For some of the example problems in this tutorial, animations of their physical responses have been made. These animations are "encased" in a Graphic User Interface (GUI) which allows for easier use. These GUIs allow the user to change various control parameters and view the response of the system. These are intended to provide a better understanding of what various control techniques change in the actual physical system. Along with the animations, response plots are also included.
The goal of the Bus Suspension example is to create a suspension system that when subjected to a step disturbance will return to its original position quickly and without large oscillations. This is achieved by adding an actuator between the suspension and the bus. For a complete discussion of the bus suspension model and control goals, please refer to the Bus Suspension: System Modeling page. The animation of this system and the control methods used in the GUI use the root locus method. To better understand what is happening in the animation it is suggested that you refer to the Bus Suspension: Root Locus Controller Design page.
The Inverted Pendulum example is made up of a cart and a pendulum. The goal of the controller is to move the cart to its commanded position without causing the pendulum to tip over. In open loop this system is unstable. For a detailed description of the inverted pendulum model and the equations of motion please refer to the Inverted Pendulum: System Modeling page. The animation and control techniques make use of the state-space equations and full state feedback. The feedback control law is determined using the lqr command found in the MATLAB Control System Toolbox. For a better understanding of how the system is controlled consult the Inverted Pendulum: State-Space Controller Design page.
The goal of the pitch controller example is to change the pitch angle of an airplane. This is achieved by adjusting the aircraft's elevator control surfaces. The aircraft is required to pitch up with little overshoot and a fast settling time. For a detailed description of the aircraft pitch model, equations of motion, and design criteria, please refer to the Aircraft Pitch: System Modeling page. The animation and control techniques use the state-space equations and full state feedback. The feedback control law is determined using the MATLAB lqr command. For a better understanding of how the system is controlled, consult the Aircraft Pitch: State-Space Controller Design page.
The goal of the Ball & Beam experiment is to control the position of a ball rolling on a beam by controlling the orientation of the beam. This system can be modeled by a double integrator and is unstable in open-loop. For the animation we are controlling the beam through a torque applied at the center of the beam. For a detailed description of the ball & beam model and the equations of motion, please refer to the Ball & Beam: System Modeling page. The system is controlled using full state feedback with reference input. For more information on the control method used for the animation consult the Ball & Beam: State-Space Controller Design page.