High-gain Observer Research Articles

Nonaffine Helicopter Control Design and Implementation Based on a Robust Explicit Nonlinear Model Predictive Control

Control design for a helicopter is a challenging problem because of its nonaffine inputs, its underactuated characteristics, and highly coupled dynamics. To solve a control problem of the helicopter under model uncertainties and disturbance present environments, an explicit nonlinear model predictive control (ENMPC), a dynamic inversion (DI), and an extended high-gain observer (EHGO) are combined in a multi-time-scale fashion. The multi-time-scale scaled structure and the ENMPC provide the framework of the control design, the DI deals with nonaffine control inputs, and the EHGO estimates the unmeasured system states and uncertainties. The proposed control design is discretized to be implemented on a small-scale helicopter. The successful outdoor experiments with the proposed control implemented on autopilot hardware demonstrate the validity of our approach in the presence of model uncertainties and wind disturbances.

Robust active disturbance attenuation control of an uncertain quadrotor

PurposeThe aim of this research is to design a robust active disturbance attenuation control (RADAC) technique combined with an extended high gain observer (EHGO) and low pass filter (LPF).Design/methodology/approachFor designing a RADAC technique, the sliding mode control (SMC) method is used. Since the standard method of SMC exhibits a chattering phenomenon in the controller, a multilayer sliding mode surface is designed for avoiding the chattering. In addition, to attenuate the unwanted uncertainties and disturbances (UUDs), the techniques of EHGO and LPF are deployed. Besides acting as a patch for disturbance attenuation, the EHGO design estimates the state variables. To investigate the stability and effectiveness of the designed control algorithm, the stability analysis followed by the simulation study is presented.FindingsThe major findings include the design of a chattering-free RADAC controller based on the multilayer sliding mode surface. Furthermore, a criterion of integrating the LPF scheme within the EHGO scheme is also developed to attenuate matched and mismatched UUDs.Practical implicationsIn practice, the quadrotor flight is opposed by different kinds of the UUDs. And, the model of the quadrotor is a highly nonlinear underactuated model. Thus, the dynamics of the quadrotor model become more complex and uncertain due to the additional UUDs. Hence, it is necessary to design a robust disturbance attenuation technique with the ability to estimate the state variables and attenuate the UUDs and also achieve the desired control objectives.Originality/valueDesigning control methods to attenuate the disturbances while assuming that the state variables are known is a common practice. However, investigating the uncertain plants with unknown states along with the disturbances is rarely taken in consideration for the control design. Hence, this paper presents a control algorithm to address the issues of the UUDs as well as investigate a criterion to reduce the chattering incurred in the controller due to the standard SMC algorithm.

Bank of High-Gain Observers in Output Feedback Control: Robustness Analysis Against Measurement Noise

This paper analyzes output feedback control of a class of unknown nonlinear systems in the presence of measurement noise using multiple high-gain observers (MHGO). It is well-known that single high-gain observers (HGO) are not able to provide satisfactory performance when the system output is contaminated by noise. More specifically, there is a trade-off between the convergence speed of state estimation and the bound of steady estimation error in HGO when the output measurement is contaminated by noise. In the presented scheme, the output feedback controller utilizes the state estimation obtained from an appropriate combination of information provided by a bank of HGOs. The proposed strategy is capable of mitigating the destructive effects of measurement noise and speeding up the convergence process, and it does that because it introduces an extra design parameter. The performance recovery capabilities of MHGO-based controllers and the stability of the closed-loop system are discussed. Simulations are performed on an underwater vehicle system and a mechanical system to evaluate the performance of the MHGO-based controller. Furthermore, a detailed comparison between the MHGO-based controller and controllers based on conventional HGO, HGO with switching gain, and multi-observer approach is provided, which shows the superiority of the MHG-based controller over the other methods.

