Robust control of uncertain fully actuated systems with nonlinear uncertainties and perturbed input matrices.

Robust control of uncertain fully actuated systems (FASs) with nonlinear uncertainties and perturbed input matrices is considered. Motivated by the recent work on this issue, two novel robust controllers are further developed for two cases under different assumptions. For both cases, the assumption on the perturbation input matrix in the previous work is relaxed to a significant extent, which allows many typical perturbation input matrices, such as constant ones, to be handled, while the previous method cannot. Moreover, for the first case, the assumption on the system uncertainty is further relaxed, and the states of the closed-loop system are globally bounded and converge into an arbitrarily small spherical domain centered at the origin. For the second case, with another requirement on the system nonlinearity imposed, the global exponential stability of the closed-loop system is achieved. The successful application in an electromechanical system verifies the effectiveness of the method.

Robust control of electrohydraulic soft robots.

This article introduces a model-based robust control framework for electrohydraulic soft robots. The methods presented herein exploit linear system control theory as it applies to a nonlinear soft robotic system. We employ dynamic mode decomposition with control (DMDc) to create appropriate linear models from real-world measurements. We build on the theory by developing linear models in various operational regions of the system to result in a collection of linear plants used in uncertainty analysis. To complement the uncertainty analyses, we utilize H ∞ ("H Infinity") synthesis techniques to determine an optimal controller to meet performance requirements for the nominal plant. Following this methodology, we demonstrate robust control over a multi-input multi-output (MIMO) hydraulically amplified self-healing electrostatic (HASEL)-actuated system. The simplifications in the proposed framework help address the inherent uncertainties and complexities of compliant robots, providing a flexible approach for real-time control of soft robotic systems in real-world applications.

Nonlinear adaptive robust control of tank bidirectional stabilizers with dead zone compensation based on extended state observer.

In this paper, the problem of highly performance motion control of tank bidirectional stabilizer with dead zone nonlinearity and uncertain nonlinearity is addressed. First, the electromechanical coupling dynamics model of bidirectional stabilizer is developed finely. Second, the dead zone nonlinearity in bidirectional stabilizer is characterized as the combination of an uncertain time-varying gain and a bounded disturbance term. Meanwhile, an adaptive robust controller with dead zone compensation is proposed by organically combining adaptive technique and extended state observer (ESO) through backstepping method. The adaptive technique is employed to reduce the impact of unknown system parameter and dead zone parameter. Furthermore, the ESO is constructed to compensate the lumped uncertainties including unmodeled dynamics and dead zone residual, and integrated together via a feedforward cancellation technique. Moreover, the adaptive robust control law is derived to ensure final global stability. In stability analysis, the asymptotic tracking performance of the proposed controller can be guaranteed as the uncertainty nonlinearities in tank bidirectional stabilizer are constant. It is also guaranteed to achieve bounded tracking performance when time-varying uncertainties exist. Extensive co-simulation and experimental results verify the superiority of the proposed strategy.

Adaptive Disturbance Suppression Method for Servo Systems Based on State Equalizer.

Disturbances in the aviation environment can compromise the stability of the aviation optoelectronic stabilization platform. Traditional methods, such as the proportional integral adaptive robust (PI + ARC) control algorithm, face a challenge: once high-frequency disturbances are introduced, their effectiveness is constrained by the control system's bandwidth, preventing further stability enhancement. A state equalizer speed closed-loop control algorithm is proposed, which combines proportional integral adaptive robustness with state equalizer (PI + ARC + State equalizer) control algorithm. This new control structure can suppress high-frequency disturbances caused by mechanical resonance, improve the bandwidth of the control system, and further achieve fast convergence and stability of the PI + ARC algorithm. Experimental results indicate that, in comparison to the control algorithm of PI + ARC, the inclusion of a state equalizer speed closed-loop compensation in the model significantly increases the closed-loop bandwidth by 47.6%, significantly enhances the control system's resistance to disturbances, and exhibits robustness in the face of variations in the model parameters and feedback sensors of the control object. In summary, integrating a state equalizer speed closed-loop with PI + ARC significantly enhances the suppression of high-frequency disturbances and the performance of control systems.

