This paper addresses the challenging problem of precise trajectory tracking control for flexible-joint manipulators (FJMs) operating under intricate uncertainties, input-saturation constraints, and limited state feedback. Existing control strategies failed to simultaneously resolve the issues of input saturation and system uncertainties while relying solely on output feedback. Motivated by this limitation, we aim to propose a novel neuro-adaptive command-filtered output-feedback backstepping control scheme, which, to the best of our knowledge, is the first to integrate these capabilities for FJMs. The key findings include: (1) a smooth hyperbolic function combined with the mean-value theorem to effectively mitigate input-saturation effects; (2) an adaptive radial basis function (RBF) neural network-based state observer to estimate unmeasurable system states; and (3) a second-order command-filtered backstepping framework enhanced with error compensation dynamics to eliminate complexity explosion and reduce filtering errors. In addition, the proposed method eliminates the need for precise FJM models while ensuring uniform ultimate boundedness of all closed-loop signals, as rigorously proven via Lyapunov stability analysis. Comparative simulations demonstrate that the controller achieves superior transient and steady-state tracking accuracy over existing backstepping approaches.

Observer-based control is the most commonly used method in the control of electro-hydraulic servo system (EHSS) with uncertainties, but it suffers from the drawback of low accuracy under the influence of large external load forces and disturbances. To address this problem, this paper proposes a novel compensation function observer-based backstepping sliding-mode control (BSMC) approach to achieve high-accuracy tracking control. In particular, the model uncertainties, including nonlinearities, parameter perturbations and external disturbances are analyzed and treated together as a lumped disturbance. Then, a fourth-order compensation function observer (CFO) is constructed, which fully utilizes the system state information to accurately estimate the lumped disturbance. On this basis, the estimate of the lumped disturbance is incorporated into the design of a backstepping sliding-mode controller, allowing the control system to compensate for the disturbance effect. The stability of the closed-loop control system under the CFO and BSMC is rigorously proven through the use of the Lyapunov theory, which guarantees that all the tracking error signals converge exponentially to the origin. Comparative simulations are carried out to show the effectiveness and efficiency of the proposed approach, i.e., compared with PID and ESO-based BSMC methods, the tracking accuracy is respectively improved by $94.86\%$ and $88.19\%$ under the influence of large external load forces and disturbances.

Flexible-joint manipulators (FJMs) have been widely used in the fields of industry, agriculture, medical service, aerospace, etc. However, the FJMs in practical applications inevitably encounter various uncertainties including matched and mismatched disturbances. In this paper, we consider the high precision tracking control problem of FJMs in the presence of unknown lumped matched and mismatched disturbances. An efficient model-assisted composite control approach is proposed by integrating two reduced-order extended state observers (RESOs), a second-order command filtered backstepping (SCFB) technique and an error compensation dynamic system. Unlike some existing methods, the RESOs constructed with partial known model information are capable of estimating and compensating the matched and mismatched disturbances simultaneously. In addition, by employing the SCFB with an error compensation system, the proposed approach can not only overcome the problem of “explosion of complexity” inherent in backstepping, but also reduce the filtering errors arising from the command filters. The stability of the resulting control system and the convergence of error signals are guaranteed by Lyapunov stability theory. Comparative simulations are conducted for a single-link FJM with both matched and mismatched disturbances, and the results show that the proposed approach achieves a better tracking performance, i.e., compared with conventional backstepping method and adaptive fuzzy command filtered control method, the tracking accuracy is improved by 99.5% and 99.2%, respectively.

The horizontal translational oscillator with a rotational actuator (TORA) is a typical underactuated mechanical system, whose control problem is still open and theoretically challenging. At present, the existing control methods are structurally complicated and require an exact knowledge of the system parameters. Moreover, few works have considered the output feedback stabilization of the TORA system subject to practical constraints of input saturation and angular velocity unmeasurement. To address these problems, this paper proposes a novel model-free amplitude-limited control approach to stabilize the TORA system at the origin using only angle feedback. Firstly, the passivity of the horizontal TORA system is analyzed, based on which a novel Lyapunov function augmented with an auxiliary signal is constructed by taking the input saturation into account. Then, an amplitude-limited control law is derived in a straightforward manner. In order to make the control law independent of velocity feedback, the auxiliary signal is designed in terms of the ball rotational angle and an output of a dynamic system. The asymptotic stability of the entire control system is rigorously guaranteed by utilizing Lyapunov theory and LaSalle’s invariance principle. Finally, simulation results with comparisons to existing methods demonstrate the effectiveness and superiority of the proposed control approach.

Observer-based control is the most commonly used method in the control of electro-hydraulic servo system (EHSS) with uncertainties, but it suffers from the drawback of low accuracy under the influence of large external load forces and disturbances. To address this problem, this paper proposes a novel compensation function observer-based backstepping sliding mode control (BSMC) approach to achieve high-accuracy tracking control. In particular, the model uncertainties, including nonlinearities, parameter perturbations and external disturbances are analyzed and treated together as a lumped disturbance. Then, a fourth-order compensation function observer (CFO) is constructed, which fully utilizes the system state information to accurately estimate the lumped disturbance. On this basis, the estimate of the lumped disturbance is incorporated into the design of an backstepping sliding mode controller, allowing the control system to compensate for the disturbance effect. The stability of the closed-loop control system under the CFO and BSMC is rigorously proven through the use of Lyapunov theory, which guarantees that all the tracking error signals converge exponentially to the origin. Comparative simulations are carried out to show the effectiveness and efficiency of the proposed approach, i.e., compared with PID and ESO-based BSMC methods, the tracking accuracy is improved by 99.93% and 99.76%, respectively.

In this paper, we consider the robust stabilization control problem of underactuated translational oscillator with a rotating actuator (TORA) system in the presence of unknown matched disturbances by employing continuous control inputs. A nonlinear continuous robust control approach is proposed by integrating the techniques of backstepping and linear extended state observer (LESO). Specifically, based on the backstepping design methodology, a hyperbolic tangent virtual control law is designed for the first subsystem of the cascaded TORA model, via which an integral chain error subsystem is subsequently constructed and the well-known LESO technique is easy to implement. Then, an LEO is designed to estimate the lumped matched disturbances in real-time, and the influence of the disturbances is compensated by augmenting the feedback controller with the disturbance estimation. The convergence and stability of the entire control system are rigorously proved by utilizing Lyapunov theory and LaSalle’s invariance principle. Unlike some existing methods, the proposed controller is capable of generating robust and continuous control inputs, which guarantee that both the rotation and translation of TORA systems are stabilized at the origin simultaneously and smoothly, attenuating the influence of disturbances. Comparative simulation results are presented to demonstrate the effectiveness and superior control performance of the proposed method.