Unknown Parametric Uncertainties Research Articles

Finite-Time Command-Filtered Composite Adaptive Neural Control of Uncertain Nonlinear Systems.

This article presents a new command-filtered composite adaptive neural control scheme for uncertain nonlinear systems. Compared with existing works, this approach focuses on achieving finite-time convergent composite adaptive control for the higher-order nonlinear system with unknown nonlinearities, parameter uncertainties, and external disturbances. First, radial basis function neural networks (NNs) are utilized to approximate the unknown functions of the considered uncertain nonlinear system. By constructing the prediction errors from the serial-parallel nonsmooth estimation models, the prediction errors and the tracking errors are fused to update the weights of the NNs. Afterward, the composite adaptive neural backstepping control scheme is proposed via nonsmooth command filter and adaptive disturbance estimation techniques. The proposed control scheme ensures that high-precision tracking performances and NN approximation performances can be achieved simultaneously. Meanwhile, it can avoid the singularity problem in the finite-time backstepping framework. Moreover, it is proved that all signals in the closed-loop control system can be convergent in finite time. Finally, simulation results are given to illustrate the effectiveness of the proposed control scheme.

Observer-Based Sensor Fault Detection in a Dark Fermenter for Hydrogen Production

In this letter, we propose a fault detection observer for a hydrogen production bioreactor in the occurrence of sensor faults. Based on the bioreactor model in presence of perturbations, we design a residual generator based on a H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞ </sub> observer in order to: (i) detect the occurrence of sensor faults (ii) estimate the glucose and biomass concentrations, and (iii) attenuate the influence of the unknown glucose input and parametric uncertainties. The design conditions, depending only on a gain matrix, can be easily transformed in a semi-definite optimization problem under linear matrix inequalities. The features of the proposed observer are assessed by numerical simulations.

Backstepping sliding-mode control of stratospheric airships using disturbance-observer

In the presence of unknown disturbances and model parameter uncertainties, this paper develop a nonlinear backstepping sliding-mode controller (BSMC) for trajectory tracking control of a stratospheric airship using a disturbance-observer (DO). Compared with the conventional sliding mode surface (SMS) constructed by a linear combination of the errors, the new SMS manifold is selected as the last back-step error to improve independence of the adjustment of the controller gains. Furthermore, a nonlinear disturbance-observer is designed to process unknown disturbance inputs and improve the BSMC performances. The closed-loop system of trajectory tracking control plant is proved to be globally asymptotically stable by using Lyapunov theory. By comparing with traditional backstepping control and SMC design, the results obtained demonstrate the capacity of the airship to execute a realistic trajectory tracking mission, even in the presence of unknown disturbances, and aerodynamic coefficient uncertainties.

Robust Output Feedback Control for Input-Saturated Systems Based on a Sliding Mode Observer

This paper designs a robust output feedback controller for input-saturated systems with parametric uncertainties and external disturbances based on the parametric Riccati equation and the sliding mode observer. The stability of the closed-loop system is ensured by the designed controller. The main advantages of the approach proposed in this paper are as follows: (a) the designed sliding mode observer can estimate unknown external disturbances and parametric uncertainties; (b) the designed output feedback controller can increase the state convergence speed; and (c) the control gain can be obtained from the solution of the parametric Riccati equation. The simulation results for a spacecraft rendezvous system illustrate the feasibility of the designed controller.

High-speed nonlinear model predictive control of an interleaved switching DC/DC-converter

This paper presents a high speed nonlinear model predictive control (MPC) strategy for (interleaved switching) buck-type DC/DC-converters. Compared to known MPC strategies the proposed approach allows for longer prediction horizons while keeping the calculation times in the range of a few µs. This is achieved by tailoring the MPC strategy to the efficient implementation on an FPGA, exploiting the inherent parallel computation capabilities of FPGAs. Moreover, the utilization of a numerically efficient envelope model in the MPC is an important building block to reach the desired fast calculation times. The MPC strategy systematically takes into account input and state constraints, features a high dynamic and accurate control performance, exhibits constant switching frequencies and enables an interleaved switching operation. The proposed MPC strategy is tested in detailed simulations and in hardware-in-the-loop (HIL) experiments. An accurate and fast closed-loop dynamics can be achieved, also with respect to unknown fast load variations and parameter uncertainties. It is finally shown that the proposed MPC strategy has the potential to outperform the control performance of existing state-of-the-art controllers for DC/DC-converters.

