In this paper, a two-degree-of-freedom control for an interval process plant with interval time delay to guarantee both robust stability and performance has been considered. A simple necessary condition and a sufficient condition for robust Hurwitz stability of an interval polynomial has been used to design a robust controller for a chemical process plant with delay subjected to unknown but bounded parameter uncertainties referred to as an interval process plant with interval time delay. A pre-filter is constructed to ensure the desired system performance. Simulation results are presented to establish the efficacy of the proposed method for an interval process plant with interval time delay.
AlefeldGHerzbergerJ (1983) Introduction to Interval Computations. New York: Academic Press, Inc.
2.
BarmishBR (1989) A generalization of Kharitonov’s four polynomial concept for robust stability problems with linearly dependent coefficient perturbations. IEEE Trans Automatic Control34: 157–165.
3.
BarmishBRHollotCVKrausFJTempoR (1992) Extreme point results for robust stabilization of interval plants with first order compensator. IEEE Trans Automatic Control37: 707–714.
4.
BarmishBRKangHI (1993) A survey of extreme point results for robustness of control systems. Automatica29: 13–35.
5.
BartlettACHollotCVHuangL (1988) Root location of an entire polytope of polynomials: it suffices to check edges. Math Control Signals Systems1: 61–71.
6.
BernsteinDSHaddadWM (1992) Robust controller synthesis using Kharitonov’s theorem. IEEE Trans Automatic Control37: 129–132.
7.
BhattachryaSP (1987) Robust Stabilization Against Structured Perturbations. (Lecture Notes in Control and Information Sciences, Vol 99), Berlin: Springer-Verlag.
8.
BhattachryaSPChapelettHKeelLH (1995) Robust Control: The Parametric Approach. Englewood Cliffs, NJ: Prentice-Hall Inc.
9.
BrosilowCB (1979) The structure and design of smith predictors from viewpoint of inferential control. In: Joint American Control Conference, Denver, CO.
10.
ChenCTFanCKPengST (2004) Robust control system design for interval time delay process systems. Chin Inst Chem Engrs35(2): 213–223.
11.
ChenCTWangMD (1997) Robust controller design for interval process systems. Comput Chem Engng21: 739–750.
12.
ChenCTWangMD (2000) A two-degrees-of-freedom design methodology for interval process systems. Comput Chem Engng23: 1745–1751.
13.
DoratoPYedavalliRK (1990) Recent Advances in Robust Control. New York: IEEE Press.
14.
GhoshBK (1985) Some new results on the simultaneous stabilization of a family of single input, single output systems. Syst Control Lett6: 39–45.
15.
GohCJLimCCTeoKLClementsDJ (1989) Robust controller design for systems with interval parameter design. Probl Control Inform Theory18: 323–338.
16.
HollotCVFangF (1990) Robust stabilization of interval plants using lead or lag compensators. Syst Control Lett14: 9–12.
17.
KharitonovVL (1978) Asymptotic stability of an equilibrium position of a family of systems of linear differential equations. Differentsial’nye Uravneniya14(11): 2086–2088 (English Transl. (1979) Differ Eqns, 14: 1483–1485).
18.
KnospeCRRoozbehaniM (2006) Stability of linear systems with interval time delays excluding zero. IEEE Trans Automatic Control51(8): 1271–1288.
19.
LaughlinDLRiveraDEMorariM (1987) Smith predictor design for robust performance. Int J Control46: 477.
20.
Mathworks Inc. (1999) Matlab: Users Guide. Natick, MA: Mathworks Inc.
21.
NieYY (1976) A new class of criterion for the stability of the polynomials. Acta Mechnica Sinica110–116.
22.
OmarFHaribKHMoustafaKA (2010) Control of interval parameter overhead cranes via Monte-Carlo simulation. Trans Inst Meas Control, DOI:10.1177/014233120935616210.1177/0142331209356162.
23.
PatreBMDeorePJ (2007) Robust stability and performance for interval process plants. ISA Transactions46(3): 343–349.
24.
RotsteinHBandoniJDesagesARomagnoliJ (1990) Mathematical programming with linear uncertain constraints—application to robust control. Comput Chem Engng14: 373–379.
25.
SohYCEvansRJPetersenIRBetzRE (1987) Robust pole assignment. Automatica23: 601–610.
26.
WangZQSkogestadS (1993) Robust control of time delay systems using the Smith predictor. Int J Control57: 1405.
