On the notions of normality, locality, and operational stability in ADRC

Treating plant dynamics as an ideal integrator chain disturbed by the total disturbance is the hallmark of active disturbance rejection control (ADRC). To interpret its effectiveness and success, to explain why so many vastly different dynamic systems can be treated in this manner, and to answer why a detailed, accurate, and global mathematical model is unnecessary, is the target of this paper. Driven by a motivating example, the notions of normality and locality are introduced. Normality shows that, in ADRC, the plant is normalized to an integrator chain, which is called local nominal model and locally describes the plant’s frequency response in the neighborhood of the expected gain crossover frequency. Locality interprets why ADRC can design the controller only with the local information of the plant. With normality and locality, ADRC can be effective and robust, and obtain operational stability discussed by T. S. Tsien. Then viewing proportional-integral-derivative (PID) control as a low-frequency approximation of second-order linear ADRC, the above results are extended to PID control. A controller design framework is proposed to obtain the controller in three steps: (1) choose an integrator chain as the local nominal model of the plant; (2) select a controller family corresponding to the local nominal model; and (3) tune the controller to guarantee the gain crossover frequency specification. The second-order linear ADRC and the PID control are two special cases of the framework.     

Trajectory tracking anti-disturbance control for unmanned aerial helicopter based on disturbance characterization index

This work studies the trajectory tracking control for unmanned aerial helicopter (UAH) system under both matched disturbance and mismatched ones. Initially, to tackle the strong coupling, an input–output feedback linearization method is utilized to simplify the nonlinear UAH system. Secondly, a set of finite-time disturbance observers (FTDOs) are proposed to estimate mismatched disturbances with their successive derivatives, which are utilized to design the feedforward controller via backstepping. Thirdly, as for matched disturbance, by defining the disturbance characterization index (DCI) to determine whether the disturbance is harmful or not for the UAH system, a feedback controller is proposed and a sufficient condition is established to ensure the convergence of the tracking error. Finally, some numerical simulations and comparisons illustrate the validity and advantages of our control scheme.     

Data‑driven disturbance observer‑based control: an active disturbance rejection approach

In this paper, a data-driven method for disturbance estimation and rejection is presented. The proposed approach is divided into two stages: an inner stabilization loop, to set the desired reference model, together with an outer loop for disturbance estimation and compensation. Inspired by the active disturbance rejection control framework, the exogenous and endogenous disturbances are lumped into a total disturbance signal. This signal is estimated using an on-line algorithm based on a datadriven predictor scheme, whose parameters are chosen to satisfy high robustness-performance criteria. The above process is presented as a novel enhancement to design a disturbance observer, which constitutes the main contribution of the paper. In addition, the control strategy is completely presented in discrete time, avoiding the use of discretization methods for its digital implementation. As a case study, the voltage control of a DC-DC synchronous buck converter afected by disturbances in the input voltage and the load is considered. Finally, experimental results that validate the proposed strategy and some comparisons with the classical disturbance observer-based control are presented.     

An adaptive series control for an interior permanent magnet synchronous motor with actuator compensation

An adaptive series speed control system for an interior permanent magnet synchronous motor (IPMSM) drive is presented in this paper. This control system consists of a current and a speed control loop, and it is intended to improve the drive’s speed tracking performance as well as to compensate for voltage distortions caused by non-ideal characteristics of the drive’s actuator, which is a voltage source inverter (VSI). To achieve these goals, a simple model that captures these characteristics of the VSI is developed and embedded in the motor’s electrical model. Then, based on the resulting model, an adaptive proportional-integral (PI) control for the current loops is designed, allowing for state regulation and actuator compensation. Additionally, to improve the drive’s speed tracking performance, a proportional-model-reference adaptive controller (MRAC) is designed for the speed loop. Techniques from machine learning are used for designing the MRAC to effectively address nonlinearities and uncertainties in the speed dynamic. Finally, simulation results are presented to illustrate the outstanding performance of the proposed multi-loop controller.     

Output feedback adaptive super twisting sliding mode control for quadrotor UAVs

In this paper, a sliding mode control with adaptive gain combined with a high-order sliding mode observer to solve the tracking problem for a quadrotor UAV is addressed, in presence of bounded external disturbances and parametric uncertainties. The high order sliding mode observer is designed for estimating the linear and angular speed in order to implement the proposed scheme. Furthermore, a Lyapunov function is introduced to design the controller with the adaptation law, whereas an analysis of finite time convergence towards to zero is provided, where sufficient conditions are obtained. Regarding previous works from literature, one important advantage of proposed strategy is that the gains of control are parameterized in terms of only one adaptive parameter, which reduces the control effort by avoiding gain overestimation. Numerical simulations for tracking control of the quadrotor are given to show the performance of proposed adaptive control–observer scheme.     