Adaptive neural formation control for underactuated unmanned surface vehicles with collision and connectivity constraints

The aim of this paper is to address the leader–follower formation control problem for a group of underactuated unmanned surface vehicles (USVs) with non-diagonal inertia matrix subject to modeling uncertainties and limited sensing capabilities. No communication is required among the USVs, but every USV is only equipped with on-board sensors to measure the line-of-sight (LOS) range and the relative bearing angle. The connectivity preserving constraint arisen from the limited sensing capability and the collision avoidance constraint resulting from the safety requirement are imposed on the LOS range and the relative bearing angle between every follower and its leader. These constraints are subsequently incorporated into the tan-type barrier Lyapunov function-based formation control design. Every USV reconstructs the velocity of its leader using the high-gain observer based solely on the available LOS range and relative bearing angle. Based on coordinate transformation, backstepping procedure, dynamic surface control (DSC) technique, and neural network approximation, a singularity-free formation controller is then developed, which guarantees the boundedness of all the closed-loop system signals and achieves satisfaction of prescribed performance specifications on the formation errors. Simulations are performed to verify the effectiveness of the formation control strategy.

Fractional synchronization involving fractional derivatives with nonsingular kernels: Application to chaotic systems

We present a novel master‐slave fractional synchronization in chaotic systems by using fractional derivatives with nonlocal and nonsingular kernel. The master system is the fractional‐order chaotic system, and then, we designed a fractional‐order high gain observer, which is the slave system, based on the chaotic system model to achieve the synchronization. We used three different oscillator systems, a novel Chen‐Burke‐Shaw chaotic attractor, a novel fractional‐order chaotic system, and the fractional‐order model of a simple autonomous Jerk circuit. Our research followed to test the performance of the fractional synchronization. We use two performance indices, the integral of the square error (ISE) and the integral of the square error multiplied by time (ITSE). We showed that by using the fractional‐order approach, we can reduce the values on the ISE and ITSE indices; hence, we guaranteed a full synchronization between the master and slave system. Our analysis shows that when using fractional derivatives with variable order, the ISE and ITSE indices have a lower value than when using the classical derivatives. We used the definition of Atangana‐Baleanu‐Caputo and Liouville‐Caputo derivatives for the three examples mentioned in this work. We numerically solved the equations using the Adams method. Our results show that when using the fractional‐order approach, the ISE and ITSE indices are lower than the integer‐order case.

An Output Feedback Based Robust Saturated Controller Design for Pavement Sweeping Self-Reconfigurable Robot

Mobile robots play a crucial role in cleaning, maintenance, and surveillance applications. This article advocates for the use of a novel robust output feedback based path following controller, for a class of self-reconfigurable mobile robot under actuator saturation. The reconfigurability property of such platforms is captured via an uncertain Euler-Lagrange dynamics. The proposed control framework estimates the unmeasurable states and the uncertain dynamics terms through two extended high gain observers, whereas the actuator limits are honored via a fast dynamic compensator. The closed-loop stability is analyzed via contraction theory, which, compared to the conventional Lyapunov based approaches, avoids the requirement of arbitrarily large controller and observer gains. Such a feature is of particular interest in view of actuator saturation. The experimental results with PANTHERA self-reconfigurable robot validate the effectiveness of the proposed technique over the state of the art.

High-Gain Observer Design for a Class of Quasi-Linear Integro-Differential Hyperbolic Systems—Application to an Epidemic Model

This article addresses the problem of high-gain observer design for a class of quasi-linear hyperbolic systems (with one characteristic velocity), possibly including nonlocal terms, making them systems of partial integro-differential equations. The design relies on distributed measurement of a part of the state vector. The observer is presented and discussed and the exponential stability in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$C^1$</tex-math></inline-formula> spatial norm of the origin for the error system is fully established via Lyapunov-based analysis. Its use is illustrated via an application to an age-dependent susceptible, infected, recovered (SIR) epidemic model.