Fractional-Order Robust Control Design under parametric uncertain approach.

This paper presents a novel methodology that combines fractional-order control theory with robust control under a parametric uncertainty approach to enhance the performance of linear time-invariant uncertain systems with integer or fractional order, referred to as Fractional-Order Robust Control (FORC). In contrast to traditional approaches, the proposed methodology introduces a novel formulation of inequalities-based design, thus expanding the potential for discovering improved solutions through linear programming optimization. As a result, fractional order controllers are designed to guarantee desired transient and steady-state performance in a closed-loop system. To enable the digital implementation of the designed controller, an impulse response invariant discretization of fractional-order differentiators (IRID-FOD) is employed to approximate the fractional-order controllers to an integer-order transfer function. Additionally, Hankel's reduction order method is applied, thus making it suitable for hardware deployment. Experimental tests carried out in a thermal system and the assessment results, based on time-domain responses and robustness analysis supported by performance indices and set value analysis in a thermal system test-bed, demonstrate the improved and robust performance of the proposed FORC methodology compared to classical robust control under parametric uncertainty.

Energy-water management system based on robust predictive control for open-field cultivation.

Food availability has been endangered by recent global events, where agriculture, the main food source for the global population, is expected to increase even more to fulfill the growing food demand. Along with food production, water and energy consumption are also increased, leading to over-extraction of groundwater and an excess emission of greenhouse gases due to fossil fuel consumption. In this context, a balance of these three resources is crucial; therefore, the water-energy-food nexus is considered to address the previous issues by designing an energy-water management system based on robust predictive control. This controller estimates the future worst-case scenario for multiple climatic conditions, such as solar radiation, ambient temperature, wind speed, precipitation, and groundwater recharge, to define an optimal irrigation volume, maximize crop growth, and minimize water consumption. At the same time, the controller schedules daily irrigation and groundwater extraction, considering energy availability from solar generation and storage, to fulfill the previously defined irrigation volume while minimizing operating costs. Climate prediction is done through fuzzy prediction intervals, whose lower or upper bound are used as worst-case to include climate uncertainty on the controller design. The energy-water management system is tested in different experiments, where results show that considering a robust approach ensures maximum crop development, avoids over-extraction of groundwater, and prioritizes renewable energy sources. This work proposes a robust energy-water management system designed to be sustainable. Considering the water-energy-food nexus, the system ensures food security and proper resource allocation, tackling global starvation, water availability, and energy access.

Robust adaptive deep brain stimulation control of in-silico non-stationary Parkinsonian neural oscillatory dynamics.

Objective. Closed-loop deep brain stimulation (DBS) is a promising therapy for Parkinson's disease (PD) that works by adjusting DBS patterns in real time from the guidance of feedback neural activity. Current closed-loop DBS mainly uses threshold-crossing on-off controllers or linear time-invariant (LTI) controllers to regulate the basal ganglia (BG) Parkinsonian beta band oscillation power. However, the critical cortex-BG-thalamus network dynamics underlying PD are nonlinear, non-stationary, and noisy, hindering accurate and robust control of Parkinsonian neural oscillatory dynamics.Approach. Here, we develop a new robust adaptive closed-loop DBS method for regulating the Parkinsonian beta oscillatory dynamics of the cortex-BG-thalamus network. We first build an adaptive state-space model to quantify the dynamic, nonlinear, and non-stationary neural activity. We then construct an adaptive estimator to track the nonlinearity and non-stationarity in real time. We next design a robust controller to automatically determine the DBS frequency based on the estimated Parkinsonian neural state while reducing the system's sensitivity to high-frequency noise. We adopt and tune a biophysical cortex-BG-thalamus network model as an in-silico simulation testbed to generate nonlinear and non-stationary Parkinsonian neural dynamics for evaluating DBS methods.Main results. We find that under different nonlinear and non-stationary neural dynamics, our robust adaptive DBS method achieved accurate regulation of the BG Parkinsonian beta band oscillation power with small control error, bias, and deviation. Moreover, the accurate regulation generalizes across different therapeutic targets and consistently outperforms current on-off and LTI DBS methods.Significance. These results have implications for future designs of closed-loop DBS systems to treat PD.