Barrier Lyapunov function-based adaptive asymptotic tracking of nonlinear systems with unknown virtual control coefficients

This paper is devoted to the adaptive asymptotic tracking control for a class of uncertain nonlinear systems with parametric uncertainties. The presence of unknown virtual control coefficients and full-state constraints makes the systems in question essentially different from those in the related works. By incorporating the lower bounds of virtual control coefficients into the barrier Lyapunov functions (BLFs), two adaptive backstepping control design schemes are proposed based on tuning function method, bound estimation approach and some smooth functions, which makes the controller powerful enough to compensate the unknown virtual control coefficients and parametric uncertainties. We also show that the overall control strategy achieves three objectives on system performance: (a) the asymptotic convergence with zero tracking error is ensured; (b) all signals in the closed-loop systems are bounded; and (c) the full-state constraints are not violated for all the time. Finally, the effectiveness of the proposed method is shown by simulation examples.

Finite-Time Adaptive Fault-Tolerant Control for a Class of Nonlinear Systems with Actuator Faults

This paper considers the problem of finite-time adaptive fault-tolerant control for a class of nonlinear systems with actuator faults. Based on the strict back-stepping method, the controllers and the corresponding adaptive update laws are designed in each step. Therefore, the effects of actuator faults and unknown parameter uncertainties on the system are effectively compensated. Furthermore, it is shown that tracking errors can converge to a small neighborhood of the origin in a finite-time, and all the closed-loop signals are bounded. Finally, simulation results are given to illustrate the efficiency of the proposed control scheme.

Adaptive control of space proximity missions with constrained relative states, faults and saturation

This paper studies a relative position and relative orientation control problem of close-range spacecraft proximity missions under control input saturation, actuator faults, relative state constraints, kinematic couplings, parametric uncertainties, and unknown external disturbances. The problem of control input saturation is handled with introducing the outputs of an augmented system into the controller, and relative state constraints are guaranteed by using barrier Lyapunov function in backstepping design. Actuator faults in dynamical model are compensated by element-wise adaptive estimations, while unknown dynamic couplings, parametric uncertainties, and unknown bounded disturbances are compensated by norm-wise adaptive estimations. Based on the developed adaptive nonlinear control strategy, relative motion states uniformly ultimately tend to small adjustable neighborhoods of zero, and if the initial relative states are constrained in the predefined ranges, then relative state constraints will never be violated. Simulation comparison validates the advantages of the control strategy.

A Modified Directional Flame Thermometer: Development, Calibration, and Uncertainty Quantification

Abstract The directional flame thermometer (DFT) is a robust device used to measure heat fluxes in harsh environments such as fire scenarios but is large when compared to other standard heat flux measurement devices. To better understand the uncertainties associated with heat flux measurements in these environments, a Bayesian framework is utilized to propagate uncertainties of both known and unknown parameters describing the thermal model of a modified, smaller DFT. Construction of the modified DFT is described along with a derivation of the thermal model used to predict the incident heat flux to its sensing surface. Parameters of the model are calibrated to data collected using a Schmidt–Boelter (SB) gauge with an accuracy of ±3% at incident heat fluxes of 5 kW/m2, 10 kW/m2, and 15 kW/m2. Markov Chain Monte Carlo simulations were used to obtain posterior distributions for the free parameters of the thermal model as well as the modeling uncertainty. The parameter calibration process produced values for the free parameters that were similar to those presented in the literature with relative uncertainties at 5 kW/m2, 10 kW/m2, and 15 kW/m2 of 17%, 9%, and 7%, respectively. The derived model produced root-mean-squared errors between the prediction and SB gauge output of 0.37, 0.77, and 1.13 kW/m2 for the 5, 10, and 15 kW/m2 cases, respectively, compared to 0.53, 1.12, and 1.66 kW/m2 for the energy storage method (ESM) described in ASTM E3057.

Adaptive Self-Regulation PID Control of Course-Keeping for Ships

Abstract To solve the nonlinear control problems of the unknown time-varying environmental disturbances and parametric uncertainties for ship course-keeping control, this paper presents an adaptive self-regulation PID (APID) scheme which can ensure the boundedness of all signals in the ship course-keeping control system by using the Lyapunov direct method. Compared with the traditional PID control scheme, the APID control scheme not only is independent of the model parameters and the unknown input, but also can regulate the gain of PID adaptively and resist time-varying disturbances well. Simulation results illustrate the effectiveness and the robustness of the proposed control scheme.

Adaptive disturbance observer for trajectory tracking control of underwater vehicles

Complex and highly coupled dynamics, time-variance, unpredictable disturbances and lack of knowledge of hydrodynamic parameters, complicate the control of underwater vehicles. This paper deals with the adaptive disturbance observer design for the robust trajectory tracking problem for underwater vehicles in presence of unknown external disturbances and parametric uncertainties. First, the dynamics of the vehicle is transformed into the so-called regular form. Then, based on the Extended State Observer technique and High Order Sliding Modes Control, a disturbance observer is proposed. Furthermore, the gains of the observer are automatically adjusted by the introduction of an adaption law. The stability of the whole controller/observer scheme is proven using Lyapunov’s arguments. The adaptive disturbance observer aims to improve the Backstepping and nonlinear PD controllers. Real-Time experiments demonstrate the effectiveness of the proposed algorithm for the trajectory tracking task under several scenarios.

