Robust Control Method Research Articles

Event-Triggered Neural Network Control for Uncertain Nonlinear Systems Without State Observer

A robust approximation-based event-triggered control method is presented for single input single output (SISO) nonlinear continuous-time systems with unmeasurable states and external disturbance. In the whole system, just one neural network (NN) is designed to approximate the unknown part in the controller, and output errors are directly used to construct the system controller and event-triggered mechanism to relieve the burden of system communication. The controller with a simple structure is easier to be realized in practical engineering. The system control signals and adaptive parameters are updated only if the event trigger condition is met, and this way further reduces the waste of network resources caused by frequent system sampling. The application of stability theory of Lyapunov proves that the weight estimation of the NN and tracking errors are ultimate and uniform boundedness, and the efficacy of the proposed scheme is verified with numerical results on a robot.

Error model-oriented vibration suppression control of free-floating space robot with flexible joints based on adaptive neural network

At the same time, considering the uncertain factors such as load variation, external interference and joint flexibility in engineering practice, a robust control method based on adaptive neural network is proposed. The dynamic model of free-floating space robot is established, and the error model caused by uncertain factors is deduced. Different from the traditional compensation algorithm that ignores the error model, a compensation controller based on Radial basis function neural network (RBFNN) is designed to approximate the error model. The approximation error is eliminated by robust controller to improve the control accuracy. In order to make full use of the nonlinear approximation ability of neural network, the error model is decomposed into four parts according to the input characteristics, and the neural network compensator is designed for separate and overall compensation, which further improves the control accuracy and robustness. The adaptive learning rates of network weights are designed to ensure online real-time adjustment without offline learning stage. A flexible compensator based on torque and a controller based on moment difference feedback controller (MDFC) are designed to suppress elastic vibration. Simulation and experimental studies show that the proposed strategy can have good compensation performance and robustness, and can better suppress elastic vibration, which proves the effectiveness and superiority of the proposed scheme.

Robust pose tracking control for a fully-actuated hexarotor UAV based on Gaussian processes

This paper presents a robust position/attitude tracking control method for a fully-actuated hexarotor unmanned aerial vehicle (UAV) based on Gaussian processes. Multirotor UAVs suffer from modelling errors due to their structure complexity and aerodynamical disturbances whose perfect mathematical formulation is intractable. To handle this issue, this paper incorporates a data-based learning technique with model-based control. The hexarotor UAV dynamical model, considering modelling errors and aerodynamic disturbances as unknown dynamics, is first derived. Gaussian process regression is next introduced as a learning method for the unknown dynamics, which provides probabilistic distributions of the predicted values. The predicted means are regarded as deterministic information and cancelled out by feedforward control inputs. The predicted variances are considered as the bounds of the model uncertainties with high probability, and a robust control method to ensure ultimate boundedness of the tracking control error is proposed for the uncertain system. The effectiveness of the proposed method is demonstrated via experiments with a self-developed hexarotor UAV testbed.

Frequency Response and Transfer Functions of Large Self-Similar Networks

Abstract Large-scale dynamical systems, no matter whether possessing interconnected appearances, are frequently modeled as networks. For instance, graphs, multi-agent systems, and materials' intricate behaviors are often treated as networked dynamical systems. However, only a few studies have approached the problem in the frequency domain, mostly due to the complexity of evaluating their frequency response. That gap is filled by this paper, which proposes algorithms computing a general class of self-similar networks' frequency response and transfer functions, no matter they are finite or infinite, damaged or undamaged. In addition, this paper shows that for infinite self-similar networks, even when they are damaged, fractional-order and irrational dynamics naturally come into sight. Most importantly, this paper illustrates that for a network under different operating conditions, its frequency response would form a set of neighboring plants, which sets the basis of applying robust control methods to dynamic networks.

