Dynamic Modeling, Predictive Control and Optimization of a Rapid Pressure Swing Adsorption System

Rapid Pressure Swing Adsorption (RPSA) is a gas separation technology with an important commercial application for Medical Oxygen Concentrators (MOCs). MOCs use RPSA technology to produce high purity oxygen (O2) from ambient air, and provide medical oxygen therapy to Chronic Obstructive Pulmonary Disease (COPD) patients. COPD is a lung disease which prevents O2 from entering a patient\u27s blood, and reduces the blood oxygen level. The standard therapy for COPD is to provide the patient with high purity (~90%) O2. MOCs have become more popular than traditional O2 gas cylinders due to their improved safety, and smaller device size and weight. The MOC market is growing rapidly and was expected to grow from $358 million in 2011 to$1.8 billion in 2017. Recently, a novel, single-bed MOC design was developed and tested to further reduce the size and weight of the device, and provide a continuous supply of O2 to the patient. This single-bed design uses a complex RPSA cyclic process with many nonlinear effects. Flow reversals, discrete valve switching, nonlinear adsorption effects, and complex fluid dynamics all make operating the RPSA system very challenging. Feedback control is necessary in a final commercial product to ensure the device operates reliably, but feedback control of PSA systems is not well studied in the current literature.In this work, a study of dynamic modeling, predictive control and optimization of this single-bed RPSA device is presented. A detailed, nonlinear plant model of the RPSA device is used to study the dynamics of the system as well as design a Model Predictive Controller (MPC) for the RPSA system. The plant model is a fully coupled, nonlinear set of Partial and Ordinary Differential Equations (PDEs and ODEs) which act as a representation of reality when design and evaluating the MPC. A sub-space model identification technique using Pseudo-Random Binary Sequence (PRBS) input signals generate a linear model which reduces the computational cost of MPC, and allows the algorithm to be implemented as an embedded controller for the RPSA device. The multivariable MPC independently manipulates the RPSA cycle step durations to control both the product composition and pressure. This MPC strategy was designed and tested in simulation before being implemented on a lab-scale device.The MPC is implemented onto a lab-scale MOC prototype using Raspberry Pi hardware, and evaluated using several MOC-relevant disturbance scenarios. The MPC is also expanded using piece-wise linear modeling to improve the performance of an RPSA device for other concentrated O2 applications. The embedded MPC features a convex quadratic optimization problem which is solved in real time using online output measurements. Additional hardware in the embedded controller operates the RPSA cycle and implements control actions supplied by the MPC.Design and optimization of RPSA systems remains an active area of research, and many PSA models have been used to optimize RPSA cycles in simulation. In this work, a model-free steady state optimization approach using the embedded hardware is presented which does not require a detailed process model, and uses experimental data and a nonlinear solver to optimize the RPSA operation given various objectives

Large Scale Constrained Trajectory Optimization Using Indirect Methods

State-of-the-art direct and indirect methods face significant challenges when solving large scale constrained trajectory optimization problems. Two main challenges when using indirect methods to solve such problems are difficulties in handling path inequality constraints, and the exponential increase in computation time as the number of states and constraints in problem increases. The latter challenge affects both direct and indirect methods. A methodology called the Integrated Control Regularization Method (ICRM) is developed for incorporating path constraints into optimal control problems when using indirect methods. ICRM removes the need for multiple constrained and unconstrained arcs and converts constrained optimal control problems into two-point boundary value problems. Furthermore, it also addresses the issue of transcendental control law equations by re-formulating the problem so that it can be solved by existing numerical solvers for two-point boundary value problems (TPBVP). The capabilities of ICRM are demonstrated by using it to solve some representative constrained trajectory optimization problems as well as a five vehicle problem with path constraints. Regularizing path constraints using ICRM represents a first step towards obtaining high quality solutions for highly constrained trajectory optimization problems which would generally be considered practically impossible to solve using indirect or direct methods. The Quasilinear Chebyshev Picard Iteration (QCPI) method builds on prior work and uses Chebyshev Polynomial series and the Picard Iteration combined with the Modified Quasi-linearization Algorithm. The method is developed specifically to utilize parallel computational resources for solving large TPBVPs. The capabilities of the numerical method are validated by solving some representative nonlinear optimal control problems. The performance of QCPI is benchmarked against single shooting and parallel shooting methods using a multi-vehicle optimal control problem. The results demonstrate that QCPI is capable of leveraging parallel computing architectures and can greatly benefit from implementation on highly parallel architectures such as GPUs. The capabilities of ICRM and QCPI are explored further using a five-vehicle constrained optimal control problem. The scenario models a co-operative, simultaneous engagement of two targets by five vehicles. The problem involves 3DOF dynamic models, control constraints for each vehicle and a no-fly zone path constraint. Trade studies are conducted by varying different parameters in the problem to demonstrate smooth transition between constrained and unconstrained arcs. Such transitions would be highly impractical to study using existing indirect methods. The study serves as a demonstration of the capabilities of ICRM and QCPI for solving large-scale trajectory optimization methods. An open source, indirect trajectory optimization framework is developed with the goal of being a viable contender to state-of-the-art direct solvers such as GPOPS and DIDO. The framework, named beluga, leverages ICRM and QCPI along with traditional indirect optimal control theory. In its current form, as illustrated by the various examples in this dissertation, it has made significant advances in automating the use of indirect methods for trajectory optimization. Following on the path of popular and widely used scientific software projects such as SciPy [1] and Numpy [2], beluga is released under the permissive MIT license [3]. Being an open source project allows the community to contribute freely to the framework, further expanding its capabilities and allow faster integration of new advances to the state-of-the-art