Robust I-PD Controller Design with Case Studies on Boiler Steam Drum and Bioreactor
G. Lloyds Raja
Abstract
Integral-proportional-derivative (I-PD) is more effective than PID controller as it provides dual-loop advantage while retaining the same number of tunable parameters. In I-PD controller, Integral action is employed on the error signal whereas PD mode is employed in the inner feedback loop. However, the studies pertaining to I-PD are not unified for unstable and integrating processes with inverse response. Routh criteria augmented with maximum sensitivity (M <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</inf> ) specification is used to design PD controller. The adjustable parameter (K <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</inf> ) of the innerloop and integral gain (K <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</inf> ) are decided from two plots: K <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</inf> vs M <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</inf> of inner-loop (M <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SS</inf> ) and K <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</inf> vs M <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</inf> of outer-loop (M <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SP</inf> ). Guidelines for choosing K <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</inf> and K <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</inf> from the aforementioned plots are also provided. Simulation studies are conducted on models of boiler steam drum and bioreactor that exhibit inverse response behavior. Qualitative and quantitative performance comparison is carried out with some recently reported works.