Model and hardware development for predictive plume control in pipe lines

The problem of model reference predictive control for eliminating contaminant cloud from a pipe fluid system by boundary control action is addressed. A lab-scale pipe fluid system prototype is developed for studying the control of fluid system. Experimental results validate the possibility of eliminating the contaminant cloud by boundary control. A model reference control architecture is constructed, in which a parameterizable reduced order mathematical model for simulating fluid particle path-lines is developed. Compared to traditional Computational Fluid Dynamics (CFD) method, this reduced order model can be solved within very short time by common Ordinary Differential Equation (ODE) solver which enables the implementation of iterative optimal control. INTRODUCTION Eliminating accidental hazardous release in buildings, transportation tunnels or water supply system can reduce the threat to human life. Solving such a problem requires an automatic hazard elimination process, including contaminant detection, prediction of spreading and fast-effective control action, such as neutralizing or capturing the contaminant cloud. Contaminant spreading problems are typically formulated as Partial Differential Equations (PDE) problems. In order to relate PDE with control theory, many mathematical methods were developed. In 1991, an adjoint based optimization method for heat conduction partial differential equations was discussed by Y. Jarny et al [1]. M. Piasecki and N. Katopodes applied this method to control of contaminant release in a river in 1997 [2]. Address all correspondence to this author. Direct Numerical Simulation (DNS)-based method for optimal feedback control was introduced by T. Bewley in 2001 [3]. In 2007, for the purpose of making use of efficient linear system theory, linearization on PDE system was illurstrated by J. Kim and T. Bewley [4]. These methods, although computational intensive, theoretically prove the possibility of manipulating PDEs by traditional control theory. Control of mixing in 2-Dimensions (2D) channel by boundary feedback was demonstrated by Aamo et al in 2003 [5]. Because their problem was studied via mathematical simulation, the entire fluid region information was known at every simulation time step. For example, the fluid velocity field was used to calculate cost function. That means an underlying assumption exists that, infinite number of ideal sensors or perfect models exist for the fluid field. In addition, the boundary control representation was a continuous function on space, which was another assumption of infinity number of virtual boundary actuators. Later in 2005, Balogh et al expended the problem to 3Dimensions (3D) [6]. In 2001, Bewley et al extended predictive control architecture to include turbulent fluid [3]. All assumed infinite sensors and actuators. In 2006, fluid control with finite sensors and finite boundary actuators was illustrated by N. Katopodes and R. Wu. [7]. Recently, a method for fluid predictive control by finite sensors and actuators was developed by N. Katopodes in 2009 [8]. Their simulation results of eliminating contaminant cloud from open channel flow were numerically illustrated. With all these simulations and theoretical analysis, together with the fast growing computational power, unlimited applications of fluid control in real world physical systems are becoming feasible. However, because of the computational intensity involved in solving fluid PDEs, traASME 2012 5th Annual Dynamic Systems and Control Conference joint with the JSME 2012 11th Motion and Vibration Conference DSCC2012-MOVIC2012 1 Copyright © 2012 by ASME DSCC2012-MOVIC2012-8857 October 17-19, 2012, Fort Lauderdale, Florida, USA Downloaded From: http://proceedings.asmedigitalcollection.asme.org/ on 02/24/2016 Terms of Use: http://www.asme.org/about-asme/terms-of-use Figure 1. CONTAMINANT CLOUD ELIMINATNG PROBLEM ditional CFD solver cannot be used when fast control response is needed due to the computational expense of these algorithms. Even though many advanced CFDmethods generate very precise solutions, delays caused by computing time cannot be avoided. Due to this reason, in this article, we develop an alternative fluid modeling method that is simple enough to implement predictive control on physical prototype real-time control system. A simplified contaminant cloud elimination problem is described in Fig. (1). The control system is composed of sensor arrays, boundary actuator ports (at strategically located points on fluid boundary), target contaminant cloud and computer. With position of the contaminant cloud captured by sensor arrays, the optimal control strategy is calculated and control action is then assigned to each boundary port. The objective is to eliminate all of the contaminant cloud from the fluid system through these ports. The model reference predictive control architecture is illustrated in Section 1. In order to predict the trajectory of contaminant cloud, the fluid system mathematical model used in the optimal control iteration process must be solved in very short time to ensure the system response. A method for building such model solving for flow steady state path line is discussed in Section 3. In Section 2, we describe the lab-scale prototype that was constructed for experiments. NOMENCLATURE Yi Contaminant cloud location information provided by i th sensor array; i = 1,2...n; n = number of sensor arrays Y Array containing all Yi; Y = [Y1 Y2 ... Yn] Y ∗ Reference contaminant cloud location, predicted by math model Qi Control command (Volumn flow rate) assigned to i th boundary port array; i = 1,2...m; m = number of boundary port sets Q Array containing all Qi; Q = [Q1 Q2 ... Qm] ! ! " # $ % &