546 † To whom correspondence should be addressed. E-mail: mynlee@yu.ac.kr Korean J. Chem. Eng., 30(3), 546-558 (2013) DOI: 10.1007/s11814-012-0161-6 INVITED REVIEW PAPER A unified approach to the design of advanced proportional-integral-derivative controllers for time-delay processes Truong Nguyen Luan Vu**, and Moonyong Lee* ,† *School of Chemical Engineering, Yeungnam University, Gyeongsan 712-749, Korea **Faculty of Mechanical Engineering, University of Technical Education of Ho Chi Minh City, Vietnam (Received 7 July 2012 • accepted 19 September 2012) Abstract-A unified approach for the design of proportional-integral-derivative (PID) controllers cascaded with first- order lead-lag filters is proposed for various time-delay processes. The proposed controller’s tuning rules are directly derived using the Padé approximation on the basis of internal model control (IMC) for enhanced stability against distur- bances. A two-degrees-of-freedom (2DOF) control scheme is employed to cope with both regulatory and servo prob- lems. Simulation is conducted for a broad range of stable, integrating, and unstable processes with time delays. Each simulated controller is tuned to have the same degree of robustness in terms of maximum sensitivity (Ms). The results demonstrate that the proposed controller provides superior disturbance rejection and set-point tracking when compared with recently published PID-type controllers. Controllers’ robustness is investigated through the simultaneous introduc- tion of perturbation uncertainties to all process parameters to obtain worst-case process-model mismatch. The process- model mismatch simulation results demonstrate that the proposed method consistently affords superior robustness. Key words: PID Controller Design, Lead-lag Filter, Disturbance Rejection, Set-point Tracking, Two-degree-of-freedom (2DOF) Control Scheme INTRODUCTION The IMC structure [1], a control structure incorporating the inter- nal 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 closed- loop performance and robustness can be directly obtained using a single parameter related to the closed-loop time constant [1-3]. 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 per- formance for various time-delay processes [4-8]. Lee et al . [4] de- scribe a typical application of this novel control scheme, wherein an IMC filter, including a lead term to neglect the process domi- nant poles suggested by Horn et al . [5], is also used. The control- ler’s performance can be significantly enhanced by 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 con- ventional 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 approxima- tions 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 [2,3,5,9]. This expansion does introduce some modeling errors, though within acceptable lim- its. To reduce this problem, a higher order Padé approximation has been used by Shamsuzzoha and Lee [7,10]. Alternatively, a Taylor expansion can be directly applied to transform an ideal feedback controller into a standard PID-type controller, as suggested by Lee et al. [4]. 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 approximat- ing 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. In this work, PID filter controllers closely approximating ideal feedback controllers are obtained by using directly high order Padé approximations, since those of previous works 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 sim- ple, of analytical form, model-based, and easy to implement in prac- tice with excellent performance for both regulatory and servo prob- lems. Several case studies are reported to demonstrate the simplic- ity and effectiveness of the proposed method compared with several other prominent design methods. The simulation results confirm that the proposed method can afford robust PID filter controllers for both disturbance rejection and set-point tracking. GENERALIZED IMC APPROACH FOR PID CONTROLLER DESIGN Consider the standard block diagrams of the feedback control