*3.2. Observer-Based Sliding-Mode Control (SMC) Design*

This section's control objective is to design a generalized proportional integral observer to estimate the time-varying disturbance and update it into the controller in real time, so as to effectively suppress the influence of the disturbance and improve the anti-jamming performance of the whole system.

Sliding-mode control uses the designed control function to make the motion state of the system in "sliding mode", which is a discontinuous switching control, so it is also called sliding-mode variable structure control. The basic idea of the sliding-mode variable structure control theory is to consider a nonlinear system and assume that there is a phase plane, which is called the sliding-mode surface, and a point in the plane is called a balance point. Using this sliding surface as a reference path, through effective design, the state variable of the system, i.e., the controlled trajectory, is attracted to slide along the set trajectory of the reference path and converges to the equilibrium point, regardless of the initial state of the system [32–34].

The sliding-mode control needs to meet the following three basic conditions: existence, accessibility, and stability. Existence refers to the existence of a sliding surface in a system. Reachability refers to the ability of points outside the sliding surface of a system state to move to the sliding surface within a finite time [35–39]. Stability refers to the ultimate stability of the system state under model control.

For the sliding-mode control, the first step is to determine the sliding surface and select the appropriate sliding-surface function, s(x). Under the action of different control functions, the trajectory of the system moves differently. As shown in Figure 10a, by designing appropriate control functions, the system can start from an arbitrary initial point, x0, in the state space and reach the switching surface (as shown in the x0→A section) in a finite time. This process is called the approach section. Once the system trajectory reaches the switching surface, it stays on it and continues to move, and this is called the slidingmode section (as shown in section A→O). The state of the system moving on the switching surface is called the sliding mode. Since the switching surface is designed according to the expected moving target of the system, no matter how the external parameters change, the system trajectory will eventually reach the preset value on the switching surface [40–43].

**Figure 10.** System motion under sliding-mode control: (**a**) the motion trajectory of the system on the sliding surface and (**b**) three types of points on the sliding surface.

In the state space, take s(x) = 0 as the sliding surface, which represents the state, as shown in Figure 10b. The space is divided into two: s(x) > 0 and s(x) < 0. The motion points on the sliding surface can be divided into three categories:


In the study of sliding-mode control, the first two types of motion points have little significance for system control and are generally ignored. If a certain area on the slidingmode surface is all termination points, it means that once the system state moves near that area, it will be attracted to the area, and this area is therefore called the "sliding mode area". Due to the fact that all points on the sliding-mode area are termination points, when the system moves near the sliding surface, there will inevitably be lim*s*→<sup>0</sup> *s* . *s* < 0 [44–46].

The specific system control is shown in Figure 11. The system block diagram includes four parts: two generalized proportional integral observers, a sliding-mode controller, a pulse width modulator (PWM), and a three-phase interleaved parallel DC/DC converter. The system works as follows: Firstly, two generalized proportional integral observers are constructed based on the feedback values of inductance current and output voltage, and the matched and unmatched disturbances are estimated, respectively. Then, a sliding-mode controller is designed using the estimated values. The controller is compared with the sawblade wave to obtain a PWM wave, and the switching tube of the DC stepdown converter is controlled by the PWM wave. The converter can output the desired voltage stably.

**Figure 11.** Control block diagram of the whole system.