On finite-time output feedback sliding mode control of an elastic multi-motor system

In this paper, the tracking control scheme is presented using the framework of finite-time sliding mode control (SMC) law and high-gain observer for disturbed/uncertain multi-motor driving systems under the consideration multi-output systems. The convergence time of sliding mode control is estimated in connection with linear matrix inequalities (LMIs). The input state stability (ISS) of proposed controller was analyzed by Lyapunov stability theory. Finally, the extensive simulation results are given to validate the advantages of proposed control design.

Observer-Based Enhanced ANFIS Control for a Quadrotor UAV

This paper introduces a new approach for optimizing the Adaptive Network Fuzzy Inference System (ANFIS) with the (metaheuristic) particle swarm optimization (PSO) algorithm to solve a trajectory tracking problem for a UAV quadrotor system. In this work, the input-output dataset is collected from the quadrotor's time response from a Proportional Integral Derivative (PID) controller. Then, before its use in the ANFIS algorithm, the collected dataset is optimized using the PSO algorithm. Moreover, an integral control action is integrated into the proposed ANFIS controller to ensure disturbance rejection. A suitable high gain observer is utilized in estimating unmeasured states for translational and rotational motions of the quadrotor system. Compared to a conventional ANFIS and traditional PID controllers, the results of two simulation tests demonstrate the efficiency and robustness of the proposed new output-feedback PSO-ANFIS controller.

Chattering-free higher order sliding mode controller with a high-gain observer for the load following of a pressurized water reactor

The load following of nuclear power plants (NPPs) has been a contentious issue in the control field. In this paper, we propose a chattering-free higher order sliding mode control scheme with a high-gain observer for the load following of a pressurized water reactor (PWR) in the presence of lumped disturbances owing to model uncertainties and external disturbances. The mathematical model of the PWR system is first set up in the form of an affine nonlinear equation. Subsequently, a high-gain observer, which achieves accurate estimations of the unmeasured state and lumped disturbances, is designed. Based on the outputs of the high-gain observer, we develop a chattering-free higher order sliding mode controller to improve the load-following performance while dealing with lumped disturbances and estimation errors of the high-gain observer. In contrast to some previous sliding mode controllers for the load following of NPPs, the proposed controller is completely free from chattering effects because the control input is obtained after integration. The asymptotic stability of the overall control scheme is demonstrated by combining the Lyapunov stability theory with backstepping technology. Finally, the simulation results reveal that the maximum absolute power error is less than 1×104W with the proposed control scheme, 5×105W with a PID controller, and 4×105W with a conventional sliding mode controller. In addition, in contrast to the conventional sliding mode controller, the proposed control scheme produces smooth control input without the chattering phenomenon. Thus, the proposed chattering-free higher order sliding mode control scheme with a high-gain observer provides smoother control input, higher load-following accuracy, and stronger robustness against lumped disturbances than the PID controller and the conventional sliding mode controller.

High-gain observer-based integral sliding mode tracking control for heavy vehicle electro-hydraulic servo steering systems

The electro-hydraulic servo steering system (EHSSS) is the key element to determine the handling and stability of heavy vehicles. Accurate steering control is challenged due to its complicated structure and a wide range of steering loads. In this paper, an output feedback integral sliding mode control (ISMC) method based on high-gain observer is proposed to solve this issue. First, a new Hurwitz matrix design method is presented for EHSSS with non-chain integrator, in order to prove the convergence of the observer error dynamics. Then, the Lyapunov stability of the observer-based controller is verified. Finally, a test bench is established to experimentally validate the proposed method's effectiveness through multiple test scenarios. The results show the tracking error of the proposed method is significantly smaller than PI and similar to full-state feedback integral sliding mode controller. This paper provides a valuable reference for high-gain observer-based nonlinear control applied to a typical electro-hydraulic servo steering system.

