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UBC Theses and Dissertations

Stochastic averaging level control and its application to broke management in paper machines Ogawa, Shiro


Averaging level control refers to liquid level control of storage tanks, where the objective is to keep the outlet flow u(t) as smooth as possible against the fluctuating inlet flow, while at the same time keeping the tank level y(t) within high and low limits. The thesis treats the stochastic averaging level control problem, where the input disturbance is a stochastic process. The problem is formulated to minimize a weighted sum of Var[u(t)] and Var[u(t)] subject to the target Var[y(t)]. The state-space linear quadratic optimal control method is used, resulting in a linear state feedback controller. When the input disturbance is modelled as the output of a first-order low-pass filter driven by white noise, the optimal controller is a phase-lag network. Broke storage tank level control is important in stabilizing the paper machine wet end. It is treated as a special type of averaging level control, where the input disturbance F[sub b](t) is a two-state continuous-time Markov process. The spectrum of F[sub b](t) is obtained and the linear optimal controller is designed with the same methodology as for the general averaging level control problem. Taking this very specific nature of F[sub b](t), a new nonlinear control scheme called the minimum overflow probability controller (MOPC) is designed, and tested against data collected from a paper machine. The MOPC performs better than the optimal linear controller and manual control. A new theorem on the state probability distribution of a continuous-time Markov jump system is presented, which leads to new methods for evaluating the mean and the variance of the state of a linear jump system, and a new reliable numerical method to calculate the state distributions of jump systems. These results are utilized to evaluate the overflow probabilities of controllers.

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