Robust Excitation Force Estimation and Prediction for Wave Energy Converter M4 Based on Adaptive Sliding-Mode Observer

The wave excitation force estimation and prediction play an important role in improving the performance of causal and noncausal controllers for wave energy converters (WECs). This article proposes a robust adaptive sliding-mode observer (ASMO) to estimate the wave excitation force subject to unknown disturbances and parametric uncertainties for a multimotion multifloat WEC, called M4. Both the convergence time and the estimation error can be explicitly bounded within expected limits by tuning the ASMO parameters, which are essentially beneficial for causal controllers to maintain the control performance. A fixed-time convergent sliding variable is designed to drive the estimation error into a small region within a fixed time. Due to the adaptive law, the overall system is proven to be finite-time stable, which allows explicit formulations of the convergence time and the estimation error. Moreover, based on the wave force estimation by the ASMO, an improved auto-regressive (AR) model whose coefficients are updated by online training is developed to predict the wave excitation force. The prediction errors can also be explicitly estimated to achieve guaranteed control performance for the noncausal controller requiring future excitation force. From the comparison based on a realistic sea wave gathered from Cornwall, U.K., it can be found that compared with the conventional Kalman filter, the ASMO achieves a smaller steady-state estimation error and has satisfactory robustness performance against 30% model mismatch.

An adaptive control approach for semi-active suspension systems under unknown road disturbance input using hardware-in-the-loop simulation

This article presents an application of the adaptive control method to semi-active suspension systems in the presence of unknown disturbance and parametric uncertainty. Due to the technical difficulties such as time delay and sensor noise, the road disturbance is assumed to be unmeasured. To overcome this problem, an observer is designed to estimate the disturbance. It is considered that the road profile consists of a finite number of the sum of sinusoidal signals with unknown amplitudes, phases and frequencies. After the parametrization of the observer, the adaptive control approach is employed to attenuate the effect of the road-induced vibrations using a magnetorheological damper. It is proved that the closed-loop system is stable, despite the adverse road conditions. Finally, the performance of the controller is illustrated with a hardware-in-the-loop simulation in which the system is subjected to sinusoidal and random profile road excitations. To demonstrate the benefits of the adaptive controller, the results are presented in comparison with a conventional proportional integral derivative (PID) controller.

Active Disturbance Rejection Control for Wheeled Mobile Robots with Parametric Uncertainties

In this paper, an efficient controller design method is proposed based on active disturbance rejection control (ADRC) scheme for stabilization problem of wheeled mobile robots with parametric uncertainties, which can make the system converge quickly. By using the extended state observer (ESO), both the system states and the unknown parametric uncertainties could be estimated. In addition, the input-state scaling technique is used to transform the system into two decoupled subsystems. Based on the decoupled subsystems, a switching controller and ADRC are designed. Simulation results show that the proposed scheme can stabilize the wheeled mobile robot system asymptotically despite the presence of parametric uncertainties.

PDE modelling and vibration control of overhead crane bridge with unknown control directions and parametric uncertainties

In this study, problems of the partial differential equation (PDE) modelling and vibration control design are first resolved for an overhead crane bridge system, which is regarded as a Timoshenko beam with an attached rigid body. With the established infinite-dimensional PDE model, a Nussbaum function-based adaptive control approach is developed in order to settle out parametric uncertainties of the system with unknown control directions. Under the proposed control method, states of the overhead crane bridge are globally bounded and finally converge to an adjustable region of zero. The stability of the closed-loop overhead crane bridge system is analysed by employing Lyapunov's direct method. The effectiveness of the developed control strategy is verified through the simulation results.

Adaptive Robust Nonlinear Control Design for Course Tracking of Ships Subject to External Disturbances and Input Saturation

An adaptive robust control law is proposed for the course tracking problem of ships in this paper incorporating a Nussbaum function and an auxiliary dynamic system into the adaptive dynamic surface control (DSC) technique. The ship steering dynamics is described by the Norrbin nonlinear model with completely unknown control coefficient, parameter uncertainties, and unknown external disturbances and input saturation caused by the rudder constraint. The Nussbaum function is adopted to deal with completely unknown control coefficient and avoid the controller singularity problem. An auxiliary dynamic system is introduced to handle the effect of input saturation. The DSC technique makes the control law be simple to compute and easy to implement in engineering practice. It is proved that the proposed course tracking control law of ships makes the course tracking error be arbitrarily small by an appropriate choice of the design parameters and guarantees the uniform ultimate boundedness of all signals in the closed-loop ship course control system. Finally, simulation results on two ships and simulation comparison with an existing adaptive neural control scheme demonstrate the effectiveness and the superiority of the proposed control scheme.