A generalized Udwadia-Kalaba control design for uncertain belt conveyor systems with inequality constraints.

Uncertainty can lead to jitter or overshoot in mechanical systems, necessitating the design of multiple constraints to stabilize them. This paper proposes a control structure based on the generalized Udwadia-Kalaba equation to address these constraints simultaneously. An uncertain dynamical model is developed, incorporating both equality and inequality constraints. By integrating diffeomorphism theory, a robust control strategy is designed to ensure compliance with these constraints. Utilizing the Lyapunov approach, the uniform boundedness and uniform ultimate boundedness of the dynamical system are demonstrated. Finally, the feasibility of the proposed control method is validated through its application to a belt conveyor system.

Piezoelectric Actuators in Smart Engineering Structures Using Robust Control.

In this study, piezoelectric patches are used as actuators to dampen structural oscillations. Damping oscillations is a significant engineering challenge, and the use of piezoelectric patches in smart structures allows for a reduction in oscillations through sophisticated control methods. This analysis involved H-infinity (H∞) robust analysis. H∞ (H-infinity) control formulation is a robust control design method used to ensure system stability and performance under disturbances. When applied to piezoelectric actuators in smart structures, H∞ control aims to design controllers that are robust to variations in system dynamics, external disturbances, and modeling uncertainties, while meeting specified performance criteria. This study outlines the piezoelectric effects and advanced control strategies. A structural model was created using finite elements, and a smart structural model was analyzed. Subsequently, dynamic loads were applied and oscillation damping was successfully achieved by employing advanced control techniques.

Fast and accurate tracking control of robotic manipulators subject to state constraints and input saturation by effectively integrating planning strategies.

This paper presents a two-loop control framework for robotic manipulator systems subject to state constraints and input saturation, which effectively integrates planning and control strategies. Namely, a stability controller is designed in the inner loop to address uncertainties and nonlinearities; an optimization-based generator is constructed in the outer loop to ensure that state and input constraints are obeyed while concurrently minimizing the convergence time. Furthermore, to dramatically the computational burden, the optimization-based generator in the outer loop is switched to a direct model-based generator when the tracking errors are sufficiently small. In this way, both a high tracking accuracy and fast dynamic response are obtained for constrained robotic manipulator systems with considerably lower computational burden. The superiority and effectiveness of the proposed structure are illustrated through comparative simulations and experiments.

Adaptive fuzzy control for tendon-sheath actuated bending-tip system with unknown friction for robotic flexible endoscope.

Introduction: The tendon-sheath actuated bending-tip system (TAB) has been widely applied to long-distance transmission scenes due to its high maneuverability, safety, and compliance, such as in exoskeleton robots, rescue robots, and surgical robots design. Due to the suitability of operation in a narrow or tortuous environment, TAB has demonstrated great application potential in the area of minimally invasive surgery. However, TAB involves highly non-linear behavior due to hysteresis, creepage, and non-linear friction existing on the tendon routing, which is an enormous challenge for accurate control. Methods: Considering the difficulties in the precise modeling of non-linearity friction, this paper proposes a novel fuzzy control scheme for the Euler-Lagrange dynamics model of TAB for achieving tracking performance and providing accurate friction compensation. Finally, the asymptotic stability of the closed-loop system is proved theoretically and the effectiveness of the controller is verified by numerical simulation carried out in MATLAB/Simulink. Results: The desired angle can be reached quickly within 3 s by adopting the proposed controller without overshoot or oscillation in Tracking Experiment, demonstrating the regulation performance of the proposed control scheme. The proposed method still achieves the desired trajectory rapidly and accurately without steady-state errors in Varying-friction Experiment. The angle errors generated by external disturbances are < 1 deg under the proposed controller, which returns to zero in 2 s in Anti-disturbance Experiment. In contrast, comparative controllers take more time to be steady and are accompanied by oscillating and residual errors in all experiments. Discussion: The proposed method is model-free control and has no strict requirement for the dynamics model and friction model. It is proved that advanced tracking performance and real-time response can be guaranteed under the presence of unknown bounded non-linear friction and time-varying non-linear dynamics.

