Linear Motor Driven Inverted Pendulum and LQR Controller Design

Inverted pendulum can verify the effectiveness of controllers. Traditional inverted pendulum is driven by a rotational motor, and its control performance is influenced by the friction and gap of transmission mechanism. We proposed an innovative Direct Driven Inverted Pendulum (dDIP) which consists of an inverted pendulum (IP) mounted on a stage driven by an ironless permanent magnet linear synchronous motor (IPMLSM). In this paper, the structure of dDIP is first analyzed and its mathematic model is built. Then, a LQR controller is designed and numerical simulations in MATLAB are carried out. Finally, the dDIP is successfully controlled by a dSPACE controller and also a TI28DSP based control card. The results show that the dDIP can be stabilized to its upright position and at the same time the cart's displacement can be also regulated to zero after exerting a step disturbance to the dDIP. Experiments show that the transition time is within 4s, which indicates that dDIP has excellent dynamic characteristics that can not be reached by a traditional IP.