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PID Controller Design For Process With Time DeLay
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The IMC structure, a control structure incorporating the internal model of plant control, has been widely utilized in the design of PID-type controllers, usually denoted IMC-PID controllers, because of its simplicity, flexibility, and apprehensibility. The most important advantage of IMC-PID tuning rules is that the tradeoff between closedloop performance and robustness can be directly obtained using a single parameter related to the closed-loop time constant. IMC-PID tuning rules can provide good set-point tracking, but have been lacking regarding disturbance rejection, which can become severe for processes with a small time-delay/time constant ratio. Disturbance rejection is more important than set-point tracking in many process control applications, and thus is an important research topic.

A 2DOF control scheme can be used to improve disturbance performance for various time-delay processes. The controller’s performance can be significantly enhanced using a PID controller cascaded with a conventional filter, something easily implementable in modern control hardware. Consequently, several controller tuning rules have been reported despite PID controllers cascading with conventional filters being often more complicated than a conventional PID controller for processes with time delay. However, this difficulty can be overcome by using appropriate low-order Padé approximations of the time delay term in the process model. Therefore, the PID-type controller can be indirectly obtained by considering the Padé approximations. Accordingly, first-order Padé approximations have been used by a number of authors. This expansion does introduce some modeling errors, though within acceptable limits. To reduce this problem, a higher order Padé approximation has been used. Alternatively, a Taylor expansion can be directly applied to transform an ideal feedback controller into a standard

PID-type controller. The performance of the resulting IMC-PID controller is largely dependent on how closely the PID controller approximates an ideal controller equivalent to the IMC controller. It also depends on the structure of the IMC filter. Many methods for approximating an ideal controller to a PID controller have been discussed, but most are case dependent. Few unified approaches to PID controller design that can be employed for all typical time-delay processes have been fully achieved. PID filter controllers closely approximating ideal feedback controllers are also obtained by using directly high order Padé approximations, since those of previous works are only indirectly used Padé approximations in terms of the time delay part. The study is focused on the design of PID controllers cascaded with a lead-lag filters to fulfill various control purposes; tuning rules should be simple, of analytical form, model-based, and easy to implement in practice with excellent performance for both regulatory and servo problems.

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