Active disturbance rejection control of nonlinear SISO Lagrangian systems via endogenous injections and exogenous feedback for trajectory tracking

This article deals with a linear classical approach for the robust output reference trajectory tracking control of nonlinear SISO Lagrangian systems with a controllable (fat) tangent linearization around an operating equilibrium point. An endogenous injections and exogenous feedback (EIEF) approach is proposed, which is naturally equivalent to the generalized proportional integral control method and to a robust classical compensation network. It is shown that the EIEF controller is also equivalent, within a frequency domain setting demanding respect for the separation principle, to the reduced order observer based active disturbance rejection control approach. The proposed linear control approach is robust with respect to total disturbances and, thus, it is efective for the linear control of the nonlinear Lagrangian system. An illustrative nonlinear rotary crane Lagrangian system example, which is non-feedback linearizable, is presented along with digital computer simulations.     

Adaptive robust simultaneous stabilization of multiple n-degree-of-freedom robot systems

In this paper, the adaptive robust simultaneous stabilization problem of uncertain multiple n-degree-of-freedom (n-DOF) robot systems is studied using the Hamiltonian function method, and the corresponding adaptive L2 controller is designed. First, we investigate the adaptive simultaneous stabilization problem of uncertain multiple n-DOF robot systems without external disturbance. Namely, the single uncertain n-DOF robot system is transformed into an equivalent Hamiltonian form using the unified partial derivative operator (UP-DO) and potential energy shaping method, and then a high dimensional Hamiltonian system for multiple uncertain robot systems is obtained by applying augmented dimension technology, and a single output feedback controller is designed to ensure the simultaneous stabilization for the higher dimensional Hamiltonian system. On this basis, we further study the adaptive robust simultaneous stabilization control problem for the uncertain multiple n-DOF robot systems with external disturbances, and design an adaptive robust simultaneous stabilization controller. Finally, the simulation results show that the adaptive robust simultaneous stabilization controller designed in this paper is very effective in stabilizing multi-robot systems at the same time.     

A neuro‑observer‑based optimal control for nonaffine nonlinear systems with control input saturations

In this study, an adaptive neuro-observer-based optimal control (ANOPC) policy is introduced for unknown nonaffine nonlinear systems with control input constraints. Hamilton–Jacobi–Bellman (HJB) framework is employed to minimize a non-quadratic cost function corresponding to the constrained control input. ANOPC consists of both analytical and algebraic parts. In the analytical part, first, an observer-based neural network (NN) approximates uncertain system dynamics, and then another NN structure solves the HJB equation. In the algebraic part, the optimal control input that does not exceed the saturation bounds is generated. The weights of two NNs associated with observer and controller are simultaneously updated in an online manner. The ultimately uniformly boundedness (UUB) of all signals of the whole closed-loop system is ensured through Lyapunov’s direct method. Finally, two numerical examples are provided to confirm the effectiveness of the proposed control strategy.     

Consensus control of feedforward nonlinear multi-agent systems: A time-varying gain method

In this paper, the leader–follower consensus of feedforward nonlinear multi-agent systems is achieved by designing the distributed output feedback controllers with a time-varying gain. The agents dynamics are assumed to be in upper triangular structure and satisfy Lipschitz conditions with an unknown constant multiplied by a time-varying function. A time-varying gain, which increases monotonously and tends to infinity, is proposed to construct a compensator for each follower agent. Based on a directed communication topology, the distributed output feedback controller with a time-varying gain is designed for each follower agent by only using the output information of the follower and its neighbors. It is proved by the Lyapunov theorem that the leader–follower consensus of the multi-agent system is achieved by the proposed consensus protocol. The effectiveness of the proposed time-varying gain method is demonstrated by a circuit system.     

Suppression of high order disturbances and tracking for nonchaotic systems: A time-delayed state feedback approach

Time-delayed state feedback is an easy realizable control method that generates control force by differencing the current and the delayed versions of the system states. In this paper, a new form of the time-delayed state feedback structure is introduced. Based on the proposed time-delayed state feedback method, a new robust tracking system is designed. This tracking system improves the conventional state feedback with integral action disturbance rejection characteristics in the presence of the disturbance signals imposed on the system dynamics or on the sensors that measure the system states. Also, the proposed tracking system tracks the ramp-shaped reference input signal, which is not achievable through conventional state feedback. Moreover, since the proposed method adds delays to the closed-loop system dynamics, the ordinary differential equation of the system changes to a delay differential equation with an infinite number of characteristic roots. Thus, conventional pole placement techniques cannot be used to design the time-delayed state feedback controller parameters. In this paper, the simulated annealing algorithm is used to determine the proposed control system parameters and move the unstable roots of the delay differential equation to the left half-plane. Finally, the efficiency of the proposed reference input tracker is demonstrated by presenting two numerical examples.     

