Performance analysis of active disturbance rejection tracking control for a class of uncertain LTI systems

The paper considers the tracking problem for a class of uncertain linear time invariant (LTI) systems with both uncertain parameters and external disturbances. The active disturbance rejection tracking controller is designed and the resulting closed-loop system׳s characteristics are comprehensively studied. In the time-domain, it is proven that the output of closed-loop system can approach its ideal trajectory in the transient process against different kinds of uncertainties by tuning the bandwidth of extended state observer (ESO). In the frequency-domain, different kinds of parameters׳ influences on the phase margin and the crossover frequency of the resulting control system are illuminated. Finally, the effectiveness and robustness of the controller are verified through the actuator position control system with uncertain parameters and load disturbances in the simulations.     

Modified reduced order observer based linear active disturbance rejection control for TITO systems

This paper proposes an observer based control approach for two input and two output (TITO) plant affected by the lumped disturbance which includes the undesirable effect of cross couplings, parametric uncertainties, and external disturbances. A modified reduced order extended state observer (ESO) based active disturbance rejection control (ADRC) is designed to estimate the lumped disturbance actively as an extended state and compensate its effect by adding it to the control. The decoupled mechanism has been used to determine the controller parameters, while the proposed control technique is applied to the TITO coupled plant without using decoupler to show its efficacy. Simulation results show that the proposed design is efficiently able to nullify the interactions within the loops in the multivariable process with better transient performance as compared to the existing proportional-integral-derivative (PID) control methods. An experimental application of two tanks multivariable level control system is investigated to present the validity of proposed scheme.     

Fractional active disturbance rejection control

A fractional active disturbance rejection control (FADRC) scheme is proposed to improve the performance of commensurate linear fractional order systems (FOS) and the robust analysis shows that the controller is also applicable to incommensurate linear FOS control. In FADRC, the traditional extended states observer (ESO) is generalized to a fractional order extended states observer (FESO) by using the fractional calculus, and the tracking differentiator plus nonlinear state error feedback are replaced by a fractional proportional-derivative controller. To simplify controller tuning, the linear bandwidth-parameterization method has been adopted. The impacts of the observer bandwidth ω_o and controller bandwidth ω_c on system performance are then analyzed. Finally, the FADRC stability and frequency-domain characteristics for linear single-input single-output FOS are analyzed. Simulation results by FADRC and ADRC on typical FOS are compared to demonstrate the superiority and effectiveness of the proposed scheme.     

基于预测函数控制和扰动观测器的永磁同步电机速度控制

设计了基于预测函数控制的速度控制器,以减小永磁同步电机的转矩波动,提高电机的转速控制精度。针对因外部扰动因素引起的控制器跟踪性能下降问题,设计了基于预测函数控制和扰动观测器的双环控制器;通过扰动观测器估计系统扰动,并据此产生转矩电流补偿量对控制量进行前馈修正,从而实现扰动的抑制。实验结果显示：当电机从静止跟踪到设定600 r/min转速时,系统没有超调,稳态精度为2 r/min;当电机以600 r/min稳速运行并加入1.6 N·m的转矩扰动时,转速最大波动为5 r/min。与传统的PI控制算法相比,所设计的控制器使转速波动减小了4.2% 。仿真分析和实验数据表明：基于预测函数控制和干扰观测器的控制器能够有效地抑制扰动,提高系统转速跟踪精度。     

基于扰动观测器的永磁同步电机电流环自适应滑模控制

针对扰动对永磁同步电机转速伺服系统性能的影响,提出了基于扰动观测器的电流环自适应滑模控制方法。设计了自适应律在线估计系统的内部参数摄动以补偿模型不确定性扰动。同时,设计了滑模扰动观测器实时估计系统外部负载扰动,并将观测值前馈补偿到电流环自适应滑模控制器,在提高系统鲁棒性的同时降低滑模控制系统的抖振。实验结果显示,采用基于扰动观测器的电流环自适应滑模控制方法,系统可快速、准确、无超调地跟踪900r/min的速度指令,调节时间为0.08s,稳态误差为±5r/min。加入0.6N·m的负载扰动,该控制方法的最大转速波动为21r/min,比PI控制方法的转速波动减小了3.4%。仿真和实验结果表明,基于扰动观测器的电流环自适应控制方法提高了永磁同步电机转速伺服系统的鲁棒性和动态响应性能,同时可有效抑制滑模控制系统的抖振。     

Design and analysis of tilt integral derivative controller with filter for load frequency control of multi-area interconnected power systems

