# Robust Optimal Tracking Control of a Full-Bridge DC-AC Converter
## 1 Introduction  
Full-bridge DC-AC converters have been widely used in mechatronic energy systems, such as high concentration photovoltaic (PV) systems, vertical axis wind turbine (VAWT) systems, and hybrid electric vehicles [1, 2, 3, 4]. It is critical for the reliable and efficient operation of these systems and their interconnection with the future power grid to ensure global welfare and sustainability. The requirements for high performance DC-AC converter systems are usually based on the following criteria: (1) Output voltage waveform with low total harmonic distortion (THD). (2) Fast transient response in case of sudden load change. (3) Steady-state errors should be as small as possible. Take the example of PV systems, the essential task of the full-bridge DC-AC converter allows the conversion amidst DC (direct current) power input produced by the PV array and a sinusoidal AC (alternating current) power output with controllable magnitude and frequency. A single-stage DC-AC converter converts DC to AC without the need for an intermediate stage. A two-stage DC-AC converter is structured by a DC-DC converter plus a DC-AC converter. The first-stage DC-DC converter supplies the maximum power processed by the maximum power pointtracking (MPPT) algorithm to the second-stage DC-AC converter, and also regulates the DC bus voltage. Whether it is a type of the single-stage or two-stage DC-AC converter, the closed-loop control technology must be employed to construct a high-quality DC-AC converter output-voltage, even under non-linear loads. The robust repetitive method has been proposed for voltage control of the power inverter. This methodology is effective in ameliorating the dynamic behavior of the system, but steady-state errors may still occur in the presence of uncertain interruption conditions [5]. A bang-bang control strategy based on the adaptive concept is proposed to establish a good micro-grid steady-state response. However, its algorithm requires time-consuming calculations and complicated models [6]. In order to produce satisfactory transient and steady-state responses, the iterative learning closed-loop control technique is used for the design of uninterruptible power supply (UPS) inverters. This technique demands exceedingly precise system parameters and modeling [7]. The high stability of the boost converter is insured by the H-Infinity control, which has been recommended. It adopts dual control loops to achieve superior command tracking while subjected to load perturbations, but such an algorithm exposes the difficulty and complexity of the implementation [8]. A mu-synthesis scheme with reduced-order characteristic and decreased cost is developed to enhance the performance of a boost converter controlled by an H-infinity controller. Although the boost output exhibits good dynamics features in the presence of input-voltage variations and sudden load changes, the problem of steady-state errors needs to be improved [9]. Robust design has been clarified by various researchers, and a worthy reference in the literature [10] has also compared and studied robust design optimization techniques. Dr. [PERSON] first introduced robust design methods to some leading industries in the United States, thus reforming the procedure design quality of production and manufacture. Although [PERSON]'s method is easy to use, it can only acquire related consequences, and cannot accurately explain what parameters have the greatest impact on the eigenvalues of the performance [11]. Regarding robust design, while diverse researchers have employed varying representations, the implication is alike. The mutual feature in these expressions shows that it is not sensitive to changes in the robust design and such notion has been embraced by the engineering fields. Technologies of robust design have been evolved using established design principles, as the following three types.