A Novel PID Controller with Second Order Lead/Lag Filter for Stable and Unstable First Order Process with Time Delay
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Praveen Kumar Medarametla
Abstract
A novel Proportional-Integral-Derivative (PID) controller is proposed for stable and unstable first order processes with time delay. The controller is cascaded in series with a second order filter. Polynomial approach is employed to derive the controller and filter parameters. Simple tuning rules are derived by analysing the maximum sensitivity of the control loop. Formulae are provided for initial guess of tuning parameter. The range of tuning parameter around the initial guess and the corresponding range of maximum sensitivity is specified based on time delay to time constant ratio. Promising results are obtained with the proposed method is compared against recently proposed methods in the literature. The comparison is made in terms of various performance indices for servo and regulatory responses separately. The proposed method is implemented for an isothermal chemical reactor at an unstable equilibrium point.
Appendix A
Consider an isothermal chemical reactor as shown in Figure 15.
Block diagram of an isothermal chemical reactor.
Mass balance equation can be written as
{Accumulation of = {Component A in}−{Component A out}+{Generation of A}Component A}
Where
F=Inflow rate (l/s)
Dividing the equation with
Under non ideal mixing conditions [21],
Where
At steady state
This isothermal chemical reactor is studied by various researchers [8, 18, 19] for values
.
Linearizing the eq. (34) at steady state
Considering a measurement lag of 20s due to concentration transducer,
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