Discrete-time Contraction Analysis and Controller Design for Nonlinear Processes

Shifting away from the traditional mass production approach, the process industry is moving towards more agile, cost-effective and dynamic process operation (next-generation smart plants). This warrants the development of control systems for nonlinear chemical processes to be capable of tracking time-varying setpoints to produce products with different specifications as per market demand and deal with variations in the raw materials and utility (e.g., energy). This thesis aims to develop controllers to achieve time-varying setpoints tracking using contraction theory. Through the differential dynamic system framework, the contraction conditions for discrete-time systems, which ensure the exponential convergence between system responses and feasible time-varying references, are derived. The discrete-time differential dissipativity condition is further developed, which can be used for disturbance rejection control designs. Computationally tractable equivalent conditions are then derived and additionally transformed into an Sum of Squares programming problem, such that a discrete-time control contraction metric and stabilising feedback controller can be jointly obtained. Synthesis and implementation details of the resulting contraction-based controller are provided, which can achieve offset-free tracking of feasible time-varying references. To do contraction analysis and control design for systems with uncertainties, which are often complex and difficult, neural networks are used. It involves training and constructing a neural network embedded contraction-based controller. Learning algorithms of uncertain system model parameters are developed. The resulting control scheme is capable of achieving efficient offset-free tracking of time-varying references, with a full range of model uncertainties, without the need for controller structure redesign as the reference or uncertain parameter changes. This neural network based approach also ensures process stability during online simultaneous control and learning of uncertain parameters. To further improve the economics of contraction-based controller, a nonlinear model predictive control approach is developed. Contraction condition is imposed as a constraint on the optimisation problem for model predictive control with an economic cost function, utilising Riemannian weighted graphs and shortest path techniques. The result is a reference flexible and fast optimal controller that can trade off between the rate of target trajectory convergence and economic benefit (away from the desired process objective).

Grantor dc:publisher

UNSW, Sydney

Year dc:date

2022

Author dc:creator

• Wei, Lai

• Nonlinear Control
• Neural Networks
• Contraction Theory
• Discrete-time Nonlinear Systems
• Nonlinear Model Predictive Control
• Graph Theory
• Discrete-time Contraction Theory
• anzsrc-for: 400407 Process control and simulation
• anzsrc-for: 400705 Control engineering

Statement dc:rights

• open access
• CC BY 4.0
• free_to_read

Licence

• https://purl.org/coar/access_right/c_abf2
• https://creativecommons.org/licenses/by/4.0/

Language dc:language

en

Identifier

https://doi.org/10.26190/unsworks/24419

OAI identifier oai:identifier

oai:unsworks.library.unsw.edu.au:1959.4/100712