Adaptive Finite-Time 6-DOF Tracking Control for Spacecraft Fly Around With Input Saturation and State Constraints

An adaptive finite-time control scheme is developed for noncooperative spacecraft fly-around subject to input saturation, full-state constraints, dynamic couplings, parameter uncertainties, and disturbances. Different from traditional fly-around model based on C–W equation, the derived 6-DOF spacecraft fly-around model can be suitable for noncooperative case in close proximity. By using the backstepping control technique, an integrated adaptive finite-time control law is designed, in which the tan-type barrier Lyapunov function (BLF) is incorporated to handle the full-state constraints. Meanwhile, the unknown dynamic couplings, parameter uncertainties, and disturbances are attenuated effectively by using adaptive estimation technique and the adverse effects raised from input saturation are reduced by the designed saturation compensator. Based on the constructed BLF, it is shown that the designed adaptive finite-time controller can guarantee that full-state constraints are not breached, but also can drive relative position and attitude tracking errors into the accurate convergent regions with finite-time convergence. Finally, the performance and advantage of the designed adaptive finite-time control scheme are demonstrated by numerical simulations.

Weighted multiple model adaptive boundary control for a flexible manipulator.

In this article, a weighted multiple model adaptive boundary control scheme is proposed for a flexible manipulator with unknown large parameter uncertainties. First, the uncertainties are approximatively covered by a finite number of constant models. Second, based on Euler-Bernoulli beam theory and Hamilton principle, the distributed parameter model of the flexible manipulator is constructed in terms of partial differential equation for each local constant model. Correspondingly, local boundary controllers are designed to control the manipulator movement and suppress its vibration for each partial differential equation model, which are based on Lyapunov stability theory. Then, a novel weighted multiple model adaptive control strategy is developed based on an improved weighting algorithm. The stability of the overall closed-loop system is ensured by virtual equivalent system theory. Finally, numerical simulations are provided to illustrate the feasibility and effectiveness of the proposed control strategy.

Adaptive Pitch Control of Variable-Pitch PMSG Based Wind Turbine

This paper presents an adaptive pitch-angle control approach for a permanent magnet-synchronous generator-based wind turbine (PMSG-WT) connecting with a power grid to limit extracted power above the rated wind speed. In the proposed control approach, a designed perturbation observer is employed for estimating and compensating unknown parameter uncertainties, system nonlinearities, and unknown disturbances. The proposed control approach does not require full state measurements or the accurate system model. Simulation tests verify the effectiveness of the proposed control approach. The simulation results demonstrate that compared with the feedback linearizing controller, conventional vector controller with proportional-integral (PI) loops, and PI controller with gain scheduling, the proposed control approach can always maintain the extracted wind power around rated power, and has higher performance and robustness against disturbance and parameter uncertainties.

An innovative optimal RPO-FOSMC based on multi-objective grasshopper optimization algorithm for DFIG-based wind turbine to augment MPPT and FRT capabilities

Abstract Doubly Fed Induction Generator (DFIG) with consideration of its exceptional capabilities, i.e.: variable speed operation, low mechanical stresses, and excellent power quality in limited-range speed applications is a famous kind of wind turbines. Even so, there is a challenge due to its nonlinear dynamic features and several uncertainties like unknown non-linear disturbances and parameter uncertainties. Hence, this paper proposes a novel Robust Perturbation Observer based Fractional Order Sliding Mode Controller (RPO-FOSMC) for DFIG to extract the maximum power and improve the Fault Ride-Through (FRT) capability. The strong nonlinear aerodynamics of wind turbine, the uncertain dynamic parameters of induction generator and the stochastic characteristics of wind waves are constructed in perturbation term which is estimated using the proposed RPO-FOSMC. Accordingly, the perturbation compensator provides an appropriate robustness concerning different uncertain models and attains an exceptional control capability during stochastic wind waves. Considering the inherent multi-objective nature of the nonlinear control design problem, Multi-Objective Grasshopper Optimization Algorithm (MOGOA) has been implemented to augment the robustness and dynamic performance of RPO-FOSMC. Three distinct conditions are considered to compare and analyse the fast and robust dynamic performance of optimal RPO-FOSMC against other conventional approaches. Eventually, the comprehensive simulation results have revealed and validated the exceptional dynamic capability of the suggested control strategy.