Constraint-Following Servo Control for the Trajectory Tracking of Manipulator with Flexible Joints and Mismatched Uncertainty

Trajectory tracking is a common application method for manipulators. However, the tracking performance is hard to improve if the manipulators contain flexible joints and mismatched uncertainty, especially when the trajectory is nonholonomic. On the basis of the Udwadia–Kalaba Fundamental Equation (UKFE), the prescribed position or velocity trajectories are creatively transformed into second-order standard differential form. The constraint force generated by the trajectories is obtained in closed form with the help of UKFE. Then, a high-order fractional type robust control with an embedded fictitious signal is proposed to achieve practical stability of the system, even if the mismatched uncertainty exists. Only the bound of uncertainty is indispensable, rather than the exact information. A leakage type of adaptive law is proposed to estimate such bound. By introducing a dead-zone, the control will be simplified when the specific parameter enters a certain area. Validity of the proposed controller is verified by numerical simulation with two-link flexible joint manipulator.

Model-free Control of Manipulator in Task Space Containing Mismatched Uncertainty

In this paper, a novel trajectory tracking control method for manipulator task space containing mismatched uncertainty is proposed. This paper considers the mismatched uncertainty that exists in the signal conversion between joint space and task space in the robotic arm system. The time delay estimation is employed to approximate the dynamic and kinematic parameters of the system to achieve model-free control. The time delay estimation errors is treated as part of the system disturbances and a disturbance observer based on an auxiliary control system capable of estimating both matched and mismatched disturbances is designed, which does not require additional design of adaptive laws to compensate for disturbances or upper bounds on the derivatives of disturbances. We transform the control error by a prescribed performance function to accomplish transient control of the error, and design a fast terminal sliding surface for the virtual control variables based on the backstepping design method to improve the convergence speed of the controller. Based on the Lyapunov criterion, the closedloop stability of the whole system is demonstrated. The feasibility and superiority of the method in this paper is demonstrated by numerical simulation compared with other control methods.

Robust control for fuzzy electric power steering system: A two-layer performance approach

This study investigates the angle tracking control of the electric power steering system, which is underactuated and with (possibly fast) time-varying uncertainties. We design the control based on constraint-following, that is, formulating the tracking goal as servo constraints. To tackle the uncertainty, especially the mismatched uncertainty, a robust control is proposed with two-layer performance: deterministically guaranteed and fuzzily optimized. Particularly, the control design is implemented in three steps. First, without considering uncertainty, a nominal control is designed. Second, an uncertainty decomposition technique is presented to account for uncertainty, which creatively allocates the mismatched uncertainty for the robust control design that also builds on the nominal system control. The robust scheme is deterministic without using any “if–then” rules and guarantees uniform boundedness and uniform ultimate boundedness for the system, that is, the deterministically guaranteed performance. Third, by using fuzzy set theory to describe uncertainty, a fuzzy-based performance index, including system performance and control cost, is introduced. A control parameter optimal design problem is formulated and analytically solved, that is, the fuzzily optimized performance. The effectiveness of the proposed approach is illustrated by rigorous proof and the simulation results on the electric power steering system.

ỨNG DỤNG ĐIỀU KHIỂN TRƯỢT NÂNG CAO TRONG CÁC HỆ PHI TUYẾN BẬC CAO CÓ YẾU TỐ BẤT ĐỊNH VÀ NHIỄU TÁC ĐỘNG

Bài báo trình bày các phân tích đánh giá một số hướng tiếp cận ứng dụng điều khiển trượt để tổng hợp điều khiển hệ phi tuyến, bất định và có nhiễu: điều khiển trượt đầu cuối (TSMC), điều khiển trượt đầu cuối không kỳ dị (NTSMC), điều khiển trượt đầu cuối nhanh không kỳ dị (NFTSMC), đề xuất cải tiến mặt trượt có sự tham gia của đánh giá nhiễu không thuộc không gian điều khiển (mismatched uncertainty) và xây dựng mặt trượt phân tầng cho hệ phi tuyến bậc cao; xây dựng mô hình mô phỏng trong matlab-simulink để kiểm chứng.