Linear Motor Driven Inverted Pendulum and LQR Controller Design

Modeling and control of a pneumatically actuated inverted pendulum

“…For the purpose of state feedback controller design, the nonlinear state variable model (9) is linearized in the vicinity of the unstable equilibrium point (upright position, θ = 0). For small deflection angles θ, the following approximations are valid: sin…”

“…In order to control all the states of the inverted pendulum, a linear state feedback controller based on the linearized inverted pendulum model can be used [7,9], and may also be extended with a disturbance observer [1] to improve the disturbance rejection performance. However, this type of controller may not be suitable for the case of large pendulum deflection angles from the equilibrium point, because in that case the linear model may not be valid.…”

“…Alternative, lower-bandwidth actuators, such as those based on pneumatic or hydraulic motors, were not considered. Typically, the deflection angle and speed of the inverted pendulum, and the speed and position of the pendulum platform were measured by means of absolute or incremental encoders [1,3,9,12,13,[20][21][22]. Additional sensors (such as gyroscopes) have been added in the special case of the two-wheeled mobile robot in order to improve its disturbance rejection [1].…”

“…Those included the following: inherent large bandwidth. These included the following: a DC servomotor linked to the pendulum platform (cart) via appropriate linking mechanism [8], or directly linked to the wheels of the pendulum-like wheeled mobile robot [1], a DC linear motor [9,22], a vector-controlled AC induction motor [19], and a permanent magnet servo-motor (PMSM) [13,21] linked to the rail-mounted inverted pendulum. Alternative, lower-bandwidth actuators, such as those based on pneumatic or hydraulic motors, were not considered.…”

A bio-inspired active tail control actuator for nano air vehicles

“…The inverted pendulum is a well-known control problem used as a standard test for control algorithms assessment [5]. Typical methods of balancing an inverted pendulum include using a translating/rotating base [6] or reaction wheel [7]. However, these systems are typically quite bulky and utilize multiple sensors to determine the complete state of the system at all times.…”