Question

IV. Given Kd-2 and Ki-5; When PID( Kd,Ki) command is executed, what will be the output value of Kp, Ki and Kd? V. In Ball and Beam system, given reference position of 200mm, but ball stops at 160. Which parameter of PID need to be changed to attain the desired result.

this is from control lab

Answer 1

In MATLAB the function pid takes 3 inputs kp ki and kd in way given below.

C = pid(kp,ki,kd);

When pid(kd,ki) is executed, MATLAB interprets the first value kd as kp and second value ki as ki and zero as kd.

therefore when this command is exucuted the output is given below.

code:

kd= 2; ki = 5;
pid(kd,ki)

result:

Continuous-time PI controller in parallel form:

1
Kp + Ki * ---
  s

With Kp = 2, Ki = 5

Question V.

from the question, it is observed that the there is  difference between the input and system's response of 200-160 = 40. this error is called steady-state error in control systems.

To reduce the steady state error, we need to increase the integral gain Ki of the controller. This integral gain increases the type of the system from zero to one. For a type 1 system, the steady state error to step changei in the reference will reduce to zero.