In the design of model reference adaptive control (MRAC) schemes, adaptive laws have been developed based on Lyapunov stability theory. Over the past few decades, it has been a common practice to use quadratic Lyapunov functions (QLF). In contrast to such development, using a new nonquadratic Lyapunov function (NQLF), this paper presents new adaptive laws for the MRAC. These new laws have the same advantage of assurance of stability of the overall system, as the earlier adaptive laws developed using the QLF. Over and above, they have an additional advantage of improved performance: in fact, the use of NQLF improved the system output error signal converging to zero. Finally, this paper also presents simulation results supporting the arguments.

Adaptive control laws are modified to obtain robust adaptive control schemes in the presence of disturbance. One of the well known modifications in robust adaptive control is the e-modification scheme; this modification has always been developed based on Lyapunov stability theory using the standard form of quadratic Lyapunov function (QLF). In contrast to such development and as a continuation to the effort done by the authors in this area, this paper presents new robust adaptive laws for e-modification scheme using novel non-quadratic Lyapunov function (NQLF) for higher order systems. These new laws offer better performance represented in a fast response of the output error signal while going to zero with a less number of oscillations. Simulation results for a third order system are illustrated in the paper to verify the advantages of using these new laws for higher order systems

In literature, design of model reference adaptive control (MRAC) schemes and adaptive laws has always been developed based on Lyapunov stability theory. Over the past few decades, it has been a common practice to use quadratic Lyapunov functions (QLFs). In contrast to such development and as a continuation to the research effort earlier published by the same authors, this paper involves the use of non-quadratic Lyapunov functions (NQLFs) for higher order systems. These new laws have the same advantage of assuring the stability of the overall system as well as improving the overall system performance whether in the absence or presence of disturbance. This improvement is considered in the fast and better convergence of the system output error signal while going to zero. Finally, this paper presents simulation results supporting the arguments

The Doubly-Fed Induction Generator (DFIG) based Wind Turbines Generator (WTG) with traditional Maximum Power Point Tracking (MPPT) control provides no inertia response under system frequency events. Recently, the DFIG wind turbines have been equipped with the Virtual Inertia Controller (VIC) to enhance the frequency stability of the power system. However, the conventional VICs with fixed gain have negative effects on the inter-area oscillations of regional networks. To cope with this drawback, this paper proposes a novel adaptive VIC to improve both the inter-area oscillations and frequency stability. In the proposed scheme, the gain of the VIC is dynamically adjusted using fuzzy logic. The effectiveness and control performance of the adaptive fuzzy VIC is evaluated under different frequency events such as loss of generation and three-phase fault with load shedding. The simulation studies are performed on a generic two-area network integrated with a DFIG wind farm, and the comparative results are presented for these three cases: DFIG without VIC, DFIG with fixed gain VIC, and DFIG with adaptive fuzzy VIC. The results confirm the ability of the proposed adaptive fuzzy VIC in improving both the interarea oscillations and frequency stability of the system.