Analysis on Biological Stability and Influencing Factors of Northern Living District Water Distribution System

The control problem of multiple-flexible-link manipulators (MFLMs) is studied in this paper.The dynamic model of MFLM is derived and separated into two-time scale by utilizing the singular perturbation technique. The active disturbance rejection control (ADRC) is adopted to the slow subsystem to track a desired trajectory. The proposed ADRC structure preshapes the desired trajectory by utilizing the tracking differentiator, estimates the disturbance and internal states with an extended state observer, and guarantees a robust performance by combining a feedback controller with a feedforward term.Two types of feedback controllers are designed, proportional derivative (PD) controller and nonlinear PD (NPD) controller. For the fast subsystem, a fast stabilizing control is designed according to the standard linear quadratic regulator approach. Simulations are performed to evaluate the proposed control scheme.Results show that, compared with the traditional PD controller, the ADRC structure based control scheme has smaller overshot and shorter settling time, suppresses vibration quickly, and is robust to the maneuver speed. In general, the control scheme utilizing ADRC structure and NPD feedback controller shows better performance.