This work presents the design and construction of a Furuta Pendulum, its mathematical modelling and acquisition of its physical parameters with subsequent synthesis and simulation of a control method using the linear quadratic regulator (LQR). The inverted pendulum system can be divided into two subsystems, the mechanical subsystem, consisting of a rotating arm and pendulum and the electromechanical subsystem, composed of the direct current (DC) motor - the plant actuator. The modelling of the mechanical subsystem is performed using the Lagrangian of the system. Regarding the modelling of the electromechanical subsystem, the approach is carried out through the identification of the dynamic equations of its electrical and mechanical components. The representation for both subsystems will be made in state space. After modelling the subsystems, the design of a real system will be covered, its parameters will be obtained through experimental and mathematical methods for the different components of the subsystems. The LQR control approach to the controllable system has the purpose of placing the poles of this system in strategic positions, this resource uses an optimal process and excludes the trial and error associated with the also known Pole Placement method. The LQR controller seeks to minimize or not the system cost function by manipulating the steady state error and
energy expended by the actuator. The simulation of the control method presented in this work is capable of generating a satisfactory and robust control, allowing manipulation of the system’s performance and availability of energy for the actuator to guarantee this operation through the
cost function.
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