Model‐based robust control design and experimental validation of collaborative industrial robot system with uncertainty

AbstractBased on the traditional PID control and robust control algorithm, a novel practical robust control method is designed for the 6‐DOF collaborative industrial robot with uncertainty. The proposed algorithm consists of a robust term and a model‐based PD control term, which we call MPDP controller. It is demonstrated by Lyapunov theoretical analysis that the algorithm is able to guarantee uniform boundedness and uniform ultimate boundedness of the system. Simulations and experiments show the good performance of MPDP control in a robot with smaller steady‐state tracking errors and better robustness compared to PID controllers.

Finite-time sliding mode control of underwater vehicles in 3D space

In this paper, trajectory tracking control of an underwater vehicle in three-dimensional (3D) space has been addressed. The assumed underwater vehicle has 6 degrees of freedom and the aim is to control all system rotations and displacements. In this paper, a finite-time sliding mode controller as a robust control method is proposed for an underwater vehicle with 6 degrees of freedom in 3D space using the method without simplifications or decouplings. Therefore, both system positions and orientations are controlled in the presence of disturbances and uncertainties. In previous research works, control of two-dimensional underwater vehicles is commonly studied. In this paper, a novel stable control algorithm is proposed for an underwater vehicle with 6 degrees of freedom. The stability of the closed-loop system is analyzed using the Lyapunov theory. The designed algorithm can cover 3D complicated tasks. Also, the designed algorithm as a robust control approach can attenuate external disturbances. The performance and stability of this approach are compared with the sliding mode controller. The numerical comparison results show that the proposed approach is effective and applicable in practice.

Nonlinear model predictive control of USC boiler-turbine power units in flexible operations via input convex neural network

Coordinated control of an ultra-supercritical (USC) boiler-turbine unit in the flexible-operation mode is challenging because of internal nonlinearity, various unknown disturbances, and the strong-coupled multivariable behavior of the unit. A novel nonlinear model predictive control (NMPC) approach is proposed to improve the flexibility of the USC unit, which introduces an input convex neural network (ICNN) to model the dynamics of the USC unit, and then computes the optimal control decisions by solving a convex model predictive control problem. Simulations are conducted on a 1000 MW USC boiler-turbine unit. The results demonstrate that the ICNN exhibits equivalent performance to a conventional neural network in learning the system dynamics. The root mean square errors of the throttle steam pressure, the separator steam enthalpy, and the power are 0.003 MPa, 0.162 kJ/kg, and 0.513 MW, respectively. In load tracking and disturbance rejection simulations, the proposed ICNN-based NMPC outperforms the linear model predictive control and conventional neural network-based NMPC. The ICNN-based NMPC provides a fast and stable load tracking capacity at a ramp rate of 10.8% MCR/min. Moreover, the superiority of the proposed approach is further confirmed by comparison with the internal-model robust adaptive control method, which is a state-of-the-art method. The proposed approach has good potential to improve the operational flexibility of USC power units.

Robust Trajectory Tracking Control for Continuous-Time Nonlinear Systems with State Constraints and Uncertain Disturbances.

In this paper, a robust trajectory tracking control method with state constraints and uncertain disturbances on the ground of adaptive dynamic programming (ADP) is proposed for nonlinear systems. Firstly, the augmented system consists of the tracking error and the reference trajectory, and the tracking control problems with uncertain disturbances is described as the problem of robust control adjustment. In addition, considering the nominal system of the augmented system, the guaranteed cost tracking control problem is transformed into the optimal control problem by using the discount coefficient in the nominal system. A new safe Hamilton–Jacobi–Bellman (HJB) equation is proposed by combining the cost function with the control barrier function (CBF), so that the behavior of violating the safety regulations for the system states will be punished. In order to solve the new safe HJB equation, a critic neural network (NN) is used to approximate the solution of the safe HJB equation. According to the Lyapunov stability theory, in the case of state constraints and uncertain disturbances, the system states and the parameters of the critic neural network are guaranteed to be uniformly ultimately bounded (UUB). At the end of this paper, the feasibility of the proposed method is verified by a simulation example.

