1019 Proportional-integral-plus control applications of state-dependent parameter models C J Taylor1*, E M Shaban1, M A Stables1, and S Ako2 1 Engineering Department, Lancaster University, Lancaster, UK 2 Bachy Soletanche Limited, Burscough, UK The manuscript was received on 10 October 2006 and was accepted after revision for publication on 23 May 2007. DOI: 10.1243/09596518JSCE366 Abstract: This paper considers proportional-integral-plus (PIP) control of non-linear systems defined by state-dependent parameter models, with particular emphasis on three practical demonstrators: a microclimate test chamber, a 1/5th-scale laboratory representation of an intelligent excavator, and a full-scale (commercial) vibrolance system used for ground improve- ment on a construction site. In each case, the system is represented using a quasi-linear state-dependent parameter (SDP) model structure, in which the parameters are functionally dependent on other variables in the system. The approach yields novel SDP–PIP control algorithms with improved performance and robustness in comparison with conventional linear PIP control. In particular, the new approach better handles the large disturbances and other non-linearities typical in the application areas considered. Keywords: control system design, non-minimal state space, state-dependent parameters, hydraulic actuators, system identification 1 INTRODUCTION but with additional dynamic feedback and input compensators introduced automatically when the process has second-order or higher dynamics, or Previous papers have considered the proportional- pure time delays greater than unity. In contrast to integral-plus (PIP) controller, in which non-minimal conventional PI/PID control, however, PIP design state-space (NMSS) models are formulated so that full exploits state variable feedback (SVF) methods, where state variable feedback control can be implemented the vagaries of manual tuning are replaced by pole directly from the measured input and output signals assignment or linear quadratic (LQ) design. of the controlled process, without resort to the To date, however, inherent non-linearities in the PIP design and implementation of a deterministic state system have been accounted for in a rather ad hoc reconstructor (observer) or a stochastic Kalman manner at the design stage, sometimes leading to filter [1–3]. reduced control performance. For example, pressure Such PIP control systems have been successfully disturbances sometimes take the ventilation rate in a employed in a range of practical applications, parti- building sufficiently far from the operating condition cularly in the areas of microclimate control for on which the linear controller is based for the agricultural buildings [4, 5], and in the automation response to such a disturbance to be relatively slow. of construction robots on building sites [6, 7]. In both Similarly, on a construction site, the behaviour of these application areas, the most common types of hydraulically driven manipulators is dominated by controller used previously have been derived from the highly non-linear, lightly damped dynamics of the ubiquitous proportional-integral-derivative (PID) the actuators [10]. approach (see, for example, references [8] and [9]). To improve PIP control in such cases, therefore, In this regard, PIP control can be interpreted as one the present paper identifies, and subsequently exploits logical extension of conventional PI/PID methods, for control system design, state-dependent para- * Corresponding author: Engineering Department, Lancaster meter (SDP) models. Here, the non-linear system is University, Faculty of Science and Technology, Bailrigg, Lancaster modelled using a quasi-linear structure in which the parameters vary as functions of the state variables, LA1 4YR, UK. email: c.taylor@lancaster.ac.uk JSCE366 © IMechE 2007 Proc. IMechE Vol. 221 Part I: J. Systems and Control Engineering i221070366 26-09-07 14:48:14 Rev 14.05 The Charlesworth Group, Wakefield 01924 204830