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Research paper thumbnail of State space control using LQR method for a cart-inverted pendulum linearised model

The Cart-Inverted Pendulum System (CIPS) is a classical benchmark control problem. Its dynamics r... more The Cart-Inverted Pendulum System (CIPS) is a classical benchmark control problem. Its dynamics resembles with that of many real world systems of interest like missile launchers, pendubots, human walking and segways and many more. The control of this system is challenging as it is highly unstable, highly non-linear, non-minimum phase system and underactuated. Furthermore, the physical constraints on the track position also pose complexity in its control design. This paper presents a control method to stabilise the unstable CIPS within the different physical constraints such as in track length and control voltage. A novel cart-inverted pendulum model is proposed where mechanical transmission and a dc motor mathematical model have been included which resembles the real inverted pendulum. Therefore problems emerged in realtime implementation can be minimised. A systematic the state feedback design method by choosing weighting matrices key to the Linear Quadratic Regulator (LQR) design is presented. Simulation experiments have been conducted to verify the controller's performances. From the obtained simulation and experiments it is seen that the proposed method can perform well stabilising the pendulum at the upright angle position while maintaining the cart at the desired position.

Research paper thumbnail of State space control using LQR method for a cart-inverted pendulum linearised model

The Cart-Inverted Pendulum System (CIPS) is a classical benchmark control problem. Its dynamics r... more The Cart-Inverted Pendulum System (CIPS) is a classical benchmark control problem. Its dynamics resembles with that of many real world systems of interest like missile launchers, pendubots, human walking and segways and many more. The control of this system is challenging as it is highly unstable, highly non-linear, non-minimum phase system and underactuated. Furthermore, the physical constraints on the track position also pose complexity in its control design. This paper presents a control method to stabilise the unstable CIPS within the different physical constraints such as in track length and control voltage. A novel cart-inverted pendulum model is proposed where mechanical transmission and a dc motor mathematical model have been included which resembles the real inverted pendulum. Therefore problems emerged in realtime implementation can be minimised. A systematic the state feedback design method by choosing weighting matrices key to the Linear Quadratic Regulator (LQR) design is presented. Simulation experiments have been conducted to verify the controller's performances. From the obtained simulation and experiments it is seen that the proposed method can perform well stabilising the pendulum at the upright angle position while maintaining the cart at the desired position.

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