In this paper, a novel Tilt Integral Derivative controller with Filter (TIDF) is proposed for Load Frequency Control (LFC) of multi-area power systems. Initially, a two-area power system is considered and the parameters of the TIDF controller are optimized using Differential Evolution (DE) algorithm employing an Integral of Time multiplied Absolute Error (ITAE) criterion. The superiority of the proposed approach is demonstrated by comparing the results with some recently published heuristic approaches such as Firefly Algorithm (FA), Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) optimized PID controllers for the same interconnected power system. Investigations reveal that proposed TIDF controllers provide better dynamic response compared to PID controller in terms of minimum undershoots and settling times of frequency as well as tie-line power deviations following a disturbance. The proposed approach is also extended to two widely used three area test systems considering nonlinearities such as Generation Rate Constraint (GRC) and Governor Dead Band (GDB). To improve the performance of the system, a Thyristor Controlled Series Compensator (TCSC) is also considered and the performance of TIDF controller in presence of TCSC is investigated. It is observed that system performance improves with the inclusion of TCSC. Finally, sensitivity analysis is carried out to test the robustness of the proposed controller by varying the system parameters, operating condition and load pattern. It is observed that the proposed controllers are robust and perform satisfactorily with variations in operating condition, system parameters and load pattern.     

Coupled-disturbance-observer-based position tracking control for a cascade electro-hydraulic system

The disturbance suppression is one of the most common control problems in electro-hydraulic systems. especially largely an unknown disturbance often obviously degrades the dynamic performance by biasing the desired actuator outputs (e.g., load forces or torques). In order to reject the dynamic disturbances in some multi-degree-of-freedom manipulators driven by electro-hydraulic actuators, this paper proposes a state feedback control of the cascade electro-hydraulic system based on a coupled disturbance observer with backstepping. The coupled disturbance observer is designed to estimate both the independent element and the coupled element of the external loads on each electro-hydraulic actuator. The cascade controller has the ability to compensate for the disturbance estimating, as well as guarantees the system state error convergence to a prescribed steady state level. The effectiveness of the proposed controller for the suppression of largely unknown disturbances has been demonstrated by comparative study, which implies the proposed approach can achieve better dynamic performance on the motion control of Two-Degree-of-Freedom robotic arm.     

Real time simulation of nonlinear generalized predictive control for wind energy conversion system with nonlinear observer

In order to make a wind power generation truly cost-effective and reliable, an advanced control techniques must be used. In this paper, we develop a new control strategy, using nonlinear generalized predictive control (NGPC) approach, for DFIG-based wind turbine. The proposed control law is based on two points: NGPC-based torque-current control loop generating the rotor reference voltage and NGPC-based speed control loop that provides the torque reference. In order to enhance the robustness of the controller, a disturbance observer is designed to estimate the aerodynamic torque which is considered as an unknown perturbation. Finally, a real-time simulation is carried out to illustrate the performance of the proposed controller.     

通过直线伺服鲁棒跟踪控制方法提高轮廓加工精度

为了减小零件加工的轮廓误差,提出了一种采用直线伺服驱动的零相位跟踪控制器(ZPETC)和干扰观测器 (DOB)相结合的鲁棒跟踪控制策略。零相位误差跟踪控制器作为前馈跟踪控制器,提高了快速性,使系统实现准确跟踪;基于干扰观测器的鲁棒反馈控制器补偿了外部扰动、未建模动态、系统参数变化和机械非线性等不确定因素,并根据预测到的干扰信息对各轴进行补偿以消除干扰对系统的影响,从而保证了系统的强鲁棒性能。仿真结果表明所提出的控制方案是有效的,既能实现完好跟踪,又有较强的鲁棒性能,从而提高了轮廓加工精度。     

Disturbance observer-based backstepping sliding mode fault-tolerant control for the hydro-turbine governing system with dead-zone input

This paper investigates a backstepping sliding mode fault-tolerant tracking control problem for a hydro-turbine governing system with consideration of external disturbances, actuator faults and dead-zone input. To reduce the effects of the unknown random disturbances, the nonlinear disturbance observer is designed to identify and estimate the disturbance term. To drastically decrease the complexity of stability functions selection and controller design, the recursive processes of the backstepping technique are employed. Additionally, based on the nonlinear disturbance observer and the backstepping technique, the sliding mode fault-tolerant tracking control approach is developed for the hydro-turbine governing system (HTGS). The stability of HTGS is rigorously demonstrated through Lyapunov analysis which is capable to satisfy a tracking control performance. Finally, comprehensive simulation results are presented to illustrate the effectiveness and superiority of the proposed control scheme.     