Operational Space Iterative Learning Control of Coupled Active/Passive Multilink Cable-Driven Hyper-Redundant Robots

Abstract The operational space control (OSC) of multilink cable-driven hyper-redundant robots (MCDHRs) is required to perform tasks in many applications. As a new coupled active-passive (CAP) MCDHR system, due to the multiple couplings between the active cables, the passive cables, the joints, and the end-effector, the OSC becomes more and more complicated. However, there is currently no robust and effective control method to solve the OSC problem of such types MCDHRs. In this paper, an OSC framework of CAP-MCDHRs using a dynamics-based iterative-learning-control (ILC) method is proposed, considering multivariate optimization. First, the multi-coupling kinematics and the series-parallel coupling dynamics equation (i.e., cable-joint-end) of the CAP-MCDHR are derived. Then, a dynamics-based trajectory tracking framework was constructed. Moreover, an OSC accuracy evaluation model based on a high-precision laser tracker was also designed. The framework allows the tracking of operational space trajectories (OSTs) online with the feasible cable tension and the joint angle. It is also shown that the tracking performance can be improved through the ILC when the desired trajectory is repeatedly performed. Finally, a simulation and an experimental hardware system are built. The results show that the proposed control framework can be easily and effectively applied to the CAP-MCDHR used in real-time.

A novel robust output-based control approach via adaptive event-triggered scheme

This paper proposes a new robust output-feedback adaptive event-triggered control (AETC) method for linear systems with parametric uncertainties. The proposed event-triggered mechanism (ETM) is obtained based on the [Formula: see text] stability condition. In this paper, two design approaches are presented, the emulation approach (pre-designed control gain) and the co-design approach. In the latter, the event-triggering law and the output-feedback controller are designed simultaneously to have a more efficient control system. The proposed adaptive event-triggered mechanism (AETM) in both approaches leads to an increase in the average of inter-event times based on linear matrix inequalities (LMIs). Consequently, in the proposed methods, the stability of the event-based system is ensured, the Zeno phenomenon is avoided, the feasibility margin and the quality of the response are well maintained, and the number of samplings is reduced, considerably. Finally, to indicate the capability of the proposed methods, two numerical simulations are presented.

Improved model-free fractional-order intelligent proportional–integral fractional-order sliding mode control with anti-windup compensator

In addition to the difficulty of system modeling, every physical system faces actuator saturation, making the real control different from the controller output (desired control input). When this occurs, the controller output does not regulate the system properly and errors occur as a result of incorrect updating. This is known as the windup phenomenon. In the event that the controller is configured to override actuator saturation, it can lead to a failure in the controller’s performance, such as large overshoots, high response time, and even system instability in the worst case. Therefore, in this paper, a new robust model-free controller method is proposed. It is a combination of four nonlinear control techniques, namely model-free controller, fractional-order sliding mode controller, fractional integral–proportional (PI) controller, and anti-windup compensator, which gives rise to the new model-free controller algorithm called hybrid fractional-order intelligent PI fractional sliding mode controller with an anti-windup compensator termed (MF-FOiPI-FOSMC-AW). However, to illustrate the effectiveness of the new proposed MF-FOiPI-FOSMC-AW method, simulation and experimental results compared to classical PI and iPI controllers (with and without an anti-windup compensator) on a hydraulic system are presented in the presence or absence of external disturbances for different types of references. Finally, simulation is conducted through an experimental comparison of the proposed approach with other strategies such as the classical anti-windup PI controller and the anti-windup intelligent PI controller, which is carried out for this purpose.

Robust Control Strategies for Microgrids: A Review

Microgrids consisting of photovoltaic (PV) power plants and wind farms have been widely accepted in power systems for reliability enhancement and power loss reduction. Microgrids are capable of providing voltage and frequency support, improving power quality, and achieving proper power-sharing. To achieve such goals and deal with the nonlinear behavior in such systems, appropriate robust control strategies are required to be adopted. This article presents a comprehensive review of robust control methods for microgrids, including AC, DC, and hybrid microgrids, with different topologies and different types of interconnection to conventional power systems based on recently published research studies. The main control objectives, along with proposed control methods, are comparatively discussed for different types of microgrids. Furthermore, several research gaps in this area related to the scalability, robustness assessment, and evaluation approach are discussed. Recommendations are made that can potentially open new research lines to enhance the effectiveness of robust controllers for AC, DC, and hybrid microgrids.

