A PID control for electric vehicles subject to input armature voltage and angular velocity signal constraints is proposed. A PID controller for a vehicle DC motor with a separately excited field winding considering the field current constant was tuned using controlled invariant set and multiparametric programming concepts to consider the physical motor constraints as angular velocity and input armature voltage. Additionally, the integral of the error, derivative of the error constraints, and were considered in the proposed algorithm as tuning parameters to analyze the DC motor dynamic behaviors. The results showed that the proposed algorithm can be used to generate control actions taking into account the armature voltage and angular velocity limits. Also, results demonstrate that a controller subject to constraints can improve the electric vehicle DC motor dynamic; and at the same time it protects the motor from overvoltage.
In this paper, the design of a piecewise affine proportional integral (PWA-PI) controller algorithm based on invariant set and multiparametric programming for constrained systems is proposed. We implemented the algorithm in a programmable logic controller (PLC) to control an industrial constrained level plant and analyze its behavior. Structured text routines were programmed and validated while controlling two systems with PLC. The results show that the constraints on the error, integral of the error, system output and control action are respected because PWA-PI controllers are tuned from the solution of an optimization problem. The evaluated performance indexes (such as mean square error, Goodhart, overshoot and settling time) show that PWA-PI can be adjusted for better performance than proportional integral (PI) controller tuned by Ziegler-Nichols (Z-N) rules. In the analyzed cases, a settling time of 108 s was obtained, whereas PI controller with Z-N rules presented a 179 s settling time. All of the analyzed performance indexes that we used to evaluate both controllers show PWA-PI as a better controller for constrained systems.
In power systems, the over-current protection scheme and, optionally with directional function, and distance function are the main protection used, principally, where the power flow is on both sides as in distribution system with distributed generation (DG), for example. However, with the increasing of DG penetration in the distribution system, these protections can not be secure and impacts in the coordination of the protection are caused due to the power flow is on both sides. Therefore, new types of protection as distance protection are candidates to solve the coordination problem in the distribution system with DG. In this paper, is proposed an application of the distance protection in the distribution system with DG, and several cases of faults and the impacts on the distance protection are evaluated in presence of DG. In the simulation and analysis of faults were varied the fault inception angle, fault type, fault resistance, and fault location. The correct and bad trips are analyzed to evaluate the distance relay performance. The distance relay used in the distribution system with DG had good performance in all simulation cases. Besides, the better performance of the distance protection proves which may be used in distribution systems with DG.Streszczenie. W systemach energetycznych zabezpieczenie przed przeciążeniem prądowym (opcjonalnie wraz z funkcją kierunku i odległości) jest główną metoda zabezpieczenia, szczególnie gdy moc może być przekazywana w dwóch kierunkach. W artykule zaproponowano nowy typ zabezpieczenia uwzględniający funkcje odległości. Uwzględniono też możliwość wykrywania błędów i możliwość określania ich położenia. Analiza zabezpieczeń uwzględniających funkcje odległości w rozproszonych systemach wytwarzania energii.
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