Fault-Tolerant Control for Three-Tank System in Case of Sensor Faults

This research paper would be devoted to the application of a fault-tolerant control (FTC) for a benchmark system composed of three interconnected tanks in case of sensor faults. The control scheme includes two blocks: fault detection and isolation (FDI) block and a control law reconfiguration block. The strategy of the FDI method is based on a bank of high gain observers; each of them is constructed to estimate the system state vector. Thus, the diagnostic signal-residuals are generated by the comparison of measured and estimated outputs and the faulty sensor is isolated. The reconfiguration block performs an update of the controller parameters according to the operating mode. The application of this method to a pilot plant demonstrates that the hydrographic system maintains quite performances after sensor faults occurrence.

Observer Design for Sampled-Data Systems via Deterministic Learning.

A unified approach is proposed to design sampled-data observers for a certain type of unknown nonlinear systems undergoing recurrent motions based on deterministic learning in this article. First, a discrete-time implementation of high-gain observer (HGO) is utilized to obtain state trajectory from sampled output measurements. By taking the recurrent estimated trajectory as inputs to a dynamical radial basis function network (RBFN), a partial persistent exciting (PE) condition is satisfied, and a locally accurate approximation of nonlinear dynamics can be realized along the estimated sampled-data trajectory. Second, an RBFN-based observer consisting of the obtained dynamics from the process of deterministic learning is designed. Without resorting to high gains, the RBFN-based observer is shown capable of achieving correct state observation. The novelty of this article lies in that, by incorporating deterministic learning with the discrete-time HGO, the nonlinear dynamics can be accurately approximated along the estimated trajectory, and such obtained knowledge can then be utilized to realize nonhigh-gain state estimation for the same or similar sampled-data systems. Simulation is performed to validate the effectiveness of the proposed approach.

Single-Gain Super-Twisting Algorithm Application to PMSM

In this article, by means of a parametrization leading to a single gain, a tuning method is proposed to simplify the implementation of the well-known super-twisting algorithm. Furthermore, inspired by ideas from the high-gain observer design, and using a Lyapunov approach, the stability analysis of the closed-loop system is presented. Thanks to a simple Lyapunov function, sufficient conditions are obtained to prove the finite-time convergence. Finally, the performances of the proposed strategy are illustrated experimentally on a permanent-magnet synchronous motor (PMSM) using an industrial benchmark for generating the desired trajectories to be tracked, in presence of external disturbances.

On the use of low-pass filters in high-gain observers

To address the well-known noise sensitivity problems associated with high-gain observers, we insert a low-pass filter on the measurement channel. Considering nonlinear plants in observability canonical form, we first motivate an architecture where the output error is filtered by a linear system parametrized by its arbitrary order and a scalar positive gain. Our main result establishes an exponential finite gain bound for the estimation error, from the measurement noise, this gain being dependent on the high-gain and filter parameters. We also prove bounds depending on the filter parameters characterizing improved high-frequency gains from the measurement noise to the estimation error. The proposed construction is shown to behave desirably in numerical simulations.

Hysteresis compensation-based robust output feedback control for long-stroke piezoelectric actuators at high frequency

Piezoelectric actuators (PEAs) are the key element for many vital applications and they play a big role in modern industries due to their operational characteristics. However, parametric uncertainties along with nonlinearities due to hysteresis and creep effects certainly impact severely the high precision tracking control of PEAs. This paper presents a robust output feedback controller for PEAs with hysterical dynamics compensated. In addition, a high gain observer is utilized to estimate the PEA’s tip velocity in order to facilitate the operation of the control algorithm. The proposed controller is designed to handle the unknown parameters and uncertainties associated with the nonlinear behavior of the PEAs. It is also tested on a commercial long-stroke PEA using different high frequency profiles. Experimental results show the effectiveness and robustness of the proposed controller compared to existing controllers.

