Texas A & M University Department of Mechanical Engineering MEEN 651 Control System Design Dr . Alexander G . Parlos

The objective of this lecture is to present some of the most fundamental elements of control loops, including open-loop and closed-loop (or feedback) control. There are two basis structures for control of dynamic systems: (a) open-loop control and (b) feedback (or closed-loop) control. These two control structures are shown in Figures 1 and 2. Let us write the equations of motion for a DC motor coupled to an inertial load. The electrical dynamics can be expressed as K e ˙ θ m (t) + L a di a (t) dt + R a i a (t) = v a (t), (1) whereas the mechanical dynamics can be expressed as J m ¨ θ m (t) + b ˙ θ m (t) = K t i a (t) + T ℓ. Let us define the output to the motor speed y(t) = ˙ θ m (t) and let's name the motor load as the disturbance w(t) = T ℓ. Taking the Laplace transforms of equations (1) and (2) and eliminating the current I a (s) we obtain an equation of the form 1 (J m L a bR a + K t K e s 2 + J m R a + bL a bR a + K t K e s + 1)Y (s) = = K t bR a + K t K e V a (s) + 1 bR a + K t K e W (s).(3) 1 NOTE: Please, do the algebra to convince yourselves of this result.