Date of Defense
30-4-2025 5:00 PM
Location
Al Jahili Hall (F1 – 1043)
Document Type
Thesis Defense
Degree Name
Master of Science in Mechanical Engineering (MSME)
College
College of Engineering
Department
Mechanical and Aerospace Engineering
First Advisor
Prof. Khalifa Harib
Keywords
Double Inverted Pendulum, Underactuated Mechanical System, Nonlinear Control, Rotary Inverted Pendulum, Feedforward Control, Optimal Control.
Abstract
This thesis is concerned with investigation of the swing-up control problem of underactuated mechanical systems namely the double rotary inverted pendulum using the optimal control theory. The research aims to develop a robust controller to achieve the swing-up and stabilization of the pendulum in the upright unstable equilibrium position while regulating the angular displacement of the rotating arm and the two pendulum angles. The performance of the designed controller was evaluated through numerical simulations in the MATLAB/Simulink environment. A comprehensive review of the literature was conducted and the challenges that researchers face in the control of underactuated mechanical systems were discussed and identified. Kinematic and kinetic analysis were then performed to derive the equations of motion of the system, which were represented in a standard input-output form suitable for controller design. A swing-up control scheme was then developed and employed in the form of a feedforward controller derived from solving a two-point boundary value optimization problem across the pendulum equilibrium points for a fixed swing-up time. The feedforward controller was then paired with a time-varying feedback controller based on a linear-quadratic regulator method in which the double rotary inverted pendulum system tracks the pre-calculated desired trajectories for the angular displacements and velocities for all pendulum joints. This was achieved through linearizing the equations of motion around the entirety of the input and output desired trajectories yielding the time-varying feedback gains which were used in the gain scheduling. The simulation results obtained in MATLAB/Simulink were shown to be indicative of the capability of the designed controller to perform a successful swing-up and stabilizing maneuver for the double rotary inverted pendulum, while exhibiting excellent trajectory tracking and disturbance rejection during the swing-up and steady state phases respectively. The simulation study also showed that the methods adopted in this research produced results that are matching results of attempts presented in the literature for swinging up double inverted pendulum systems such as the double inverted pendulum on a cart. This was attributed to the accurate modelling of the system and the successful implementation of the feedforward control and the optimization of the feedback control gain scheduling. In addition, a virtual model of the system was constructed in MATLAB/Simscape to validate the controller performance in a semi-empirical environment where the link parameters and mechanical properties were inherited from the three-dimensional model directly without approximation. The results obtained from the virtual model validation showed good agreement with the results obtained from numerical simulations but with slightly higher torque values as measured at the rotating arm’s joint. The work presented in this thesis not only served to verify the controller’s effectiveness in achieving the complex swing-up maneuver but also provided valuable insights into potential challenges to be addressed in order to bridge between theory, simulations, and real-world implementations. With limited number of experimental validations performed for this system, a prototype of an experimental setup is currently under development at the United Arab Emirates University, which is planned to be used as a future continuation of the current work to experimentally validate the results presented here.
INVESTIGATION OF CONTROL STRATEGIES FOR SWING-UP MANEUVER OF A DOUBLE INVERTED PENDULUM ON ROTATING LINK
Al Jahili Hall (F1 – 1043)
This thesis is concerned with investigation of the swing-up control problem of underactuated mechanical systems namely the double rotary inverted pendulum using the optimal control theory. The research aims to develop a robust controller to achieve the swing-up and stabilization of the pendulum in the upright unstable equilibrium position while regulating the angular displacement of the rotating arm and the two pendulum angles. The performance of the designed controller was evaluated through numerical simulations in the MATLAB/Simulink environment. A comprehensive review of the literature was conducted and the challenges that researchers face in the control of underactuated mechanical systems were discussed and identified. Kinematic and kinetic analysis were then performed to derive the equations of motion of the system, which were represented in a standard input-output form suitable for controller design. A swing-up control scheme was then developed and employed in the form of a feedforward controller derived from solving a two-point boundary value optimization problem across the pendulum equilibrium points for a fixed swing-up time. The feedforward controller was then paired with a time-varying feedback controller based on a linear-quadratic regulator method in which the double rotary inverted pendulum system tracks the pre-calculated desired trajectories for the angular displacements and velocities for all pendulum joints. This was achieved through linearizing the equations of motion around the entirety of the input and output desired trajectories yielding the time-varying feedback gains which were used in the gain scheduling. The simulation results obtained in MATLAB/Simulink were shown to be indicative of the capability of the designed controller to perform a successful swing-up and stabilizing maneuver for the double rotary inverted pendulum, while exhibiting excellent trajectory tracking and disturbance rejection during the swing-up and steady state phases respectively. The simulation study also showed that the methods adopted in this research produced results that are matching results of attempts presented in the literature for swinging up double inverted pendulum systems such as the double inverted pendulum on a cart. This was attributed to the accurate modelling of the system and the successful implementation of the feedforward control and the optimization of the feedback control gain scheduling. In addition, a virtual model of the system was constructed in MATLAB/Simscape to validate the controller performance in a semi-empirical environment where the link parameters and mechanical properties were inherited from the three-dimensional model directly without approximation. The results obtained from the virtual model validation showed good agreement with the results obtained from numerical simulations but with slightly higher torque values as measured at the rotating arm’s joint. The work presented in this thesis not only served to verify the controller’s effectiveness in achieving the complex swing-up maneuver but also provided valuable insights into potential challenges to be addressed in order to bridge between theory, simulations, and real-world implementations. With limited number of experimental validations performed for this system, a prototype of an experimental setup is currently under development at the United Arab Emirates University, which is planned to be used as a future continuation of the current work to experimentally validate the results presented here.