H_∞ Robust Control For High Rise High Speed Elevators

The elevator vertical motion and control design problem are discussed for high-rise/highspeed elevators in this paper. The goal of the control is to realize tracking control and releveling control under the condition of desired control performance. A kind of two-degree-of-freedom (2DOF) control method is proposed for elevators on the basis of vertical motion control description. This method can reject effectively the affect of papameter variation for system and the good tracking characteristic and high precision releveling performance can be achieved simultaneously.The performance requirements for modem elevators are very stringent. Furthermore these requirements must be achieved in the presence of considerable model uncertainty and unmodeled dynamics. The performance requirements entails metrics such as flight time, landing accuracy, position overshoot and riding quality, etc. The robustness requirement demands the control system must account for both parametric uncertainty and unmodeled dynamics associated with, for instance, the rope dynamics. For high rise/high speed elevators, the "effective length"(distance between the car and drive sheave) of hoist rope varies during elevator transition, so in fact the elevator vertical motion is nonlinear. Also the stiffness and damping coefficients of hoist rope and compensation rope are varies during elevator transition, ie. there exists the affect of uncertainties for system. Under the consideration of rope dynamics performance and the existence of system parameter uncertainties (the rope stiffness and damping), the tracking and releveling prolems of robust 2DOF elevator control system are maily discussed in this paper.The 2DOF is composed of feedforward of input signal and feedback of error control. The socalled 2DOF control is that adjust the target.value tracking characteristic optimal parameters and outer disturbance rejecting characteristic optimal parameters independently. The robust 2DOF controller proposed in this paper can meet elevator performance requirements with the height of 500m, the maximum run speed of 15m/s. It can reject effectively the affect of parameter variation for system and the good tracking characteristic, disturbance rejection characteristic, robustness and high precision releveling performance can be achieved simultaneously. First, the design of speed controller is converted into a standard H_∞control problems. Second, with the help of LMI approach, an output feedback suboptimal H_∞controller is obtained. Finally, an H_∞optimal controller is gained by solving a convex optimization problem so as to guarantee system robustness. The simulation results show that this method is effective.