Generalized S.V.D. Reduced Order Observers for Noisy Linear and Nonlinear systems
Open Access
- Author:
- Dada, Gbolahan P
- Graduate Program:
- Chemical Engineering
- Degree:
- Master of Science
- Document Type:
- Master Thesis
- Date of Defense:
- November 20, 2019
- Committee Members:
- Antonios Armaou, Thesis Advisor/Co-Advisor
Ali Borhan, Special Signatory
Phillip E Savage, Program Head/Chair
Monty Alger, Committee Member
Robert Rioux, Committee Member - Keywords:
- GSVD
State estimation
Process Control
Reduced order observer
Measurement noise
Nonlinear system
LTI system
Generalized singular value decomposition - Abstract:
- The use of observers for improvement of output feedback process control is important for achieving increased accuracy and processing efficiency, especially for large multivariate process systems. Reduced-order observers are particularly advantageous for reducing the computational complexity of estimating state variables. For chemical processes that can be modeled as a linear time-invariant continuous system with stochastic elements of white Gaussian noise accounting for both process disturbances and sensor inaccuracies. Noise contributions to multiple sensors are characterized and scaled before being filtered by a soft sensor. The soft sensor design here is based on a best linear unbiased estimation (BLUE) of output measurements using generalized singular value decomposition (GSVD) of the coefficient matrices of measured variables and noise respectively. The resulting state estimates are obtained through a reduced-order Kalman-Bucy observer superstructure. Using chemical process examples of a biochemical continuous stirred tank reactor (CSTR) and the simplified Tennessee Eastman model, this design is shown to outperform the ordinary Kalman filter design with noisy measurements that deviate from a Gauss-Markov model. A nonlinear observer design method is also proposed for the reduced order observation of nonlinear systems in the presence of sensor and process noise. Supernumerary sensors to the measured states are assumed to be available, and state variables unavailable for observation by measurement are estimated with the proposed observer structure that requires lower computation than full order observers. By modeling output measurements as a generalized linear combination of observable states and measurement noise, this method combines generalized singular value decomposition (GSVD) static estimation of noisy output measurement and reduced order observer theory for estimating unmeasured state variables in nonlinear systems. Using chemical process examples of a biochemical continuous stirred tank reactor (CSTR) and an iso-thermal reactor, this design is shown as a viable low computation alternative to full-order observation, with potential economic advantage in model predictive control (MPC) applications.