vehicle active suspension system is guaranteed. Finally, an example is presented as an illustration of the effectiveness of the proposed method.

A new design method of the repetitive control system for linear systems with time-varying norm-bounded uncertainties is presented, which can design a low-pass filter of the repetitive controller and a stabilizing controller simultaneously in the repetitive control system. Using a Lyapunov functional for the repetitive control system, sufficient conditions are derived in terms of a linear matrix inequality (LMI), which ensure robust stability of the repetitive control system and achieve the prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> performance. Based on derived conditions, the problem of designing a stabilizing controller and finding the cut-off frequency of a low-pass filter is reformulated as an optimization problem with an LMI constraint of the free parameter. Then, an iterative algorithm is presented to calculate the largest cut-off frequency of a low-pass filter and design the corresponding state-feedback controller simultaneously. A numerical example is presented to illustrate the validity of the proposed method.

In this paper, an improved optimal sliding mode control strategy is proposed for multi-motor driving servo system. Some states of multi-motor drive system are not measurable and there exists unknown nonlinearity. To solve this problem, the disturbance observer and extended state observer are both applied to estimate the unknown states and nonlinearity. Based on optimal control theory, the optimal sliding surface is selected to guarantee the optimal dynamic performance of the sliding mode of the system. The effectiveness of designed control methods is illustrated by simulation results.