Improving Optical Flow Sensor Using a Gimbal for Quadrotor Navigation in GPS-Denied Environment.

This paper proposes a new sensor using optical flow to stabilize a quadrotor when a GPS signal is not available. Normally, optical flow varies with the attitude of the aerial vehicle. This produces positive feedback on the attitude control that destabilizes the orientation of the vehicle. To avoid this, we propose a novel sensor using an optical flow camera with a 6DoF IMU (Inertial Measurement Unit) mounted on a two-axis anti-shake stabilizer mobile aerial gimbal. We also propose a robust algorithm based on Sliding Mode Control for stabilizing the optical flow sensor downwards independently of the aerial vehicle attitude. This method improves the estimation of the position and velocity of the quadrotor. We present experimental results to show the performance of the proposed sensor and algorithms.

An adaptive predefined time sliding mode control for uncertain nonlinear cyber-physical servo system under cyber attacks.

Malicious attacks are often inevitable in cyber-physical systems (CPS). Accuracy in Cyber physical system for position tracking of servos is the major concern now a days. In high precision industrial automation, it is very hard to achieve accuracy in tracking especially under malicious cyber-attacks, control saturations, parametric perturbations and external disturbances. In this paper, we have designed a novel predefined time (PDT) convergence sliding mode adaptive controller (PTCSMAC) for such kind of cyber physical control system. Main key feature of our control is to cope these challenges that are posed by CPS systems such as parameter perturbation, control saturation, and cyber-attacks and the whole system then upgrade to a third-order system to facilitate adaptive control law. Then, we present an adaptive controller based on the novel PDT convergent sliding mode surface (SMS) combined with a modified weight updated Extreme Learning Machine (ELM) which is used to approximate the uncertain part of the system. Another significant advantage of our proposed control approach is that it does not require detailed model information, guaranteeing robust performance even when the system model is uncertain. Additionally, our proposed PTCSMAC controller is nonsingular regardless of initial conditions, and is capable of eradicating the possibility of singularity problems, which are frequently a concern in numerous CPS control systems. Finally, we have verified our designed PTCSMAC control law through rigorous simulations on CPS seeker servo positioning system and compared the robustness and performance of different existing techniques.

Research on Human-Robot Collaboration Method for Parallel Robots Oriented to Segment Docking.

In the field of aerospace, large and heavy cabin segments present a significant challenge in assembling space engines. The substantial inertial force of cabin segments' mass often leads to unexpected motion during docking, resulting in segment collisions, making it challenging to ensure the accuracy and quality of engine segment docking. While traditional manual docking leverages workers' expertise, the intensity of the labor and low productivity are impractical for real-world applications. Human-robot collaboration can effectively integrate the advantages of humans and robots. Parallel robots, known for their high precision and load-bearing capacity, are extensively used in precision assembly under heavy load conditions. Therefore, human-parallel-robot collaboration is an excellent solution for such problems. In this paper, a framework is proposed that is easy to realize in production, using human-parallel-robot collaboration technology for cabin segment docking. A fractional-order variable damping admittance control and an inverse dynamics robust controller are proposed to enhance the robot's compliance, responsiveness, and trajectory tracking accuracy during collaborative assembly. This allows operators to dynamically adjust the robot's motion in real-time, counterbalancing inertial forces and preventing collisions between segments. Segment docking assembly experiments are performed using the Stewart platform in this study. The results show that the proposed method allows the robot to swiftly respond to interaction forces, maintaining compliance and stable motion accuracy even under unknown interaction forces.

