http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Maximizing allowable disturbances in uncertain, non-minimum phase unstable systems
A frequency domain design methodology for maximizing the allowable size of step disturbances for a class of uncertain plants subjected to hard time domain constraints on the control, internal states and the output is extended to Non-Minimum Phase (NMP) and unstable systems. The design technique is based on mapping the time domain constraints into the frequency domain to obtain point-wise constraints on the magnitude and phase of the nominal loop transfer function at each frequency. Once these boundaries are obtained, classical loop shaping realizes an acceptable nominal loop transfer function. To extend the design methodology to NMP and/or unstable systems, the effects of right-half-plane zeros and poles of the system on its feedback properties are studied first. Then, the design methodology is modified to accommodate such systems. For NMP systems, an inner-outer factorization is used to transform the frequency domain design boundaries on the nominal NMP loop transfer function into equivalent bounds on the corresponding MP transfer function. For unstable systems similar difficulties are also noted which in most cases can be dealt with as for the NMP case. Alternatively, prestabilization can be used, which in fact becomes necessary when the system has imaginary-axis poles. Consequently, issues regarding the type of stabilization technique that should be used, the desirable locations for placing the closed loop poles, and the effect of prestabilization on the maximum tolerable size of the step disturbance are addressed. Furthermore, a necessary condition for the existence of a solution is given which is based on transforming the design boundaries on the loop transfer function into equivalent bounds on the sensitivity function. As an application, the problem of controlling the position of a ball rolling on a beam is treated. Finally, a loop shaping algorithm is included. The algorithm is based on converting the loop shaping problem into a parameter identification scheme giving a discrete-time domain transfer function representation of the loop. The resulting pulse transfer function is then transformed back into the continuous-time domain giving an approximate transfer function for the nominal loop.
"Major subject: Mechanical Engineering."