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.

In this paper, a robust dual-current control is proposed for a three-phase grid-tied inverter under unbalanced grid voltage. To compensate the unbalanced grid current rooted by the grid voltage dips or faults, an additional negative sequence compensator is considered in this proposed controller. The current control for both positive and negative sequence utilizes state feedback with integral control to archive fast reference tracking without steady-state error. The robust control gain is computed by solving a linear matrix inequality-based optimization problem to obtain fast convergence rate in the presence of the uncertainty of the system. The positive sequence current reference is used to regulate the amount of current flow from DC source to the grid, and the zero negative sequence reference is used to compensate the unbalanced grid current. To verify the efficacy of this control method, a comparison between the proposed robust dual-current control and robust current control without negative sequence compensator is conducted using simulation.

The dq-synchronous frame method is a widely used framework for three-phase converters due to its DC like character. However, a single-phase wave form cannot be converted directly into a dq-signal. Thus, this proposed controller utilizes all-pass filters to create imaginary B-signals from the original AC voltage and current. Then, aB-signals can be simply converted into dq-signals using the transform matrix. This proposed controller consists of a double loops control, robust inner loop, and outer loop PI control. The robust control uses state feedback with integral control to eliminate steady state error and bring stability to the system. The gains of controller determine by solving optimization problem so that the convergence time is minimize with the presence of uncertainty of the L-filter. The simulation studies are conducted to verify the efficiency of the proposed method using 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.