## 1 Introduction  
PWM power converters have been utilized in several industrial applications, such as communication systems, modern power grids, and renewable energy systems [1]. Sliding-mode control (SMC) has been studied and applied to power converters due to its fast transient response, ease of implementation, and robustness against system parameter variation. It is also considered one of the common nonlinear control techniques that is suited for variable structure systems, including power supplies [2]. However, a common issue that is associated with this control method is the steady-state error at the output voltage. This is attributed to the implementation of the SMC via a pulse-width modulator, which is utilized to obtain a constant switching frequency, minimize EMI issues, and reduce the complexity of filter design [3, 4]. In other words, the derivation of the equivalent control law in the PWM-based SMC method eliminates the high and variable switching frequency issues, but it degrades the tracking performance, which results in an undesirable dc error [3]. Considerable research work has been conducted to eliminate the steady-state error using double-integral sliding-mode control (DI-SMC), which is also known as proportional-integral sliding-mode control (PI-SMC) [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30]. The DI-SMC system has been applied to the quadratic boost converter [5], bridgeless converter [6], dual-active-bridge converter [7], four-quadrant quasi-Z-source converter [8], and MPPT of photovoltaic systems [9]. A nonlinear controller that combines backstepping and DI-SMC techniques for dc-dc boost converters has been proposed in [10]. Previous research endeavors have presented robust control design techniques, but they fall short of developing systematic design procedures that are suitable for low-cost commercial and industrial applications. In [11], a double-integral sliding surface for indirect analog SMC for dc-dc converters was introduced. However, the control scheme requires two PI compensators and an output capacitor current, which increase the control complexity and analog implementation cost. In addition, the capacitor current sensor degrades the power converter efficiency via increasing the effective series resistance (ESR) value in the capacitor branch [4]. The PI-SMC method has been proposed for boost converter [12], SEPIC converter [13], three-level converter [14], third-order super-lift Luo converter [15], fourth-order Cuk converter [16], and multiport power supply system [17]. The modified PI-SMC of hybrid boost converter [18], hybrid DI-SMC of buck converter [19], hierarchal PI-SMC of buck converter [20], and PI Hyperplane SMC of buck-boost converter [21] have been reported. Cascaded PI-SMC schemes have also been introduced for classical dc-dc boost [22] and buck-boost [23] converters. However, the detailed design procedure and analog realization of the control law were not reported. Considering digital and intelligent control methods, a digital PI-SMC using an interpolation-predictive strategy was given in [24]. Furthermore, the SMC has been incorporated with advanced techniques such as nonlinear deep reinforcement learning [25], extended state observer [26], particle swarm optimization [27], genetic algorithm [28], and fuzzy neural network [29]. The intelligent controls provide reliable methods to tune the controller gains according to the operating conditions, but the complexity of the practical implementation increases dramatically. The nonlinear control schemes in the previous endeavors also fall short of introducing robust DI-SMC methods that can be translated into analog circuits. Analog DI-SMC circuits have been introduced in [3; 10] for dc-dc converters, but the presence of double-PI compensators and an output capacitor current branch in the control scheme were unavoidable issues.