This paper discusses a systematic control design for a three-phase L-filtered grid-connected inverter using linear matrix inequality-based optimization method. A state feedback control is employed to provide stability to the inverter system and with the inclusion of integral control the offset error can be eliminated. In addition, the proposed control is implemented in dq-synchronous frame with help from a phase locked-loop to track the grid phase angle. The optimization criterion of this proposed control is to reduce the convergence time to the steady state as short as possible. The set of robust stabilizing gain is systematically discussed in this paper and computed using MATLAB toolbox. Then, the effectiveness of this proposed control algorithm is verified by implementing on PSIM simulation tool.

This paper presents a new method to determine the control inputs and control gains of robust tracking control-based interpolation control. To obtain the proposed control input, the implement two different types of control gains are needed, tight and loose gains. A linear matrix inequality (LMI) is considered with input constraint, feasibility, and invariant sets to define the control inputs of tight gain and loose gain in the sense of robust tracking control. Thus, in simulations, if the control input of tight gain satisfies the input constraint, no interpolation is needed. Then, the tight control can be used directly to start the inverter system. In contrast, if the control input with tight gain is infeasible then the implementation of a new technique is needed to define the control input based on tight and loose control gains. By interpolating between these two control inputs, a new set of control input which is called interpolation-based control is created. Finally, by using the interpolation an exceptional performance is yielded for the output response, satisfies with input constraint, and has a broad enough size of an invariant set. In this work, a MATLAB, PSIM simulation is conducted to verify the efficacy of the control algorithms.

Uncertain grid impedance is often common in power distribution networks; therefore, it is crucial to design an efficient controller in this situation. An issue that frequently occurs is the problem of unpredictable grid impedance, which can cause voltage fluctuations, power quality problems, and potential damage to equipment. This work provides a systematic control strategy to tackle these issues by supplying well-regulated power from a DC source to an AC power grid. A linear matrix inequality (LMI)-based robust optimal control is proposed in this paper to provide stability to the inverter system without offset error at the output side. The convergence time to steady state is minimized by solving the LMI problem to maximize the eigen value of the closed-loop system with the inclusion of the uncertainty of the filter parameter and grid impedance. Furthermore, the uncertainties in this study include the potential variation of values for the filters and the grid's impedance. These uncertainties occur because the grid impedance can fluctuate fast in the event of a fault or termination of a transmission line, while the filter's impedance can also be affected by changes in operating temperature. The simulation study of this proposed control includes a comparison between wide and narrow uncertainty ranges, as well as a performance comparison under uncertain parameters. Furthermore, this approach exhibits a lower power ripple in comparison to existing PI control method.

This paper proposes a systematic control design for a single-phase LC-filtered inverter considering uncertain system parameters. One major difficulty in controlling single-phase power converters is the lack of a direct conversion method for transforming single-phase signals into dq-frame signals. By employing an all-pass filter in this proposed approach, it is possible to control the output voltage in terms of DC quantity or the dq-rotating frame. Furthermore, voltage stability and harmonic distortion (THD) minimization of the uninterruptible power supply (UPS) are major concerns in inverter design. Therefore, this controller uses integral action to get rid of steady-state errors and stabilize the closed-loop system by the state feedback control. In order to enlarge and guarantee the stability range in the presence of potential parameter fluctuations, an uncertainty model is being considered. In this context, the uncertainty models refer to the potential model with variations in the filter's inductance and capacitance caused by operating temperature, aging, and various external factors. The efficacy of the control approach is assessed through simulations and experiments, with the objective of comparing its results with those of the PI control using a control board featuring a TMS320F28335 digital signal processor. Consequently, the proposed approach offers lower THD at every load step with lesser afford in performance tuning in comparison to the PI method.

Grid impedance variation has the possibility of leading to voltage oscillation and control instability, which poses a serious problem to electric vehicle (EV) charger design. In response to this problem, this paper proposes a robust control approach that is capable of dealing with grid impedance variation and system uncertainties. The proposed dual-loop control strategy is composed of an outer-loop proportional–integral (PI) controller and an inner-loop robust state feedback controller with integral action. The benefits of control are maximized according to linear matrix inequality (LMI) techniques. This paper aims to address the effects of grid impedance variation by including the uncertainty model considering the potential varying parameters in the control design process. Additionally, the uncertainty model considers sixteen possible sets, which are described by variations in the four most important parameters: grid impedance, grid resistance, filter impedance, and filter resistance. The simulations suggest that the proposed controller maintains stable current regulation for uncertainty factors as high as γ = 3.3, where all closed-loop poles remain within the unit circle. For all the tested uncertainty levels, the grid-current tracks the reference of 10 A with a faster settling time at γ = 1.1 and no overshoot for higher uncertainty levels.