Quantifying the performance enhancement facilitated by fractional-order implementation of classical control strategies for nanopositioning.

For most nanopositioning systems, maximizing positioning bandwidth to accurately track periodic and aperiodic reference signals is the primary performance goal. Closed-loop control schemes are employed to overcome the inherent performance limitations such as mechanical resonance, hysteresis and creep. Most reported control schemes are integer-order and combine both damping and tracking actions. In this work, fractional-order controllers from the positive position feedback family namely: the Fractional-Order Integral Resonant Control (FOIRC), the Fractional-Order Positive Position Feedback (FOPPF) controller, the Fractional-Order Positive Velocity and Position Feedback (FOPVPF) controller and the Fractional-Order Positive, Acceleration, Velocity and Position Feedback (FOPAVPF) controller are designed and analysed. Compared with their classical integer-order implementation, the fractional-order damping and tracking controllers furnish additional design (tuning) parameters, facilitating superior closed-loop bandwidth and tracking accuracy. Detailed simulated experiments are performed on recorded frequency-response data to validate the efficacy, stability and robustness of the proposed control schemes. The results show that the fractional-order versions deliver the best overall performance.

Model-free finite-time robust control using fractional-order ultra-local model and prescribed performance sliding surface for upper-limb rehabilitation exoskeleton.

To address the trajectory tracking issue of upper-limb rehabilitation exoskeleton with uncertainties and external disturbances, this paper proposes a fractional-order ultra-local model-based model-free finite-time robust controller (FO-FTRC) using predefined performance sliding surface. Different from previous model-free control strategies, a novel multi-input multi-output (MIMO) fractional-order ultra-local model which is a virtual model is proposed to approximate the complex uncertain nonlinear exoskeleton dynamics in a short sliding time window. This allows the design of controller to be independent of any exoskeleton model information and reduces the difficulty of controller design. The developed robust model-free control method incorporates a fractional-order quasi-time delay estimator (FO-QTDE), unknown disturbance estimator (UDE) as well as prescribed performance sliding mode control (PPSMC). The FO-QTDE is utilized to estimate the unknown lumped uncertainties which employs short time delayed knowledge only about the control input. However, the low-pass filter is always added for FO-QTDE when disturbances change fast, which leads to unavoidable estimation error. Then, UDE is designed to further eliminate the estimation error of FO-QTDE to enhance control performance. The PPSMC is constructed to converge sliding surface to zero in a finite time. Besides, the sliding surface is always limited in performance boundaries. After that, the overall system stability and convergence analyses are demonstrated by using the Lyapunov theorem. Finally, with the comparison to other methods of α-variable adaptive model free control (α-AMFC), time-delay estimation-based continuous nonsingular fast terminal sliding mode controller (TDE-CNFTSMC), time delay estimation (TDE)-based model-free fractional-order nonsingular fast terminal sliding mode control (MFF-TSM) and fractional-order proportion-differential (PDß), the co-simulation results on 7-degree-of-freedom (DOF) iReHave upper-limb exoskeleton virtual prototype and experiment results on 2-DOF upper-limb exoskeleton are obtained to illustrate the effectiveness and superiority of the proposed FO-FTRC method.

Adaptive robust control with slipping parameters estimation based on intelligent learning for wheeled mobile robot.

