8. Modelling and PID control of a DC motor

The aim of this project is to design a pid controller for accurate position control of a DC motor even under disturbance. The main objective of this is to evaluate the method of independent joint control which is widely used in many robotic applications. Using a generic motor model such as:

we can derive the closed loop transfer function through:

𝜃(s) = (E2-D) x 1/(Js^(2)+Bs)

E2 = E1 x (KP+Ki/s)- 𝜃 x KD x s

E1 = (𝜃d - 𝜃(S))

E2 = (𝜃d - 𝜃) x (KP+Ki/s)- 𝜃 x KD x s

𝜃(s) x (Js^(3)+(B+KD ) x s^2+ KP+Ki)= ((𝜃d ) x (KP x s+KI)-D x s)

Assuming (Js^(3)+(B+KD ) x s^2+ KP+Ki) = 𝛥(s)

𝜃(s) = (𝜃d ) x (KP x s+KI)/𝛥(S) - D x s/𝛥(s)

Using the model above with desired 𝜃 at 50 and a constant disturbance input of 50 with KP = 230 KD =78.004 and KI = 0.0001 we achieve the desired position with settling time below 5s overshoot below 1% and no steady state error. The PID gains for this project were obtained through Matlab's PID tuner.

Simulation result:

Click on this for Matlab files

RiseTime: 51.8937

Settling Time: 84.6280

Overshoot: 0.032