## 3 Hierarchical State-of-the-Art Control
### Overview of the Inner-Loop Control Methods
However, while the DB controller provides robustness in its performance, its implementation leads to a suffocated control structure. * _Hysteresis control (H)_: In the hysteresis approach, the designed controller has to be attached to an adaptive band to achieve fixed switching frequency. The output is the state of the switches that offers variable switching frequency. Worth mentioning, the hysteresis approach is allocated to the predictive control group. Numerous techniques and algorithms to achieve fixed switching frequency are presented in the literature [53; 54; 55; 56]. In [57], a hysteresis current regulator is applied for the neutral-point clamped inverter as well as the flying capacitor three-phase inverter, where the measured switched phase-leg voltages are adjusted to the phase leg according to the switching frequency. The hysteresis current regulator is distinguished for its robustness against load variations, for exhibiting high-speed transient performance, and for its simple implementations. Despite the several advantages of the hysteresis controller, it still has drawbacks, such as the high switching frequencies in the inverter due to being interphase-based. * _Predictive control (P)_: Predictive control is a sophisticated control process satisfying a set of constraints. It uses the system model to forecast the future behavior of the controlled variables. In such a way, it can accurately track the reference current while minimizing the forecasting error within zero error. The model predictive power control (MPPC) and voltage control (MPVC) are proposed in [58]. These schemes can ensure stable DC-bus voltages of BESS as well as a stable AC-bus voltage output and a decent power sharing. Both control schemes provide a simpler control algorithm and better performance. However, the predictive control is prone to network variations. Therefore, in [59], a robust disturbance observer for model predictive control has been proposed for a grid-connected inverter to regulate the current output. The observer is designed to estimate the lumped disturbances (model uncertainties and grid voltage disturbances). An improvement in the reference error tracking is made in [60] by applying an adaptive reference model predictive control to track virtual references rather than actual references. A flexibly modeled virtual multi-input-multi-output (MIMO) generates the error and thus no tuning process is required for different operating points. A seamless transition of mode operations of VSI is presented in [61] through predictive detection and the estimation of control algorithm. It can be achieved through the cost function, thus simplifying the controller's algorithm. The advantage of predictive control design-wise is that it can be implemented more simply depending on the applications. Despite the simple implementation, some predictive controls can be more complicated. * _Sliding mode control (SMC)_: This control is recognizable by having a robust performance and a fast response time in the variability of system parameters over sizeable operating points [62]. The controller takes vigorous actions if the plant experiences deviations from its average operating point [63]. In such a way, the desired dynamics can be ensured through an essential selection of desired dynamics and control law. However, SMC's performance significantly deteriorates due to the chattering phenomenon in discrete implementation. Therefore, the enhancement of SMC has been made through the output ripple optimization. The works in [24; 64] have shown that SMC is employed in the secondary control scheme and is used in both frequency and voltage regulators to enhance power sharing performance and battery charging scheme. SMC shows reliable performance during transients and has better disturbance rejection and low sensitivity to parameter value changes.