Sensorless intelligent second-order integral sliding mode maximum power point tracking control for wind turbine system based on wind speed estimation

Aiming at the maximum power point tracking for wind turbine, a sensorless intelligent second-order integral sliding mode control based on wind speed estimation is proposed in this article. The maximum wind energy capture is realized by controlling permanent magnet synchronous motor to adjust the speed of wind turbine. First, an intelligent second-order integral sliding mode control is designed for the speed loop and current loop control, which has fast convergence speed, strong robustness and can effectively reduce chattering. Second, a novel cascade observer based on direct sliding mode observer and extended high-gain observer is used to estimate the rotor speed and position. Besides, combined radial basis function neural network is used to estimate the valid value of wind speed. Both simulation and experiment are implemented, which verify the effectiveness of the proposed strategy under the condition of considering both model uncertainty and external disturbance.

Adaptive Observer-Based Sliding Mode Control for a Two-Wheeled Self-Balancing Robot under Terrain Inclination and Disturbances

This paper investigates an output feedback sliding mode control scheme for a two-wheeled self-balancing robot under terrain inclination and disturbances. First of all, an adaptive high-gain observer is designed for the robot to estimate, simultaneously, the unmeasured states and the unknown terrain inclination angle which appears nonlinearly in the dynamics of the wheeled robot, using the only measured linear and angular positions. Then, the estimated states and the reconstructed unknown inclination angle are used by an appropriate continuously implemented sliding mode controller whose the design is based on the boundary layer approximation approach to reduce the chattering phenomenon. The objective of the proposed robust controller is to ensure the tracking control of the two-wheeled robot despite the unknown terrain inclination and the presence of friction disturbances. The stability of the adaptive observer-based output feedback system is established through a Lyapunov analysis, and it is inspired from sliding modes theory. Numerical simulations results highlight the effectiveness of the proposed tracking control scheme applied on two-wheeled self-balancing robot subject to terrain inclination even in the presence of unavailable disturbances.

Adaptive Fuzzy Robust Control of a Bionic Mechanical Leg With a High Gain Observer

In this paper, an observer-based adaptive fuzzy robust controller is proposed for trajectory tracking control of a bionic mechanical leg (BML) with unmeasured system states, dynamic uncertainties and external disturbances. A high gain observer (HGO) is constructed to estimate the unavailable joint velocities using the joint position feedback signals, while an adaptive fuzzy logic system (AFLS) is employed to address the lumped uncertainties. The nonlinear robust controller is then synthesized via backstepping method to improve the position tracking performance. The stability of the closed loop system is mathematically demonstrated via the Lyapunov’s stability theory. It is proven that under the proposed controller all the closed-loop signals are bounded and the trajectory tracking errors converge to a small neighborhood of the origin with appropriate design parameters. The effectiveness of the proposed control scheme is illustrated by simulation studies.

Saturated Output-Feedback Hybrid Reinforcement Learning Controller for Submersible Vehicles Guaranteeing Output Constraints

In this brief, we propose a new neuro-fuzzy reinforcement learning-based control (NFRLC) structure that allows autonomous underwater vehicles (AUVs) to follow a desired trajectory in large-scale complex environments precisely. The accurate tracking control problem is solved by a unique online NFRLC method designed based on actor-critic (AC) structure. Integrating the NFRLC framework including an adaptive multilayer neural network (MNN) and interval type-2 fuzzy neural network (IT2FNN) with a high-gain observer (HGO), a robust smart observer-based system is set up to estimate the velocities of the AUVs, unknown dynamic parameters containing unmodeled dynamics, nonlinearities, uncertainties and external disturbances. By employing a saturation function in the design procedure and transforming the input limitations into input saturation nonlinearities, the risk of the actuator saturation is effectively reduced together with nonlinear input saturation compensation by the NFRLC strategy. A predefined funnel-shaped performance function is designed to attain certain prescribed output performance. Finally, stability study reveals that the entire closed-loop system signals are semi-globally uniformly ultimately bounded (SGUUB) and can provide prescribed convergence rate for the tracking errors so that the tracking errors approach to the origin evolving inside the funnel-shaped performance bound at the prescribed time.