Stabilization of the Cart-Inverted-Pendulum System Using State-Feedback Pole-Independent MPC Controllers

Area of Science:

• Control Systems Engineering
• Robotics
• Applied Mathematics

Background:

• The cart-inverted-pendulum is a benchmark system for control strategies.
• Stabilizing such systems requires robust and efficient control algorithms.
• Existing methods often face limitations in achieving desired performance trade-offs.

Purpose of the Study:

• To propose a novel pole-independent, single-input, multi-output (SIMO) explicit linear Model Predictive Control (MPC) controller.
• To enhance the stability and performance of the fourth-order cart-inverted-pendulum system.
• To develop an MPC controller with tunable parameters for specific performance objectives.

Main Methods:

• A generalized prediction model was developed to address stability issues.
• Four tuning parameters were introduced: horizon time, relative cart-pendulum weight, pendulum velocity weight, and cart velocity weight.
• Two parameters were automatically adjusted for gain margin and pendulum response, while the others remained tunable.
• The proposed SIMO MPC controller was compared against optimal control methods.

Main Results:

• The proposed SIMO MPC controller demonstrated superior average peak efficiency compared to optimal control methods.
• The controller achieved a system gain margin exceeding the limits of other compared controllers.
• Performance trade-offs were observed, with slightly reduced speed efficiency for enhanced peak efficiency and gain margin.

Conclusions:

• The developed explicit linear MPC controller provides an effective solution for stabilizing the cart-inverted-pendulum system.
• The controller offers a favorable balance between peak efficiency and speed efficiency, with adjustable gain margins.
• This approach presents a significant advancement in control strategies for complex dynamic systems.