Collective Sliding-Mode Technique for Multivariable Bumpless Transfer Fabricio Garelli,* ,† Ricardo J. Mantz, ‡ and Herna ´ n De Battista § Laboratorio de Electro ´ nica Industrial Control e Instrumentacio ´ n, UniVersidad Nacional de La Plata, C.C.91 (1900) Argentina This paper proposes a strategy for the reduction of the undesired effects caused by manual-automatic or controller switching in multivariable process control. The proposal takes advantage of dynamic sliding mode properties to avoid inconsistency between the off-line controller outputs and the plant inputs. As a consequence, jumps at the plant inputs are prevented (which is known as bumpless transfer) and undesired transients on controlled variables are significantly reduced. Some advantages of the proposed algorithm are that (1) its implementation is extremely simple, (2) it presents distinctive robustness properties, which are characteristic of sliding regimes, and (3) it does not need the model of the plant. 1. Introduction A common practice in automatic control, especially in the chemical industry, is to take the plant manually to the operating point and just then to connect the controller so that the system starts operating automatically. As is well-known, such a mode switch may cause jumps at the plant inputs and a deterioration of the system response if no action is taken to avoid it. The suppression of the jumps at the plant inputs and their associated transient effects is referred to as bumpless transfer. Because of the practical importance of this topic, there has been a lot of research in this area. Many contributions have dealt with bumpy transfers together with windup problem (caused by plant input constraints) because of their similarities. One of the earliest published methodologies was proposed by Hanus et al., 1 which is based on the concept of “realizable reference”, and it has been applied to many real-life projects. Among the large number of articles that have been subsequently reported in the literature, concepts of linear quadratic theory, 2 linear matrix inequalities, 3 L 2 bounds on state mismatch, 4 state/ output feedback, 5,6 and H ∞ optimization 7 have also been exploited to find solutions to windup and bumpy transfers. Contributions on this field also allow achieving smooth com- mutations between multiple linear controllers, which is particu- larly significant when switched control of nonlinear systems is considered. 8 This work introduces concepts of variable structure system theory and the associated sliding regimes to solve the problems that arise from switching between open-loop (OL) and closed- loop (CL) operation or from commutations between controllers for different operating points in MIMO systems. One of the main advantages of the resulting proposal is that it is applicable to controllers for which conventional bumpless algorithms were not conceived, like multivariable controllers with general transfer matrix, and even then it requires minimal design and imple- mentation effort. It also presents distinctive robustness proper- ties, which are characteristic of sliding regimes. Furthermore, the chattering phenomenonswhich usually degrades the per- formance of variable structure controlsdoes not affect at all the present application, and the model of the plant is not necessary for the methodology to be applied. The paper is organized as follows. Section 2 reviews some basic concepts on sliding-mode control for multi-input/multi- output (MIMO) systems. In Section 3, the sliding-mode (SM) algorithm proposed in this article to achieve bumpless transfer is described. This section also gives sufficient conditions for assuring the reach of the corresponding surface and analyzes the hidden dynamics of the conditioning loop once SM is established. The approach properties are verified through simulations on a benchmark MIMO process in Section 4. Finally, some final comments and concluding remarks are given. 2. Basic Concepts on Sliding Mode A variable structure system comprises a set of continuous subsystems with a switching logic that is a function of the system state. A particular operation is achieved when switching occurs at a very high frequency constraining the system state to a surface, named a sliding surface. This kind of operation is called sliding mode (SM) and has many attractive properties. It is robust to parameter uncertainties and external disturbances, it reduces the order of the sliding dynamics that become dependent on the designer-chosen sliding surface, and it is easy to implement. 9 Because of its interesting features, a large number of papers presenting practical applications of SM control have been reported. For instance, in refs 10-14, the application of SM to chemical process control is discussed. Consider the following dynamical system, where x ∈ R n is the system state and w ∈ R m is the control vector. Matrices A and B (and its column vectors b i ) are of consistent dimensions. The variable structure control law is defined componentwise as according to the sign of the scalar switching functions s i (x) ) R i - k i T x. The sliding surface S is defined as the intersection of the m so-called individual sliding surfaces S i defined by * Corresponding author. E-mail: fabricio@ing.unlp.edu.ar. Tel./ Fax: +54 221 425 9306. † Prof. Garelli is a member of CONICET. ‡ Prof. Bianchi is member of CICpBA. § Prof. De Battista is a member of CONICET. x 3) Ax + ∑ i)1 m b i w i ) Ax + Bw (1) w i ) { w i + if s i (x) > 0 w i - if s i (x) < 0 , i ) 1 ‚‚‚ m (2) S i ) {x ∈ R n : s i (x) ) 0} (3) 2721 Ind. Eng. Chem. Res. 2008, 47, 2721-2727 10.1021/ie070870q CCC: $40.75 © 2008 American Chemical Society Published on Web 03/12/2008