Abstract
In this paper, a model is described for a system consisting of an inverted pendulum attached to a cart. We design for this model a feedback optimal control based on Linear Quadratic regulator, LQR by using the generating Function technique. This design with hard and soft constraints will help the pendulum to stabilize in the upright position. A solution of the continuous low-thrust optimal control problem based on LQR method is implemented. An example applied to this control design for a hard constraint boundary condition.
Highlights
The traditional problem for the field of control systems is the inverted pendulum system see e.g. [1], [3], [5], [6] and [9]
Both the torque and the force produced from the motor of the cart are the feedback-control forces. there are two equilibrium points for the inverted pendulum system, one of them is that when the pendulum is pointing downwards which is stable, the other one is at the upwards position which is unstable
The feedback control of inverted pendulum control system is made by linearizing the dynamics about the nominal trajectory and by applying the classic control theory to such linear dynamical system
Summary
The traditional problem for the field of control systems is the inverted pendulum system see e.g. [1] , [3] , [5] , [6] and [9]. The system is consist of an inverted pendulum exposed to a torque and attached to a cart which equipped with a motor that drives it along a friction horizontal track. Both the torque and the force produced from the motor of the cart are the feedback-control forces. There are two equilibrium points for the inverted pendulum system, one of them is that when the pendulum is pointing downwards which is stable, the other one is at the upwards position which is unstable. The unstable equilibrium corresponds to a state in which the pendulum points strictly upwards and, requires a control force to maintain this position. In order to use the feedback optimal control approach the lateral dynamics is expressed in a state vector form with adding the control forces to the equations of motion
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