Robust Control Method of Grid-Connected Inverters With Enhanced Current Quality While Connected to a Weak Power Grid

In order to improve the robust stability of the grid-connected inverter of wind power or photovoltaic power generation while connected to a weak power-grid, the robust model of grid-connected inverter under weak power-grid is established, and the influence mechanism of power-grid impedance and voltage distortion on the stability and current quality of grid-connected inverter is analyzed. On this basis, an adaptive robust <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H_∞</i> control method is proposed, in which there is no need to online measure the power-grid impedance, and the control parameters do not change with the change of the power-grid impedance. Then, the calculation method of each reference quantity and the design method of control parameters are introduced. Finally, an experimental platform is built, and the correctness and effectiveness of the theoretical analysis and the proposed control method are verified by experiments. Compared with other control methods, the adaptive robust <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H_∞</i> control method realizes the stability of the system when the power-grid impedance varies in a wide range, which optimally restrains the power-grid voltage distortion and improves the quality of grid-connected current.

Robust observable control of open and closed quantum systems

In recent work, we introduced the asymptotic theory of quantum robust control, which enables control of moments of quantum observables and gates in the presence of Hamiltonian uncertainty or field noise. In this paper, we extend this theory of quantum robust control to encompass two of the most important generalizations: robust control of arbitrary quantum observables and robust control of quantum systems sustaining environmental decoherence. In addition, we present deterministic Pareto optimization algorithms that can be applied in conjunction with either asymptotic or leading order measures of robustness. This enables robust control of any observable in quantum systems with any initial density matrix, and for which the entropy can change arbitrarily during the time evolution. Methods for robust optimal control of open quantum systems are presented that maximize the expected value of a quantum control objective while minimizing the expected environmentally induced decoherence.

Stability analysis of doubly-fed wind generation systems under weak power grid based on virtual synchronous control combined with adaptive robust control

Doubly-fed induction generator (DFIG) of wind generation system is generally located at the end of the distribution power-grid. Under the weak power grid, the grid connection of wind turbines is unstable, and the current quality is poor. Based on DFIG output impedance model, a stability analysis method combined with adaptive control method is proposed in this paper. The DFIG impedance model with power outer-loop is derived based on the virtual synchronous control of DFIG by using adaptive robust control method. Using generalized Nyquist criterion, the impacts of different power grid conditions and control parameters on the system stable operation under virtual synchronous control are analyzed and verified. The proposed control method in this paper is verified by experiments. The proposed control method improves the quality of grid-connected current.

Secure tracking control against sensor and actuator attacks: A robust model-reference adaptive control method

This paper is concerned with secure tracking control problems for cyber-physical systems subjected to a class of sensor and actuator attacks via the model-reference control techniques. The considered attack signals are the unknown bounded signals generated from any linear or nonlinear finite-L2-gain exogenous dynamical system. The auxiliary outputs produced from a high-gain approximate differentiator are first used in co-design for the inputs of the systems and introduced filter, so that the matching condition on the system input and output matrices in the existing results is relaxed. Furthermore, with the aid of the auxiliary outputs, attack’s property and small-gain control methods, a novel model-reference controller with a robust adaptive attack compensator is proposed, such that (a) the tracking error converges to a small set around zero where the set bound can be adjusted by the design parameters, and (b) the desired disturbance attenuation performance is obtained. Different from the existing results, the developed one not only compensates the effect of the attacks automatically by online adjusting the adaptive parameter, but also improves the robustness against the attacks efficiently. Finally, the developed method is validated by a simulation example.

Temperature targets, deep uncertainty and extreme events in the design of optimal climate policy

We study optimal climate policy consistent with the constraint that average global temperature remains below 1.5 ∘ C relative to pre-industrial levels. We consider a holistic representation of uncertainty including traditional risk, deep uncertainty and stochastic arrivals of climate-related disasters. Using robust control methods, we derive optimal emission and carbon tax paths and calculate when temperature exceeds the target in the absence of the constraint. We show that policy under deep uncertainty requires strong action now relative to pure risk but the policy stringency is reversed later. Preliminary estimates suggest that the COVID-19 impact on attainment of the temperature target is negligible.

