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This paper proposes a systematic method using the hybrid automata (HA) model for supervisory management design of power systems to increase stability. The HA model monitors the behavior of the power system and derives a model from which the system's stability is evaluated. In the modeling framework, the hybrid system formalism regulates continuous dynamics and discrete switching behavior. The proposed method extracts a system's control graph, state space, and transfer function, facilitating voltage stability evaluation. A discrete event system (DES) is employed to manage disturbances resulting from load surges, generator outages, capacitor banks, and under-load tap changer (ULTC) transformers. The ULTC transformer and the capacitor bank are utilized to examine the feasibility and effectiveness of the proposed supervisory controller design approach in the presence of distributed generation (DG). Simulation results showed the effectiveness of the HA-based supervisory controller in improving the control and voltage stability, as demonstrated by the generator rotor angle and bus voltage responses, power system eigenvalues, and the stability theorem of linear switching systems. The proposed method provides a promising solution for managing power system stability. [ABSTRACT FROM AUTHOR]

Double Inverted pendulums are typical examples of unstable systems and have been used for the verification of designed control systems and control education in laboratories. This paper proposed a robust multi-objective state feedback controller for a double inverted pendulum system using the satisfaction additional constraints. Mixture of different synthesis specifications such as the guarantees H∞ performance, minimizes H2 performance and regional pole placement constraints, which are converted into the Linear Matrix Inequality (LMI). Then convex program minimized linear objective under LMI constraints is applied. The robust state feedback controller is designed and simulated in MATLAB and results show that the system with the proposed state feedback controller has a good response to initial condition with respect to parameters of output performance. The simulation is also displayed a system with proposed controller is robust against input disturbances and plant uncertainty. [ABSTRACT FROM AUTHOR]