This paper investigates the benefits of using non-dimension analysis to develop a control law for a flexible electro-mechanical system. The system that is analyzed consists of a DC motor connected to a load inertia through a set of gears. A state space system model is derived using LaGrange's equation and then non-dimensionalized using a linear transformation. The resulting system model reveals the system character more clearly through the resulting dimensionless parameters. The parameters highlight the interaction between system properties and motor constants and demonstrate the benefits of a concurrent mechatronics design process. Open-loop behavior is analyzed and an optimal value for these paramaters can be found by varying the gear ratio. Once the best possible gear ratio is determined, a PID control law is developed and the closed loop performance is analyzed. With the optimal gear ratio, the power required to control the system is minimized. Also, dynamic inversion is applied to control the system. Dynamic inversion requires a square "B" matrix in the state space model. A new method to apply dynamic inversion to a system with a non-square "B" matrix is demonstrated. To make the matrix invertible, a linear transform is applied to the state space model. A Linear-Quadratic Regulator (LQR) design method is applied to find the transformation matrix values that will make the "B" matrix invertible. The power consumption of this control law is also minimized when the system contains the optimal gear ratio.
Library of Congress Subject Headings
Electromechanical devices--Dynamics; Mechatronics; H2 control
Mechanical Engineering (MS)
Department, Program, or Center
Mechanical Engineering (KGCOE)
Wilson, Michael H., "Enhanced closed loop performance using non-dimensional analysis" (2004). Thesis. Rochester Institute of Technology. Accessed from
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