This paper proposes a frequency-adaptive current control design for a grid-connected inverter with an inductive–capacitive–inductive (LCL) filter to overcome the issues relating to both the harmonic distortion and frequency variation in the grid voltage. The current control scheme consists of full-state feedback control to stabilize the system and integral control terms to track the reference in the presence of disturbance and uncertainty. In addition, the current controller is augmented with resonant control terms to mitigate the harmonic component. The control scheme is implemented in the synchronous reference frame (SRF) to effectively compensate two harmonic orders at the same time by using only one resonant term. Moreover, to tackle the frequency variation issue in grid voltage, the frequency information which is extracted from the phase-locked loop (PLL) block is processed by a moving average filter (MAF) for the purpose of eliminating the frequency fluctuation caused by the harmonically distorted grid voltage. The filtered frequency information is employed to synthesize the resonant controller, even in the environment of frequency variation. To implement full-state feedback control for a grid-connected inverter with an LCL filter, all the state variables should be available. However, the increase in number of sensing devices leads to the rise of cost and complexity for hardware implementation. To overcome this challenge, a discrete-time full-state current observer is introduced to estimate all the system states. When the grid frequency is subject to variation, the discrete-time implementation of the observer in the SRF requires an online discretization process because the system matrix in the SRF includes frequency information. This results in a heavy computational burden for the controller. To resolve such a difficulty, a discrete-time observer in the stationary reference frame is employed in the proposed scheme. In the stationary frame, the discretization of the system model can be accomplished with a simple offline method even in the presence of frequency variation since the system matrix does not include the frequency. To select desirable gains for the full-state feedback controller and full-state observer, an optimal linear quadratic control approach is applied. To validate the practical effectiveness of the proposed frequency-adaptive control, simulation and experimental results are presented.

This paper presents a frequency-adaptive current control design for a grid-connected inverter (GCI) with an inductive-capacitive-inductive (LCL) filter in the presence of grid disturbance such as the grid frequency variation and grid voltage harmonic distortion as well as polytopic uncertainties in the LCL filter parameters. The grid current control is achieved by augmenting integral and resonant terms into the LCL-filtered inverter system model to constitute integral-resonant full-state feedback control for zero steady-state error and current harmonic attenuation. To realize the full-state feedback control, the information on all the state variables is essential. However, additional sensors for state measurements increase the implementation cost as well as the complexity. To overcome this issue, a full-state discrete-time observer is employed in the stationary reference frame. Furthermore, to maintain the quality of grid currents injected into the grid, a frequency-adaptive current control is introduced. For this aim, the grid frequency is estimated through an adaptive observer rapidly and precisely. Then, the estimated grid frequency is used to adaptively change the frequency information in the augmented resonant controller for the purpose of producing high-quality grid currents even under both distorted grid voltages and grid frequency variation. In addition, to ensure the robustness against LCL filter parameter perturbation, a linear matrix inequalitylinear quadratic regulator (LMI-LQR) approach is proposed for polytopic uncertainties in the LCL filter parameters to design full-state feedback control as well as a full-state observer. To verify the effectiveness of the proposed control scheme, the simulation and experimental results are given. INDEX TERMSAdaptive observer, frequency-adaptive control, grid-connected inverter, linear matrix inequality (LMI), polytopic uncertainties.

AbstrakPendulum terbalik memiliki pusat gravitasi yang berada diatas poros putar sehingga menyebabkan pendulum terbalik tidak seimbang. Suatu kendali khusus dibutuhkan agar pendulum seimbang dengan cara menggerakkan kereta beroda yang menjadi tumpuan dari pendulum. Penerapan pendulum terbalik dapat ditemui pada balancing robot. Tujuan dari penelitian ini adalah merancang bangun sebuah sistem pengendalian robot dengan dua roda menggunakan sistem kendali untuk membuat robot yang seimbang (balancing robot).            Sistem ini mempunyai masukan akselerometer yang digunakan untuk mengukur percepatan sudut (m/s2) dan giroskop untuk mengukur kecepatan sudut (rad/s). Luaran dari akselerometer dan giroskop digabungkan dengan metode complementary filter untuk mendapatkan nilai sudut. Sudut yang diperoleh kemudian dibandingkan dengan set point yang nilainya 0o. Nilai selisih dari set point dan sudut complementary filter diolah menggunakan metode kendali Proporsional Integral Derivatif. Proses kendali PID ini diprogram pada Arduino IDE yang hasilnya diumpankan ke motor DC untuk mengatur kecepatan putar motor DC. Untuk arah putar motor DC ditentukan apabila sudut complementary filter kurang dari nol, maka motor akan berputar mundur. Sedangkan jika sudut complementary filter lebih dari nol, maka motor akan berputar maju.            Nilai konstanta PID berdasarkan hasil tuning  dengan metode Ziegler-Nichols metode osilasi adalah Kp=1.5, Ki=0.75, Kd=1.85 dan nilai koefisien pada algoritma complementary filter adalah a=0.96. Kata kunci—inverted pendulum, balancing robot, kendali PID, IMU, complementary filter Abstract            Center of gravity’s inverted pendulum is located above its pivot point therefore inverted pendulum is unstable. Specific control is needed so that inverted pendulum stable which is by move the cart where the pendulum is mounted. Inverted pendulum application can be found in balancing robot. The purpose of this research is to design a system to control a two wheeled robot using the control system to balance it.The inputs are accelerometer to measure angular acceleration (m/s2) and gyroskop to measure angular velocity (rad/s). The output’s of accelerometer and gyroscope are fused by complementary filter algorithm method to get the actual angle. The actual angle is then compared to set point which is 0o. The differences between set point and actual angle are processed using Proportional Integral Derivative control method. The process of PID control is programmed using Arduino IDE which its result is fed to DC motors. The direction of DC motors are determined by two conditions, if actual angle less than zero then DC motors will spin backwards. Whereas if actual angle more than zero then DC motors will spin forward.             The PID control’s constans value based on Ziegler-Nichols Oscillation tuning method are Kp=1.5, Ki=0.75, Kd=1.875 and complementary filter’s coefficient is a=0.96. Keywords— inverted pendulum, balancing robot, PID control, IMU, complementary filter