Globally stable adaptive pole placement

(1988) Globally stable adaptive pole placement. PhD thesis, King Fahd University of Petroleum and Minerals.


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The problem of global stability of indirect adaptive pole assignment for time-invariant system forms the issue addressed in this thesis. Two different algorithms are discussed. The first one is based on the right model representation (r.m.r.), and the second on the left model representation (l.m.r.). The adaptive control based on (r.m.r.) as well as (l.m.r.) and its associated stability analysis are discussed in detail for the SISO case. The key idea to establish global stability is to show that any possible unbounded signal is observable form the equation error. Linear boundedness of a partial state vector derived from the equation error is then used to establish boundedness of all signals. Moreover the equation error is also shown to converge asymptotically to zero. The result of global stability is applicable to a wide class of estimation schemes. It is proved that uniform boundedness of system signals and convergence of the equation error to zero is not conditional on convergence of the estimated parameters to their true values. This results in a minimum number of required assumptions. In particular neither the assumption on the block length N nor on the persistency of excitation of the reference signal is required. To obtain convergence of the system parameters to their true values, knowledge of the system order n is required, together with the persistency of excitation of the reference signal. Furthermore, if the idea of block processing is used, bounds on the rate of convergence could be obtained. The analysis includes a number of estimation schemes. The global stability of adaptive pole assignment based on the (l.m.r.) is extended to MIMO systems. It is shown that the resultant closed-loop system is globally stable with convergence of the system parameters to their true values when driven by a persistently exciting external reference signal or signals. Fast exponential convergence is obtained for some version of least-squares algorithms which gives some robustness properties to the adaptive algorithms. It is also shown that uniform boundedness of all signals is independent from the convergence of the system parameters to their desired values. Several computer simulations and results on a real experimental setup using microcomputers are presented to validate the effrectiveness of the theory presented.

Item Type: Thesis (PhD)
Subjects: Electrical
Department: College of Engineering and Physics > Electrical Engineering
Committee Advisor: Abdel-Magid, Youssef L.
Committee Members: Penbeci, Suleyman S. and Bakri, Talal M. and Saggaf, Ubaid M. and Ahmed, M. S.
Depositing User: Mr. Admin Admin
Date Deposited: 22 Jun 2008 13:50
Last Modified: 01 Nov 2019 13:51