As a part of a machine, a DC motor is used to move a metal piece in a linear motion. The metal piece slides over a rolle
Posted: Fri Apr 29, 2022 9:47 am
As a part of a machine, a DC motor is used to move a metal piece
in a linear motion. The metal piece slides over a roller that
rotates with the motor shaft, as shown in the figure below. Assume
a negligible friction through the system. The metal piece is to be
controlled given the parameters for the DC motor and the metal
piece in the table below.
Mathematical Modeling:
Represent the given system by a schematic model, and find the
state space representation of the system. If the desired controlled
output is the metal piece position X(s), obtain the open loop
transfer function.
Controller Design
A controller is added to reduce the disturbances in the system,
assuming that the desired output is the rotor angle 𝜃(𝑠). Find the
closed loop transfer function in the case of (a) proportional
controller (b) proportional-derivative controller assuming zero
motor induction. The desired time specification for the system is
as follows: The system rise time should not exceed 3 seconds, the
system response should settle within 5 seconds, limiting the
overshoot to less than 5%, and with aim to reduce the steady state
error to the minimum (ess = 0). Calculate the range for the gain
parameters such that the system response follows the given
specification.
Metal Piece DC Motor Roller
Parameter Mass of the metal piece (M) System Inertia (Im) Roller radius (r) Motor damping (bm) Torque constant (Km) Back emf constant (Kb) Motor resistance (Rm) Motor inductance (Lm) Value 12.653kg 10.91 x 10-3 kg.m? 31.75 x 10-3 m т 0.268 N.ms/rad 0.8379N.m/amp 0.838 V s/rad 1.3612 3.6 mH
Vals) G(s) X(s)
in a linear motion. The metal piece slides over a roller that
rotates with the motor shaft, as shown in the figure below. Assume
a negligible friction through the system. The metal piece is to be
controlled given the parameters for the DC motor and the metal
piece in the table below.
- As A Part Of A Machine A Dc Motor Is Used To Move A Metal Piece In A Linear Motion The Metal Piece Slides Over A Rolle 1 (27.95 KiB) Viewed 33 times
- As A Part Of A Machine A Dc Motor Is Used To Move A Metal Piece In A Linear Motion The Metal Piece Slides Over A Rolle 2 (77.42 KiB) Viewed 33 times
Represent the given system by a schematic model, and find the
state space representation of the system. If the desired controlled
output is the metal piece position X(s), obtain the open loop
transfer function.
- As A Part Of A Machine A Dc Motor Is Used To Move A Metal Piece In A Linear Motion The Metal Piece Slides Over A Rolle 3 (3.53 KiB) Viewed 33 times
A controller is added to reduce the disturbances in the system,
assuming that the desired output is the rotor angle 𝜃(𝑠). Find the
closed loop transfer function in the case of (a) proportional
controller (b) proportional-derivative controller assuming zero
motor induction. The desired time specification for the system is
as follows: The system rise time should not exceed 3 seconds, the
system response should settle within 5 seconds, limiting the
overshoot to less than 5%, and with aim to reduce the steady state
error to the minimum (ess = 0). Calculate the range for the gain
parameters such that the system response follows the given
specification.
Metal Piece DC Motor Roller
Parameter Mass of the metal piece (M) System Inertia (Im) Roller radius (r) Motor damping (bm) Torque constant (Km) Back emf constant (Kb) Motor resistance (Rm) Motor inductance (Lm) Value 12.653kg 10.91 x 10-3 kg.m? 31.75 x 10-3 m т 0.268 N.ms/rad 0.8379N.m/amp 0.838 V s/rad 1.3612 3.6 mH
Vals) G(s) X(s)