Author ORCID Identifier

https://orcid.org/0009-0008-1582-0956

Semester

Spring

Date of Graduation

2023

Document Type

Dissertation

Degree Type

PhD

College

Statler College of Engineering and Mineral Resources

Department

Chemical and Biomedical Engineering

Committee Chair

Fernando V. Lima

Committee Co-Chair

Debangsu Bhattacharyya

Committee Member

Stephen E. Zitney

Committee Member

Robert Mnatsakanov

Committee Member

Heleno Bispo

Committee Member

Juan Salazar

Abstract

Nonlinear dynamic analysis serves an increasingly important role in process systems engineering research. Understanding the nonlinear dynamics from the mathematical model of a process helps to find the boundaries of all achievable process conditions and identify the system instabilities. The information on such boundaries is beneficial for optimizing the design and formulating a control structure. However, a systematic approach to analyzing nonlinear dynamics of chemical processes considering such boundaries in a quantifiable and adaptable way is yet to exist in the literature. The primary aim of this work is to formulate theoretical concepts for dynamic operability, as well as develop the practical implementation methods for the analysis of dynamic performance in chemical processes. Process operability is a powerful tool for analyzing the relationships between the input variables, the output variables, and the disturbances via the geometric computation of variable sets. The operability sets are described by unions of polyhedra, which can be translated to sets of inequality constraints, so the results of the operability analysis can be used for process optimization and advanced process control. Nonetheless, existing process operability approaches in the literature are currently limited for steady-state processes and a generalized definition of dynamic operability that retains the core principles of steady-state operability as a controllability measure. A unified dynamic operability concept is proposed in this dissertation with two different adaptations to represent the complex relationships between the design, control structure, and control law of a given process. The existing operability mapping methods discretize the input space by partitioning the ranges of each input variable evenly, and all possible input combinations are simulated to achieve the output sets. The procedure is repeated for each value in the expected disturbance set to find the output regions that are guaranteed to be achieved regardless of the disturbance scenario. However, for dynamic systems, the same set of manipulated inputs can take different values at different time intervals, so the number of possible input combinations, which is also the number of simulations required, increases exponentially with the number of time intervals. This tractability challenge motivates the development of novel dynamic operability mapping approaches. A linear time-invariant dynamic system is first considered to tackle the dynamic mapping of achievable output sets. For a linear system, the achievable output set (AOS) at a fixed predicted time is the smallest convex hull that contains all the images of the extreme points of the available input set (AIS) when propagated through the dynamic model. Given a collection of AOS’s at all predicted times, referred to as the achievable funnel, a set of output constraints is infeasible if its intersection with the achievable funnel is empty. Under the influence of a stochastic disturbance, the achievable funnel is shifted according to the definition of the expected disturbance set (EDS). If the EDS is bounded, the intersection of all achievable funnels at each disturbance realization is the tightest set of transient output constraints that is operable. Additionally, given a fixed setpoint, an AOS is referred to as a feasible AOS if a series of inputs from the AIS always brings any output to the setpoint regardless of the realization of the disturbance within the EDS. Thus, novel developed theories and algorithms to update the dynamic operability mapping according to the current state variables and the disturbance propagations are proposed to reduce the online computational time of the constraint calculation task. Dynamic operability mapping for nonlinear processes is an expansion of the above linear mapping. A novel state-space projection mapping is proposed by taking advantage of the discrete-time state-space structure of the dynamic model to reduce the number of input mapping combinations. This method augments the AIS at the current step to include the AOS of the state variables from the previous time step. The nonlinear dynamic operability mapping framework consists of three components: the AOS inspector, the AIS divider, and the merger of the AOS from the previous time with the AIS. Specifically, the AOS inspector evaluates if the current input-output combinations are approximately accurate to the real AOS when all input combinations are mapped to the output space. If the AOS inspector gauges that the current AOS is not sufficiently precise, the AIS divider systematically generates more input-output combinations based on the current AOS. This feedback process is repeated until an accuracy tolerance is reached. Finally, a novel grey-box model identification algorithm for process control is developed by integrating dynamic operability mapping and Bayesian calibration. The proposed dynamic discrepancy reduced-order model-based approach calibrates the rates of changes of the grey-box model to match the plant instead of compensating for the time-varying output differences. The model reduction framework is divided into three steps: formulating the dynamic discrepancy terms, calibrating the hyperparameters, and selecting the least complex model that is neither underfitted nor overfitted. To demonstrate the effectiveness of the reduced-order model, the developed approach is implemented into a model predictive controller for a high-fidelity model as the simulated plant.

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