Optimal control for spatial-temporal distributed nonlinear autoregressive with exogenous inputs correlation model of steel rolling reheating furnace: a coordinated time-sharing control approach

Accurate control of slab temperature and heating rate is an important significance to improve product performance and reduce carbon emissions for steel rolling reheating furnace (SRRF). Firstly, a spatial temporal distributed–nonlinear autoregressive with exogenous inputs correlation model (STD-NARXCM) to spatial temporal distributed–autoregressive with exogenous inputs correlation model (STD-ARXCM) in working point is established. Secondly, a new coordinated time-sharing control architecture in different time periods is proposed, which is along the length of the SRRF to improve the control performance. Thirdly, a hybrid control algorithm of expert-fuzzy is proposed to improve the dynamic of the temperature and the heating rate during time period 0 to t1. A hybrid control algorithm of expert-fuzzy-PID is proposed to enhance the control accuracy and the heating rate during time period t1 to t2. A hybrid control algorithm of expert-active disturbance rejection control (ADRC) is proposed to boost the anti-interference and the heating rate during time period t2 to t3. Finally, the experimental results show that the coordinated time-sharing algorithm can meet the process requirements, the maximum deviation of temperature value is 8–13.5?C.     

Extended state observer‑based pressure control for pneumatic actuator servo systems

A pneumatic actuator is a fast and economical tool that converts compressed air into mechanical motion. In this paper, an extended state observer (ESO)-based sliding mode controller (SMC) is developed to adjust the air pressure of the actuator for accurate position control. Specifcally, an impedance control module is established to produce desired air pressure based on the relationship between forces and desired positions. Then, the ESO-based SMC is implemented to adjust the air pressure to the required level despite the presence of system uncertainties and disturbances. As a result, the position of the actuator is controlled to a setpoint through the regulation of pressure. The performance of ESO-based SMC is compared with that of a classic active disturbance rejection controller (ADRC) and a SMC. Simulation results demonstrate that the ESO-based SMC shows comparable performance to ADRC in terms of precise pressure control. In addition, it requires the least control efort necessary to excite valves among the three controllers. The stability of ESO-based SMC is theoretically justifed through Lyapunov approach.     

Event-triggered H∞ consensus control for input-constrained multi-agent systems via reinforcement learning

This article presents an event-triggered H∞ consensus control scheme using reinforcement learning (RL) for nonlinear second-order multi-agent systems (MASs) with control constraints. First, considering control constraints, the constrained H∞ consensus problem is transformed into a multi-player zero-sum game with non-quadratic performance functions. Then, an event-triggered control method is presented to conserve communication resources and a new triggering condition is developed for each agent to make the triggering threshold independent of the disturbance attenuation level. To derive the optimal controller that can minimize the cost function in the case of worst disturbance, a constrained Hamilton–Jacobi–Bellman (HJB) equation is defined. Since it is difficult to solve analytically due to its strongly non-linearity, reinforcement learning (RL) is implemented to obtain the optimal controller. In specific, the optimal performance function and the worst-case disturbance are approximated by a time-triggered critic network; meanwhile, the optimal controller is approximated by event-triggered actor network. After that, Lyapunov analysis is utilized to prove the uniformly ultimately bounded (UUB) stability of the system and that the network weight errors are UUB. Finally, a simulation example is utilized to demonstrate the effectiveness of the control strategy provided.     

Adaptive feedback control for nonlinear triangular systems subject to uncertain asymmetric dead-zone input

In this paper, an adaptive control strategy is proposed to investigate the issue of uncertain dead-zone input for nonlinear triangular systems with unknown nonlinearities. The considered system has no precise priori knowledge about the dead-zone feature and growth rate of nonlinearity. Firstly, a dynamic gain is introduced to deal with the unknown growth rate, and the dead-zone characteristic is processed by the adaptive estimation approach without constructing the dead-zone inverse. Then, by virtue of hyperbolic functions and sign functions, a new adaptive state feedback controller is proposed to guarantee the global boundedness of all signals in the closed-loop system. Moreover, the uncertain dead-zone input problem for nonlinear upper-triangular systems is solved by the similar control strategy. Finally, two simulation examples are given to verify the effectiveness of the control scheme.     

Adaptive tracking H-infinity control for switched nonlinear systems with unknown control gain sign

This paper addresses the adaptive tracking control scheme for switched nonlinear systems with unknown control gain sign. The approach relaxes the hypothesis that the upper bound of function control gain is known constant and the bounds of external disturbance and approximation errors of neural networks are known. RBF neural networks (NNs) are used to approximate unknown functions and an H-infinity controller is introduced to enhance robustness. The adaptive updating laws and the admissible switching signals have been derived from switched multiple Lyapunov function method. It’s proved that the resulting closed loop system is asymptotically Lyapunov stable such that the output tracking error performance and H-infinity disturbance attenuation level are well obtained. Finally, a simulation example of Forced Duffing systems is given to illustrate the effectiveness of the proposed control scheme and improve significantly the transient performance.     