Design of gain-scheduling cascade control for a motion compensated gripper frame

The offshore wind market is growing, resulting in larger wind turbines being installed farther away from the coast and into deeper waters. This trend brings challenges to an industry strongly depending on the use of jack-up vessels. A floating vessel equipped with a Dynamic Positioning (DP) system and a Motion Compensated Gripper Frame (MCGF) provides a more efficient solution to guide XXL monopoles during the installation phase. According to strict regulations, the offset angle of monopiles shall not be over 0.25°. To ensure this, a robust control method is required to deal with gradual change in soil stifness, wave induced motions and sensor delays. The control force exerted by the gripper frame can significantly affect the floating vessel dynamics, hence, this should be optimized.Therefore, the research goal is to analyse the system and design a robustly stable control for the MCGF. In the context of this research, cascade PID control with gain-scheduling is chosen, which is able to control the Gripper Frame during all installation steps for different soil stiffness and to reject wave disturbances.With the use of the lumped multiplicative uncertainty structure, the changing and uncertain soil-characteristics are modelled. The sensor delay to measure the monopile inclination, has a significant impact on system stability. Robust stability criteria are validated using the Nyquist criterion and by analysing the system’s closed-loop poles. With the use of gain-scheduling it is possible to switch control settings during the installation. Time-domain results show that with this design approach the installation criteria are met such as the maximum monopile angle and the applied control force.Ultimately, it is shown that robust PID control with gain-scheduling for a MCGF can ensure safe, efficient and cost-effective installation of the next generation wind turbines. Future research should focus into the definition and implementation of the gain-scheduling switching criteria.

Robust Predictive Stator Current Control Based on Prediction Error Compensation for a Doubly Fed Induction Generator Under Nonideal Grids

Traditional model-based predictive current control (MBPCC) for a doubly fed induction generator (DFIG) is easily affected by machine parameter variations. Recently, a model-free predictive current control (MFPCC) was proposed to enhance the parameter robustness of DFIG systems by using the past current difference to predict the future current difference under the same switching state. However, this approach has the problems of high sampling frequency, variable switching frequency, and high steady ripples. To solve these problems, this article proposes a robust predictive stator current control (RPCC) method for DFIGs. Different from the prior MFPCC, the current error between the measured value and the predicted value is not only used in the stage of the stator current prediction, but also in the calculation of rotor voltage vector. Hence, the performance deterioration caused by machine parameter variations is significantly alleviated. Furthermore, a support vector machine can be combined with the proposed RPCC. In this way, the proposed method ensures strong parameter robustness and small steady-state power ripples. Finally, by recalculating the current reference value, the method can also achieve a good performance even under nonideal grids. The proposed RPCC is compared with MBPCC and MFPCC and its effectiveness is confirmed by the presented simulation and experimental results.

Metric Learning for Robust Gait Phase Recognition for a Lower Limb Exoskeleton Robot Based on sEMG

This study aims to develop a robust myoelectric control method for gait phase recognition in a lower-limb exoskeleton robot. In the proposed method, a metric learning-based temporal convolution network (ML-TCN) was utilized to extract discriminative features of the surface electromyography (sEMG) signals and recognize four gait phases: heel strike (HS), foot flat (FF), heel off (HO), and swing (SW). Vicon validated the effectiveness of the sEMG data-acquisition system. The proposed method acquires significantly more discriminative features than long short-term memory (LSTM) or common temporal convolutional network (TCN). The experimental results show that the proposed model has a higher prediction accuracy and stronger robustness against disturbances in complex terrain. Finally, under the complex terrain of level ground-ramp ascending-ramp descending walking, the proposed model’s accuracy of gait phase recognition is 96.22%, which is better than LSTM’s 91.20%. Noise disturbances of 10%, 20%, 30%, 40%, and 50% were added to the test set. Compared with LSTM, the resistance to disturbances of the proposed method increased by 8.15%, 8.79%, 9.67%, 10.6%, and 10.61%, respectively.