A decentralized observer-based optimal control for interconnected systems using the block pulse functions

The paper proposes a method to integrate numerically an interconnected system, based on an idea of orthogonal approximation of functions. Here, block pulse functions (BPFs) are chosen as the orthogonal set. The main advantage of using this technique is its ability to transform the original optimal control problem to a mathematical programming problem relatively easier to solve. The primary focus of this paper is to exploit and rigorously develop the BPFs parametrization technique for the synthesis of a decentralized observer-based optimal control for large-scale interconnected systems. In addition, we develop a mathematical model of a double-parallel inverted pendulum coupled by a spring, taking into account all possible changes of the connecting position of the elastic spring. In so doing, we conducted advanced simulations applying the new optimal control method to the studied interconnected system. Our results demonstrate the validity and the effectiveness of the developed decentralized observer-based optimal control approach.

Decentralized observer-based optimal control using two-point boundary value successive approximation approach application for a multimachine power system

In this paper, we present a new decentralized observer for a class of nonlinear interconnected systems, based on an optimal control law using the two-point boundary value (TPBV) successive approximation approach. This technique, used previously to develop a nonlinear decentralized suboptimal control for a multimachine power system, inspired us to develop a new method to design a decentralized observer-based suboptimal control law for the same system. The TPBV approach is characterized by the transformation of each high order coupling nonlinear TPBV problem into a sequence of linear decoupling TPBV problems that uniformly converge to the optimal control for nonlinear interconnected large-scale systems. Sufficient conditions for the asymptotic stability of the developed feedback control scheme are proposed in terms of linear matrix inequalities (LMIs) constraints, which can be efficiently solved by the LMI optimization techniques, to compute the control and the observation gains of the overall system. We applied this approach to a three-machine power system which generators are nonlinear systems strongly interconnected. We demonstrated clearly, via advanced simulations, that this approach was able to bring good performances, improving effectively transient stability of this power system in few iterative sequences while allowing the reconstruction of its non-measurable state variables.

Robust optimal decentralized observer for multi-phase flow measurement

In this paper, a non-fragile optimal observer is proposed for the decentralized multiphase flow measurement based on the interconnections between the two subsystems, that is, gas and liquid, constituting the whole system. Due to the dynamic model of system and presence of disturbances and slowly varying quantities, a non-fragile decentralized observer is designed and the states of the condensate and gas sub-systems were separately estimated. Lyapunov-based stability conditions are converted to linear matrix inequality (LMI) and observer gains are optimally selected from solution set such that the effect of the disturbance on the states’ estimation error becomes minimized. The estimation is conducted using the real-time measurements including lines pressures, single-phase gas flow, and single-phase liquid flow in the refinery outlet. To check the stability and performance of the system against the changes, the Lyapunov theory has been used. Finally, the estimation results are compared with real-world data from the industry showing the high accuracy of this method as the estimations were consistent with the operation data. In all stages, the investigations were based on the data collected from the actual process in the South Pars Gas Complex (SPGC), Iran. Additionally, the Extended Kalman Filter (EKF) based on the simplified drift flux model (DFM) was used to estimate the states then both methods’ results are compared and using the HYSYS simulator with the real process data, it is found that both observers are capable to identify the states with some differences in performance and DFM model is sufficient for estimation of parameters and states of the multiphase flow entering the gas refinery. As a result, these techniques not only can be substituted for the existing system at the gas refinery, but also can be as a backup for available measurement systems.