In this paper, we propose a fuzzy approach for optimal robust control design of an automotive electronic throttle (ET) system. Compared with the conventional ET control systems, we establish the fuzzy dynamical model of the ET system with parameter uncertainties, nonlinearities, and external disturbances, which may be nonlinear, (possibly fast) time varying. These uncertainties are assumed to be bounded, and the knowledge of the bound only lies within a prescribed fuzzy set. A robust control that is deterministic and is not the usual if-then rules-based control is presented to guarantee the controlled system to achieve the deterministic performance: uniform boundedness and uniform ultimate boundedness. Furthermore, a fuzzy-based system performance index including average fuzzy system performance and control cost is proposed based on the fuzzy information. The optimal design problem associated with the control can then be solved by minimizing the fuzzy-based performance index. With this optimal robust control, the performance of the fuzzy ET system is both deterministically guaranteed and fuzzily optimized.

While designing control for a class of underactuated mechanical systems (UMSs), the uncertainty and the prescribed nonholonomic tracking trajectories should be taken into consideration. Uncertainty considered in this article is time varying and bounded, and the bound of uncertainty is described using the fuzzy set theory, namely, fuzzy UMSs. An analytical dynamics-based view is taken in which the prescribed tracking trajectories are viewed as servo constraints which can be linear, nonlinear, holonomic, and nonholonomic. Using this view, a novel closed form solution of adaptive robust control is found with leakage type adaptive law to guarantee deterministic system performance, including uniform boundedness and uniform ultimate boundedness. In order to find the optimal dual gain parameters of the designed control, a two-player cooperative game is proposed for which the Pareto optimality can always be guaranteed. The effectiveness of the proposed control is shown through numerical simulation of a two-wheeled inverted pendulum vehicle.

The main objective of this article is to address the position tracking control problem for permanent magnet linear motor by using a novel model-based robust control method. Specifically, based on the assumed upper bound of the lumped model uncertainties and external disturbances, we design a novel nonlinear control algorithm, which is characterized by error-based and model-based inheriting from traditional proportional-integral-derivative (PID) control and robust control. The proposed control can be considered as an improved PID control or a redesigned robust control, with simple implementation and practical effectiveness. Theoretical analysis is provided to demonstrate that the controller can guarantee the uniform boundedness and uniform ultimate boundedness of the system. Moreover, on the experimental platform, rapid controller prototyping cSPACE is designed to avoid long time programming and debugging, and provides great convenience for practical operation. Numerical simulations and real-time experimental results are finally presented to illustrate the effectiveness and the achievable control performance of the control design.