Antlion optimizer-ANFIS load frequency control for multi-interconnected plants comprising photovoltaic and wind turbine

This paper proposes optimal load frequency control (LFC) designed by Adaptive Neuro Fuzzy Inference System (ANFIS) trained via antlion optimizer (ALO) for multi-interconnected system comprising renewable energy sources (RESs). Two systems are modeled and investigated; the first one has two plants of grid connected photovoltaic (PV) system with maximum power point tracker (MPPT) and thermal plant while the second comprises four plants of thermal, wind turbine and grid connected PV systems. ALO is employed to get the optimal gains of Proportional–Integral (PI) controller such that the integral time absolute error (ITAE) of frequency and tie line power deviations is minimized. The input and output of the optimized PI controller are used to train the ANFIS-LFC with Gaussian surface membership functions. Different load disturbances are studied and the results are compared with other reported approaches. The obtained results confirmed the accuracy and reliability of the proposed approach in designing LFC for multi-interconnected power systems.     

Extended observer based on adaptive second order sliding mode control for a fixed wing UAV

This paper addresses the design of attitude and airspeed controllers for a fixed wing unmanned aerial vehicle. An adaptive second order sliding mode control is proposed for improving performance under different operating conditions and is robust in presence of external disturbances. Moreover, this control does not require the knowledge of disturbance bounds and avoids overestimation of the control gains. Furthermore, in order to implement this controller, an extended observer is designed to estimate unmeasurable states as well as external disturbances. Additionally, sufficient conditions are given to guarantee the closed-loop stability of the observer based control. Finally, using a full 6 degree of freedom model, simulation results are obtained where the performance of the proposed method is compared against active disturbance rejection based on sliding mode control.     

On the rejection of internal and external disturbances in a wind energy conversion system with direct-driven PMSG

This paper deals with the critical issue in a wind energy conversion system (WECS) based on a direct-driven permanent magnet synchronous generator (PMSG): the rejection of lumped disturbance, including the system uncertainties in the internal dynamics and unknown external forces. To simultaneously track the motor speed in real time and capture the maximum power, a maximum power point tracking strategy is proposed based on active disturbance rejection control (ADRC) theory. In real application, system inertia, drive torque and some other parameters change in a wide range with the variations of disturbances and wind speeds, which substantially degrade the performance of WECS. The ADRC design must incorporate the available model information into an extended state observer (ESO) to compensate the lumped disturbance efficiently. Based on this principle, a model-compensation ADRC is proposed in this paper. Simulation study is conducted to evaluate the performance of the proposed control strategy. It is shown that the effect of lumped disturbance is compensated in a more effective way compared with the traditional ADRC approach.     

Path following control for towing system of cylindrical drilling platform in presence of disturbances and uncertainties

Towing is a critical process to deploy a cylindrical drilling platform. However, the towing process faces a great variety of risks from a complex nautical environment, the dynamics in towing and maneuvering, to unexpected events. Therefore, safely navigating the towing system following a planned route to a target sea area is essential. To tackle the time-varying disturbances induced by wind, current and system parametric uncertainties, a path following control method for a towing system of cylindrical drilling platform is designed based on linear active disturbance rejection control. By utilizing Maneuvering Modeling Group model as well as a catenary model, we develop a three degree-of-freedom dynamic mathematical model of the towing system under external environmental disturbances and internal uncertainties. Furthermore, we design a linear active disturbance rejection control path following controller for real-time tracking error correction based on a guidance method combining cross-track error and parallax. Finally, the path following performance of the towing system is evaluated in a simulation environment under various disturbances and internal uncertainties, where the corresponding tracking error is analyzed. The results show that the linear active disturbance rejection control performs well under both the external disturbance and inherent uncertainties, and better satisfy the tracking performance criteria than a traditional proportional–integral–derivative controller.     

Active disturbance rejection control based human gait tracking for lower extremity rehabilitation exoskeleton

This paper presents an active disturbance rejection control (ADRC) based strategy, which is applied to track the human gait trajectory for a lower limb rehabilitation exoskeleton. The desired human gait trajectory is derived from the Clinical Gait Analysis (CGA). In ADRC, the total external disturbance can be estimated by the extended state observer (ESO) and canceled by the designed control law. The observer bandwidth and the controller bandwidth are determined by the practical principles. We simulated the proposed methodology in MATLAB. The numerical simulation shows the tracking error comparison and the estimated errors of the extended state observer. Two experimental tests were carried out to prove the performance of the algorithm presented in this paper. The experiment results show that the proposed ADRC behaves a better performance than the regular proportional integral derivative (PID) controller. With the proposed ADRC, the rehabilitation system is capable of tracking the target gait more accurately.     

