Question
Download Solution PDFThe standard form of a PID controller is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFProportion + Integral + Derivative:
The PID controller produces on output, which is the combination of outputs of proportional, integral, and derivative controllers.
This is defined in terms of differential equations as:
\(u\left( t \right) = {K_p}\;e\left( t \right) + {K_I}\smallint e\left( t \right) \cdot dt + {K_D} \cdot \frac{{de\left( t \right)}}{{dt}}\)
Applying Laplace transform, we get:
\(U\left( s \right) = \left( {{K_p} + \frac{{{K_I}}}{s} + {K_D}s} \right)E\left( s \right)\)
Transfer function will be:
\(\frac{{U\left( s \right)}}{{E\left( s \right)}} = {K_p} + \frac{{{K_I}}}{s} + {K_D} \cdot s\)
Integral control:
It is the control mode where the controller Output is proportional to the integral of the error with respect to time.
Integral controller output = k × integral of error with time, i.e.
\({G_C}\left( s \right) = \frac{{U\left( s \right)}}{{E\left( s \right)}} = \frac{{{K_I}}}{s}\)
Proportional + Derivate:
The additive combination of proportional & Derivative control is known as P-D control.
Overall transfer function for a PD controller is given by:
\({G_C}\left( s \right) = \frac{{U\left( s \right)}}{{E\left( s \right)}} = {K_P} + s{K_D}\)
It is equivalent to a High-pass filter.
Last updated on Jun 24, 2025
-> ISRO Scientist Engineering apply online 2025 link has been activated (ISRO:ICRB:03(CEPO):2025).
-> A total of 39 vacancies are announced for the ISRO recruitment in Civil, RAC and other disciplines
-> ISRO Scientist Engineering recruitment 2025 notification has been released for 320 vacancies. The last date to fill ISRO application form is June 16 (Advt No. ISRO:ICRB:02(EMC):2025).
-> ISRO Scientist Engineer recruitment 2025 for 31 vacancies has been released.
->ISRO Scientist recruitment 2025 notification has been released.
->The last date to apply for ISRO scientist recruitment 2025 is May 30 ( Advt.No. ISRO:ICRB:01:(EMC):2025).
->Candidates with BE/BTech degree in the respective discipline can only apply for ISRO Scientist recruitment 2025.
-> Candidates can refer ISRO Scientist previous year paper to prepare for the exam.