The widespread use of wheeled mobile robots (WMRs) in many fields has created new challenges. A critical issue is wheel slip, which, if not accurately determined and controlled, causes instability and deviation from the robot's path. In this paper, an intelligent approach for estimating the longitudinal and lateral slip of wheels is proposed that can effectively compensate for the negative effects of slippage. The proposed algorithm relies on three regression networks to estimate the longitudinal slip ratio of the right and left wheels and sideslip angle on terrains with different friction coefficients. The datasets collected during tests on different surfaces with various maneuvers are used to train the artificial neural networks (ANNs). A developed dynamic model of a WMR considering wheel slip and modified traction force is presented. The adaptive robust controller, based on sliding mode control (SMC), is introduced to deal with the problems related to slipping, unknown uncertainties, and disturbances. The simulation results demonstrate that the presented controller has better performance than SMC in handling external disturbances and uncertainties, which leads to reduction in tracking error and faster convergence to zero. The proposed controller with an intelligent slip estimator, has been applied to a four-wheel mobile robot to demonstrate its effectiveness and feasibility. The high accuracy of slip estimation in the mentioned intelligent algorithm has resulted in the presented method being on average 26% more effective in reducing the tracking error than the control method without slip compensation in each test for circular trajectory.

Optimal Robust Control of Nonlinear Systems with Unknown Dynamics via NN Learning with Relaxed Excitation.

This paper presents an adaptive learning structure based on neural networks (NNs) to solve the optimal robust control problem for nonlinear continuous-time systems with unknown dynamics and disturbances. First, a system identifier is introduced to approximate the unknown system matrices and disturbances with the help of NNs and parameter estimation techniques. To obtain the optimal solution of the optimal robust control problem, a critic learning control structure is proposed to compute the approximate controller. Unlike existing identifier-critic NNs learning control methods, novel adaptive tuning laws based on Kreisselmeier's regressor extension and mixing technique are designed to estimate the unknown parameters of the two NNs under relaxed persistence of excitation conditions. Furthermore, theoretical analysis is also given to prove the significant relaxation of the proposed convergence conditions. Finally, effectiveness of the proposed learning approach is demonstrated via a simulation study.

Adaptive-Robust Controller for Smart Exoskeleton Robot.

Rehabilitation robotics has seen growing popularity in recent years due to its immense potential for improving the lives of people with disabilities. However, the complex, uncertain dynamics of these systems present significant control challenges, requiring advanced techniques. This paper introduces a novel adaptive control framework integrating modified function approximation (MFAT) and double-integral non-singular terminal sliding mode control (DINTSMC). The goal is to achieve precise tracking performance, high robustness, a fast response, a finite convergence time, reduced chattering, and effective handling of unknown system dynamics. A key feature is the incorporation of a higher-order sliding mode observer, eliminating the need for velocity feedback. This provides a new solution for overcoming the inherent variations and uncertainties in robot manipulators, enabling improved accuracy within fixed convergence times. The efficacy of the proposed approach was validated through simulations and experiments on an exoskeleton robot. The results successfully demonstrated the controller's effectiveness. Stability analysis using Lyapunov theory proved the closed-loop system's uniform ultimate boundedness. This contribution is expected to enable enhanced control for rehabilitation robots and improved patient outcomes.

Sparse successive approximation for nonlinear H2 and H∞ optimal control problems under residual errors.

Successive approximation techniques are effective approaches to solve the Hamilton-Jacobi-Bellman (HJB)/Hamilton-Jacobi-Isaacs (HJI) equations in nonlinear H2 and H∞ optimal control problems (OCPs), but residual errors in the solving process may destroy its convergence property, and related numerical methods also pose computational burden and difficulties. In this paper, the HJB/HJI partial differential equations (PDEs) for infinite-horizon nonlinear H2 and H∞ OCPs are handled in a unified formulation, and a sparse successive approximation method is proposed. Taking advantage of successive approximation techniques, the nonlinear HJB/HJI PDEs are transformed into sequences of easily solvable linear PDEs, to which the solutions can be computed point-wise by handling simple initial value problems. Extra constraints are also incorporated in the solving process to guarantee the convergence under residual errors. The sparse grid based collocation points and basis functions are then employed to enable efficient numerical implementation. The performance of the proposed method is also numerically demonstrated in simulations.