A model-based sliding mode control methodology applied to the HDA-plant Guido Herrmann, Sarah K. Spurgeon*, Christopher Edwards Department of Engineering, Control and Instrumentation Research Group, University of Leicester, University Road, Leicester, LE1 7RH, UK Abstract A sliding mode control methodology using output information is demonstrated in application to the HDA-plant, a plant for production of benzene. This process is a highly integrated, non-linear large scale process with non-minimum phase and relative degree zero characteristics. The non-linear control law is designed on the basis of a linear observer-based control system. The non- linear control law uses the states of the linear observer. The performance in the sliding mode is determined by a linear stable sub- manifold of the linear closed loop control system chosen via a robust pole selection scheme. The sliding mode control is optimized to operate in a wide operating region. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: Sliding-mode control; H 1 -Control; Chemical processes 1. Introduction The HDA-plant, a chemical plant for production of benzene, has been of longstanding interest to chemical process engineers [1–3] and control engineers [4–6]. Since this non-linear, large scale and relative degree zero process is highly integrated and non-minimum phase, it forms an important test bed for new control approaches. The HDA-process model was initially implemented as a 68 state model by Brognaux [4] and then extensively re-developed into a 270-state system by Cao et al. [7] under SpeedUp. 1 The model has been re-implemented under Aspen Custom Modeler 1 by the authors for this paper. The plant has undergone a detailed analysis with respect to the available combinations of single-input– single-output (SISO) control schemes and the most effective actuators [5,8,9]. However, control schemes have been generally limited to SISO-control methods as seen in Luyben et al. [6] for a different HDA-model simulation set-up. Hence, the application of model- based, multi-variable control as considered here is novel. For the multivariable control, a linear mixed sensitivity H 1 -control problem is posed. Enforcing pole separation for the linear controller and observer system, a non-linear control is augmented using the observer states. The non-linear controller improves robustness and performance via pseudo-sliding forcing the closed loop states into the vicinity of a stable manifold of the linear closed loop control. The article discusses first the plant, problems of non- linearity, the tracking problem and the control method- ology. Finally, the model reduction, controller design and simulation results are presented. 2. The HDA-plant: a benzene producing chemical process In the HDA-plant (Fig. 1), benzene is produced via hydrodealkylation (HDA) of toluene. The reactions taking place comprise an exothermic reaction and an equilibrium reaction. There are two input substances, toluene and hydrogen and three product substances, benzene, diphenyl and methane (Fig. 1). For basic oper- ation, Brognaux [4] and also Cao et al. [7] introduced PID controllers to stabilize the system and to keep certain plant variables in a well-defined range. The remaining measurable output values in Table 1 have to be con- trolled. A tracking controller is supposed to follow production demand changes while keeping the interac- tion with the other four measurements as low as possi- ble. Theoretical input/ouput controllability analysis applied to the HDA-plant by Cao and Rossiter [8], Cao and Rossiter [9] and Cao et al. [5] showed that six out of 0959-1524/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0959-1524(02)00023-9 Journal of Process Control 13 (2003) 129–138 www.elsevier.com/locate/jprocont * Corresponding author. Tel.: +44-116-252-2531; fax: +44-116- 252-2619. E-mail addresses: gh17@sun.engg.le.ac.uk (G. Herrmann), eon@le.ac.uk (S.K. Spurgeon), ce14@le.ac.uk (C. Edwards). 1 SpeedUp and Aspen Custom Modeler are trademarks of Aspen Technology, Inc., Cambridge, USA.