Discrete-time setpoint-triggered reset integrator design with guaranteed performance and stability

According to Bode's gain-phase relationship, in linear time-invariant controllers, introducing an integral action to eliminate the steady-state error has an adverse effect of increased phase delay and overshoot, leading to performance deterioration. Moreover, increasing the bandwidth of the closed-loop system to enhance the low-frequency disturbance rejection invariably amplifies the sensitivity to high-frequency disturbances. Hence, the performance of the linear controllers is always limited due to these fundamental frequency- and time-domain limitations. Motivated by the desire to address the fundamental limitations of linear controllers and improve the time-varying closed-loop performance, we put forward a novel setpoint-triggered reset integrator strategy that varies the integrator cut-off frequency based on the setpoint information. Particularly, to tackle the time-varying disturbances and setpoint profiles, the proposed controller consists of a nominal linear controller and a variable-gain reset integrator. We show the global asymptotic stability of the proposed methodology using positive-real lemma along with the LaSalle's invariance principle and experimentally validate using measured frequency response function. Moreover, the efficacy of the proposed technique compared to that of the linear controller is experimentally demonstrated on a benchmark rotary servo system. Experimental results assessed using the tracking error and cumulative power spectral density substantiate that the proposed control strategy can not only improve the low-frequency disturbance rejection but also augment the high-frequency trajectory tracking performance.     

Improvement in automatic generation control of two-area electric power systems via a new fuzzy aided optimal PIDN-FOI controller

Automatic generation control (AGC) executes a vital role to supply quality power in an interconnected power system. To cultivate good quality of power supply via preserving area frequency and tie-line power oscillations following consumer's load demand disturbances, the controller designed for AGC of power system should display excellent disturbance rejection expertise. Hence, in this paper, a maiden attempt is made to propose a fuzzy aided integer order proportional integral derivative with filter-fractional order integral (FPIDN-FOI) controller for AGC of multi-area power systems. A more recent intelligent optimization technique termed as imperialist competitive algorithm (ICA) is fruitfully employed for concurrent tuning of various parameters of the proposed controller. It is observed from the simulation results that the proposed FPIDN-FOI controller outperforms the various existing control strategies and PID/PIDN/FPIDN controller designed in the study for five different power system models. Effect of variation in fractional order value of integral on the system performance is analyzed. A sensitivity analysis is conducted to test the robustness of the designed controller under variations in the system parameters, load demands and existence of the system nonlinearities. It is perceived that the proposed controller is robust and executes adequately under variations in system parameters, random load disturbance patterns and nonlinearities.     

Disturbance observer and adaptive controller design for a linear-motor-driven table system

This paper presents a disturbance observer and adaptive controller design for a direct drive motion control system. An indirect adaptive controller is implemented to achieve desired tracking performance as well as deal with system parameters variation. To reduce tracking errors, a newly designed adaptive feed-forward controller is proposed based on an on-line estimated inverse model of the linear motor drive system. A digital disturbance observer is implemented to be included in the proposed feedback-feed-forward control structure to compensate for the undesired nonlinearity and external load disturbance of the direct drive system. Experimental results show that this control scheme can achieve superior contouring accuracy, disturbance rejection and robustness under the influence of friction and cogging force.     

Finite-time tracking control of nth-order chained-form non-holonomic systems in the presence of disturbances

This paper addresses the problem of finite-time tracking controller design for nth-order chained-form non-holonomic systems in the presence of unknown disturbances. To this aim, a generalized disturbance observer based controller is proposed and combined with a recursive terminal sliding mode approach which guarantees finite-time convergence of the disturbance observer dynamic. By introducing a time-varying transformation and introducing a new control law, the existence of the sliding around the recursive terminal sliding mode surfaces is guaranteed. Finally, the proposed approach is applied for a wheeled mobile robot with a fourth-order chained-form non-holonomic model. The simulation results demonstrate the desirable and robust tracking performance of the proposed approach in the presence of unknown disturbance.     

Composite disturbance rejection control based on generalized extended state observer

Traditional extended state observer (ESO) design method does not focus on analysis of system reconstruction strategy. The prior information of the controlled system cannot be used for ESO implementation to improve the control accuracy. In this paper, composite disturbance rejection control strategy is proposed based on generalized ESO. First, the disturbance rejection performance of traditional ESO is analyzed to show the essence of the reconstruction strategy. Then, the system is reconstructed based on the equivalent disturbance model. The generalized ESO is proposed based on the reconstructed model, while convergence of the proposed ESO is analyzed along with the outer loop feedback controller. Simulation results on a second order mechanical system show that the proposed generalized ESO can deal with the external disturbance with known model successfully. Experiment of attitude tracking task on an aircraft is also carried out to show the effectiveness of the proposed method.