Licentiate thesis 2014-002

Output Feedback Control - Some Methods and Applications

Johannes Nygren

27 March 2014

This thesis studies some output feedback control laws. Particularly, iterative learning control (ILC) and decentralized network based algorithms are studied. Applications to control of wastewater treatment plants are outlined. For a linear, discrete time MIMO plant, it is shown that the size of the global controller gain, also referred to as the diffusion matrix, plays an important role in stabilization of a decentralized control system with possibly non-linear output feedback. Based on information from a step response experiment of the open loop system, a controller gain which is sufficient for stability can be found. For the SISO case, frequency response expressions are derived for the choice of this controller gain. The results relate nicely to notions of optimality and the Nyquist stability criterion. Various types of ILC algorithms are analysed and numerically illustrated. In particular, new expressions of the asymptotic control error variance for adjoint based iterative learning control (ILC) are derived. It is proven that the control error variance converges to its minimum if a decreasing learning gain matrix is used for ILC. In a simulation study ILC is applied to control a sequencing batch reactor. It is shown numerically that an adjoint based ILC outperforms inverse based ILC and model-free, proportional ILC. A merge of an activated sludge process simulator and a simulator for a wireless sensor network is described and used for illustrating some control performance. Finally, in a numerical optimization study it is shown that the aeration energy can be decreased if many dissolved oxygen sensors are used for aeration control in a biological reactor for nitrogen removal. This results may support future use of inexpensive wireless sensor networks for control of wastewater treatment plants.

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