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针对一类非线性非最小相位系统,利用微分几何控制理论,首先通过引入动态反馈对其扩维以获得稳定的零动态,然后采用标准的线性系统方法设计非线性控制器;进一步利用哈密顿—雅可比—贝尔曼方程和中心流形理论分别证明所设计控制律的最优性以及闭环系统的稳定性。结合水轮机调速系统模型,求得大型水轮发电机组水门开度非线性最优控制律。对川渝—华中电网的仿真结果表明,与常规控制器相比,所设计的调速系统控制律能够显著提高电力系统的暂态稳定性。
Aiming at a class of nonlinear non-minimum phase systems, the differential geometry control theory is used to expand the dimension to obtain steady zero dynamic state by introducing dynamic feedback. Then a nonlinear system is designed by using the standard linear system method. Furthermore, The Jacobian-Bellman equation and the center manifold theory respectively prove the optimality of the designed control law and the stability of the closed-loop system. Combined with the hydraulic turbine speed control system model, the optimal control law for the opening degree of water gate of a large hydroelectric generating set is obtained. The simulation results of Sichuan-Chongqing-Huazhong Power Grid show that compared with the conventional controller, the designed control law of the speed governing system can significantly improve the transient stability of the power system.