Sliding mode control of I/O linearizable systems with uncertainty Mohan Krothapally a , Juan C. Cockburn b, *, Srinivas Palanki a a Department of Chemical Engineering, Florida A & M University±Florida State University, 2525 Pottsdamer Street, Tallahassee, FL 32310-6046, USA b Department of Electrical Engineering, Florida A & M University±Florida State University, 2525 Pottsdamer Street, Tallahassee, FL 32310-6046, USA Abstract In this paper we explore the application of sliding mode control to process control problems. Sliding mode control is presented as a natural tool for robust design of state feedback controllers for minimum phase input±output linearizable systems with uncertainty. An example is presented to illustrate some of the issues involved in the design of sliding mode robust controllers. # 1998 Elsevier Science Ltd. All rights reserved. Keywords: Sliding mode control; Robust nonlinear control; State feedback linearization Nomenclature A Eective heat transfer area of reactor (m 2 ) A d Frequency factor for the rate constant k d (s 1 ) A fm Frequency factor for the rate constant, k fm (m 3 kgmol 1 s 1 ) A p Frequency factor for the rate constant, k p (m 3 kgmol 1 s 1 ) A t Frequency factor for the rate constant, k t (m 3 kgmol 1 s 1 ) E d Activation energy for the rate constant, k d (kcal kgmol 1 ) E fm Activation energy for the rate constant, k fm (kcal kgmol 1 ) E p Activation energy for the rate constant, k p (kcal kgmol 1 ) E t Activation energy for the rate constant, k t (kcal kgmol 1 ) H P Heat of propagation reactions (kJ kgmol 1 ) I Concentration of initiator (kgmol m 3 ) J Performance index L f h Lie derivative of scalar ®eld h with respect to vector ®eld f L f h rth order Lie derivative of scalar ®eld h with respect to vector ®eld f M Concentration of monomer (kgmol m 3 ) P Concentration of total dead polymer (kgmol m 3 ) R Universal gas constant (kJ kgmol K 1 ) R   Total polymer radical concentration (kgmol m 3 ) R H Overall rate of heat generation by reac- tions (KJ m 3 s 1 ) T Reactor temperature (K) T sp Optimal temperature trajectory (K) ISA TRANSACTIONS 1 ISA Transactions 37 (1998) 313±322 0019-0578/98/$Ðsee front matter # 1998 Elsevier Science Ltd. All rights reserved. PII: S0019-0578(98)00033-0 * Corresponding author. Tel.: +1-850-410-6462; fax: +1- 850-410-6479; e-mail: cockburn@eng.fsu.edu