Evaluating Fractional PID Control in a Nonlinear MIMO Model of a Hydroelectric Power Station

Abstract

In this paper a Fractional PID Control is presented. This control was designed for a hydropower plant with six generation units working in an alternation scheme. The parameters and other features of such a set of hydrogeneration units have been used to perform the respective tuning up. In order to assess the behavior of this controlled system, a model of such nonlinear plant is regulated through a classical PID by classical linearization of its set points, and then a pseudo-derivative part is substituted into a Fractional PID. Both groups of signals contain variations of voltage suggesting some abrupt changes in the supply of electricity fed to the network. Both sets of resulting signals are compared; the simulations show that the Fractional PID has a faster response with respect to those plots obtained from the classical PID used.

Parametrical Non-Complex Tests to Evaluate Partial Decentralized Linear-Output Feedback Control Stabilization Conditions from Their Centralized Stabilization Counterparts

“…The replacement of Equation 3into Equations (1) and (2) yields Equation (7)-(9). Since the (1) and (2) is linear output stabilizable, a stabilizing controller gain K c ∈ R m×p has to exist such that (7)- (9) are solvable and the closed-loop dynamics is stable.…”

“…Proof. It is obvious from Assertions 1 and 2 that, when replacing (9) and 12), the second replacement happens under sparser parameterizations.…”

“…Some extra constraints inherent to some systems, like solution positivity in the case of biological systems or human migrations or the needed behavior robustness against parametrical changes of disturbance actions add additional complexity to the related investigations and need the use of additional mathematical or engineering tools for the research development, [5][6][7]. A large variety of modeling and design tools have to be invoked and developed in the analysis depending on the concrete systems under study and their potential applications as, for instance, the presence of internal and external delays, discretization, dynamics modeling based on fractional calculus, the existence of complex systems with interconnected subsystems, [8][9][10][11][12][13], hybrid coupled continuous/digital tandems, nonlinear systems and optimization and estimation techniques [14][15][16][17][18][19] as well as robotic and fuzzy-logic based systems, [20,21]. In particular, decentralized control is a useful tool for controlling dynamic systems by cutting some links between the dynamics coupling a set of subsystems integrated in the whole system at hand.…”

“…The proposed robust model predictive control is much simpler than the traditional versions since the information of the upper and lower bounds of the time-varying delay are used for design purposes. On the other hand, in [9], a control law might be synthesized for a hydropower plant with six generation units working in an alternation scheme. To assess the behavior of the controlled system, a model of such a nonlinear plant is controlled by a fractional proportional/integral/derivative control device through a linearization of its set points, the fractional part being relevant in the approach on the controller derivative actions.…”

Saturation Based Nonlinear FOPD Motion Control Algorithm Design for Autonomous Underwater Vehicle

“…Except from these three parameters, fractional-order PID type controllers may have two extra parameters, namely the integral and differential orders [21]. Benefiting from these two parameters, systems controlled by FOPID type controllers are proved to be capable in achieving better transient performance as well as robustness [22][23][24][25]. A fractional sliding mode control algorithm for a fully actuated underwater vehicle subjected to the non-differentiable disturbance was proposed in [26].…”