Position control of synchronous motor drive by modified adaptive two-phase sliding mode controller

A modified adaptive two-phase sliding mode controller for the synchronous motor drive that is highly robust to uncertain-ties and external disturbances is proposed in this paper. The proposed controller uses two-phase sliding mode control (SMC) where the 1st phase mainly controls the system in steady states and disturbed states-it is a smoothing phase. The 2nd phase is used mainly in the case of disturbed states. Also, it is an autotuning phase and uses a simple adaptive algorithm to tune the gain of conventional variable structure control (VSC). The modified controller is useful in position control of a permanent magnet synchronous drive.     

Robust non-aggressive three-axis attitude control of spacecraft: dynamic sliding mode approach

Conventional sliding mode control (SMC) has been extensively applied in controlling spacecrafts because of its appealing characteristics such as robustness and a simple design procedure. Several methods such as second-order sliding modes and discontinuous controllers are applied for the SMC implementation. However, the main problems of these methods are convergence and error tracking in a finite amount of time. This paper combines an improved dynamic sliding mode controller and model predictive controller for spacecrafts to solve the chattering phenomenon in traditional sliding mode control. To this aim, this paper develops dynamic sliding mode control for spacecraft’s applications to omit the chattering issue. The proposed approach shows robust attitude tracking by a set of reaction wheels and stabilizes the spacecraft subject to disturbances and uncertainties. The proposed method improves the performance of the SMC for spacecraft by avoiding chattering. A set of simulation results are provided that show the advantages and improvements of this approach (in some sense) compared to SMC approaches.     

Simplifying ADRC design with error‑based framework: case study of a DC–DC buck power converter

In this work, the problem of designing a robust control algorithm for a DC-DC buck power converter is investigated. The applied solution is based on a recently proposed error-based version of the active disturbance rejection control (ADRC) scheme, in which the unknown higher-order terms of the reference signal are treated as additional components of the system “total disturbance”. The motivation here is to provide a practical following of a reference voltage trajectory for the buck converter in specifc cases where neither the analytical form of the desired signal nor its future values are known a’priori, hence cannot be directly used for control synthesis. In this work, the application of the error-based ADRC results in a practically appealing control technique, with compact structure, simplifed control rule, and intuitive tuning (inherited from the conventional output-based ADRC scheme). Theoretical, numerical, and experimental results are shown to validate the efcacy of the error-based ADRC in buck converter control, followed by a discussion about the revealed theoretical and practical limitations of this approach.     

Sliding mode-based adaptive tube model predictive control for robotic manipulators with model uncertainty and state constraints

In this paper, the optimal tracking control for robotic manipulatorswith state constraints and uncertain dynamics is investigated, and a sliding mode-based adaptive tube model predictive control method is proposed. First, utilizing the high-order fully actuated system approach, the nominal model of the robotic manipulator is constructed as the predictive model. Based on the nominal model, a nominal model predictive controller with the sliding mode is designed, which relaxes the terminal constraints, and realizes the accurate and stable tracking of the desired trajectory by the nominal system. Then, an auxiliary controller based on the node-adaptive neural networks is constructed to dynamically compensate nonlinear uncertain dynamics of the robotic manipulator. Furthermore, the estimation deviation between the nominal and actual states is limited to the tube invariant sets. At the same time, the recursive feasibility of nominal model predictive control is verified, and the ultimately uniformly boundedness of all variables is proved according to the Lyapunov theorem. Finally, experiments show that the robotic manipulator can achieve fast and efficient trajectory tracking under the action of the proposed method.     

Prediction method for energy consumption per ton of fused magnesium furnaces using data driven and mechanism model

This paper gives an overview of early development of nonlinear disturbance observer design technique and the disturbance observer based control (DOBC) design. Some critical points raised in the development of the methods have been reviewed and discussed which are still relevant for many researchers or practitioners who are interested in this method. The review is followed by the development of a new type of nonlinear PID controller for a robotic manipulator and its experimental tests. It is shown that, under a number of assumptions, the DOBC consisting of a predictive control method and a nonlinear disturbance observer could reduce to a nonlinear PID with special features. Experimental results show that, compared with the predictive control method, the developed controller significantly improves performance robustness against uncertainty and friction. This paper may trigger further research and interests in the development of DOBC and related methods, and building up more understanding between this group of control methods with comparable ones (particularly control methods with integral action).