PID Controller Design for Integrating Plus Time-Delay Processes

Abstract

Many industrial processes can be modeled as Integrating Plus Time-Delay (IPTD)
systems and controller design for such systems has gained a considerable research interest
in recent times. In this work, different Proportional-Integral-Derivative (PID) control
structures are investigated for various process models with an emphasis on IPTD processes.
First, an Internal Model Control (IMC) based PID control design is presented for IPTD
processes. Conventionally, IMC yields a PD type controller for IPTD processes which
leads to poor load-disturbance rejection. In the proposed IMC structure, besides the PD
controller responsible for set-point tracking, a second compensator is introduced to improve
the disturbance rejection. The PD controller is designed in two different ways: using inverse
plant model and Frequency Loop Shaping (FLS). Further, the design method is extended to
first- and second-order process models with time-delay.
To address the delay robustness problem associated with IMC for the IPTD processes
having large time-delay, a Smith Predictor based all-PD control strategy is proposed. To
attain a good performance with lesser overshoot, PD controllers are used in both the set-point tracking and load-disturbance rejection loop. Explicit controller tuning formulas for both the PD controllers are obtained with Gain Margin (GM) and Phase Margin (PM) specifications. Moreover, same settings for both the controllers makes the design method more simpler.
Model based controllers, e.g. IMC, Smith predictors, have demerits such as controller
complexity, difficult to tune on-line. To overcome this, a set-point weighted 2DOF PID
control for different class of IPTD processes is proposed next. Explicit controller tuning
formulas for different class of IPTD processes are obtained with GM, PM and inverse plant
model specifications.
Next, we consider input saturation issue, which is predominant for IPTD plants. It is
observed that a zero on the real axis near to the origin may lead to overshoot and consequently actuator saturation in set-point tracking. But, all the above controllers discussed above may introduce zeros on the real axis. To address this issue, an I-PD control strategy for pure IPTD processes is presented next. Explicit controller tuning rules are obtained with GM, PM and critical gain. Based on pole placement and FLS, additional two approaches for I-PD controller tuning is presented.
Recently, Fractional-Order PID (FOPID) controllers are preferred over integer order
ones for controlling fractional-order as well as integer-order processes. FOPID controllers
are known to yield better performance due to having more tunable parameters. However, real-time implementation of FOPID controllers are complex. This is circumvented by
higher-order approximations of the fractional-order operator. Lastly, integer-order PID
controller design methods are developed for control of fractional-order processes with
time-delay. Three integer order PID controller design techniques are considered next to
control fractional- as well as integer-order processes. The proposed controller parameters
are obtained with FLS, IMC and Oustaloup approximation. It is observed that, if tuned
properly a comparable performance and robustness can also be achieved with integer order
PID controllers avoiding implementation issues.
To test the effectiveness of the obtained controllers, simulation comparisons with some
recently developed controllers are included along with performance comparisons based on
ISE, ITAE and IAE. Moreover, all the designs are validated through experiments on a
temperature control plant that can be modeled as an IPTD one.