This paper proposes an adaptive funnel control (FC) scheme for servo mechanisms with an unknown dead-zone. To improve the transient and steady-state performance, a modified funnel variable, which relaxes the limitation of the original FC (e.g., systems with relative degree 1 or 2), is developed using the tracking error to replace the scaling factor. Then, by applying the error transformation method, the original error is transformed into a new error variable which is used in the controller design. By using an improved funnel function in a dynamic surface control procedure, an adaptive funnel controller is proposed to guarantee that the output error remains within a predefined funnel boundary. A novel command filter technique is introduced by using the Levant differentiator to eliminate the ``explosion of complexity'' problem in the conventional backstepping procedure. Neural networks are used to approximate the unknown dead-zone and unknown nonlinear functions. Comparative experiments on a turntable servo mechanism confirm the effectiveness of the devised control method.

Most function approximator (e.g., neural network or fuzzy system) based control designs can only prove uniform ultimate boundedness of the controlled system due to the unavoidable approximation errors. Moreover, the transient response of conventional adaptive control may be sluggish because high-gain learning is not preferable for guaranteeing system safety. To address these issues, this paper proposes and experimentally validates an alternative robust adaptive control for servo mechanisms with unknown dynamics and bounded disturbances. This control can guarantee asymptotic tracking error convergence in the steady-state, while the transient response can also be prescribed by using an improved prescribed performance function. An echo state network augmented by a smooth friction model is used to accommodate the unknown nonlinearities. The residual approximation error and other bounded disturbances are compensated by using a robust integral of sign of the error term. Comparative experiments based on a practical turntable servo mechanism are conducted to validate the effectiveness of the proposed control scheme and show improved control performance.

Although adaptive control design with function approximators, for example, neural networks (NNs) and fuzzy logic systems, has been studied for various nonlinear systems, the classical adaptive laws derived based on the gradient descent algorithm with σ-modification or e-modification cannot guarantee the parameter estimation convergence. These nonconvergent learning methods may lead to sluggish response in the control system and make the parameter tuning complex. The aim of this paper is to propose a new learning strategy driven by the estimation error to design the alternative adaptive laws for adaptive control of nonlinear servo systems. The parameter estimation error is extracted and used as a new leakage term in the adaptive laws. By using this new learning method, the convergence of both the estimated parameters and the tracking error can be achieved simultaneously. The proposed learning algorithm is further tailored to retain finite-time convergence. To handle unknown nonlinearities in the servomechanisms, an augmented NN with a new friction model is used, where both the NN weights and some friction model coefficients are estimated online via the proposed algorithms. Comparisons with the σ-modification algorithm are addressed in terms of convergence property and robustness. Simulations and practical experiments are given to show the superior performance of the suggested adaptive algorithms.

This article presents a new adaptive parameter estimation method and the corresponding control design for nonlinear servo mechanisms with friction compensation. A continuous friction model is employed to capture the friction dynamics of servo mechanisms. Then, the unknown system parameters including friction model parameters are online estimated via the derived adaptive law. Hence, a new adaptive law is proposed to achieve faster and more accurate parameter estimation over classical adaptive laws so as to suppress the undesired transient dynamics. For this purpose, an auxiliary filter is introduced to extract the estimation error for driving the parameter updating law. Moreover, an adaptive control is designed in conjunction with a robust integral of the sign of the error feedback term to address the bounded disturbances and enhance the tracking precision. Simulations and experiments are given to validate the efficiency of the developed control scheme.

In this paper, a predefined time sliding mode control with prescribed performance is presented for dual-inertia driving systems with unknown disturbances. A modified prescribed performance function (PPF) without requiring the accurate initial error is designed to guarantee that the tracking error remains within the prescribed boundary. An adaptive law is then constructed to estimate the unknown upper boundary parameters of the lumped dynamics (e.g., parameter uncertainties and external disturbances), so that the prior knowledge of the upper bound of uncertainties is not required. The parameter estimation is incorporated into the control design to eliminate the effects of the unknown dynamics. Using the sliding mode technique, an adaptive predefined time sliding mode control is developed. The proposed control method can achieve fast convergence rate of the tracking error, and the stability of the closed-loop system is proved via the Lyapunov function method. Comparative experiments are carried out based on a dual-inertia driving system to validate the efficacy of the proposed approach.