MPC enhancement for tracking of complex profiles — The basic technique Meaghan Charest n , Rickey Dubay University of New Brunswick, Department of Mechanical Engineering, 15 Dineen Drive, P.O.Box 4400, Fredericton, New Brunswick, Canada E3B 5A3 article info Article history: Received 12 March 2014 Accepted 17 September 2014 Keywords: Complex trajectory tracking Predictive control Prediction enhancement Correction constant η abstract This paper develops a unique approach that can be imposed on conventional predictive control schemes to provide tighter control when tracking complex setpoint trajectories. The method introduces a correction parameter η, independent of plant gain, evaluated online at each control timestep to drive the plant output to its reference more accurately than the original schemes. The strategy was applied to various systems that possess deadtime, higher order and multivariable characteristics with improved closed loop control. This is evidenced by significant reductions of mean square errors when using η. The strategy was applied on a nonlinear system and a practical setup, with reduced tracking error. & 2014 Elsevier Ltd. All rights reserved. 1. Introduction Research on Model-based Predictive Control (MPC) associated with theoretical work and practical applications has flourished over the past 30 years. A broad body of literature and a number of survey papers attest to this fact (Lee, 2011; Qin & Badgwell, 2003). MPC algorithms display a number of desirable features that enable them to be robust. They can perform in the presence of nonlinea- rities and modeling errors and can handle constraints and multi- variable plants (Diehl, Amrit, & Rawlings, 2011; Runzi & Low, 2009). As the field of MPC is an ongoing area of research, recent developments on new MPC algorithms include M-Shifted, extended predictive control, fast MPC, and latent variable MPC (Abu-Ayyad & Dubay, 2006; Dubay, Kember, Lakshminarayan, & Pramujati, 2006; Jesus & MacGregor, 2005). This in combination with advancements in the computer industry have allowed the MPC algorithm to extend to applications requiring small sampling times (Bolognani, Peretti, & Zigliotto, 2009; Diehl et al., 2011). Early application of MPC algorithms to the process industry were generally subjected to relatively simple reference or setpoint trajectories. In standard applications the reference often settles at a fixed setpoint such as a temperature, a fluid level, or a speed in the case of motor speed control. The MPC methodology has been recently introduced to applications that include the field of robotics and Unmanned Aerial Vehicles (UAV) (Gregor & Skrjanc, 2007; Kim & Shim, 2003; Ren & Beard, 2004). Other current applications of MPC schemes include flexible manipulators (Hassan, Dubay, Li, & Wang, 2007) and plastic injection molding (Dubay, Pramujati, Han, & Strohmaier, 2007). In these cases the desired reference trajectories can be more complex. Standard MPC algorithms exhibit difficulty when tracking complex profiles (Golshan, MacGregor, Bruwer, & Mhaskar, 2010). Little work has been done in terms of complex reference tracking with MPC control. It is becoming increasingly important for advanced control schemes to be able to track more complex reference trajectories for more efficient control (Ali, Yu, & Hauser, 2001; Mayne, Rawlings, Rao, & Scokaert, 2000). From an industrial per- spective, tighter trajectory tracking can lead to better part quality and energy consumption. Latent variable MPC is one algorithm that has been recently designed in order to optimize trajectory tracking performance (Jesus & MacGregor, 2005). The latent variable scheme has successfully been applied to batch processes (Golshan et al., 2010; Lauri, Rossiter, Sanchisa, & Martíneza, 2010). The method is an effective solution to the complex trajectory tracking problem but cannot be readily adapted to common or conventional forms of MPC. The tracking offset apparent when tracking complex reference trajectories is identified as a result of the open loop system time constants that are not accounted for in controller prediction for- mulations. Different methods to correct steady state offset due to disturbance or model mismatch have been developed (Magni & Scattolini, 2005; Rawlings & Mayne, 2009). These methods have been designed for constant reference trajectory tracking and do not eliminate the offset tracking that exist when tracking slopes. Evi- dence of the complex trajectory tracking offset problem can be seen in Yang and Gao (2000), Dubay et al. (2007), Dalamagkidis, Valavanis, and Piegl (2011), and Li, Su, Shao-Hsien Liu, and Chen (2012). This paper investigates the development of a strategy to improve complex trajectory tracking that can be superimposed on standard predictive schemes such as DMC and GPC. This superposition approach is selected because of the dominance of MPC algorithms Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/conengprac Control Engineering Practice http://dx.doi.org/10.1016/j.conengprac.2014.09.012 0967-0661/& 2014 Elsevier Ltd. All rights reserved. n Corresponding author. E-mail address: charest.meaghan@unb.ca (M. Charest). Control Engineering Practice 33 (2014) 136–147