Pole shift hypothesis

Abstract: A method for shifting the real parts of the open-loop poles to any desired positions while preserving the imaginary parts is presented. The method is based on the mirror-image property which has been reported by Molinari. In other words, Molinari's results are extended and then a recursive approach is developed. In each step of this approach, it is required to solve a first-order or a second-order linear matrix Lyapunov equation for shifting one real pole or two complex conjugate poles respectively. The presented method yields a solution which is optimal with respect to a quadratic performance index. The attractive feature of this method is that it enables solutions to complex problems to be easily found without solving any non-linear algebraic Riccati equation.

Abstract: We reexamined the Late Cretaceous-early Tertiary apparent polar wander path for the Pacific plate using 27 paleomagnetic poles from seamounts dated by (40)Ar/(39)Ar geochronology. The path shows little motion from 120 to 90 million years ago (Ma), northward motion from 79 to 39 Ma, and two groups of poles separated by 16 to 21 degrees with indistinguishable mean ages of 84 +/- 2 Ma. The latter phenomenon may represent a rapid polar wander episode (3 to 10 degrees per million years) whose timing is not adequately resolved with existing data. Similar features in other polar wander paths imply that the event was a rapid shift of the spin axis relative to the mantle (true polar wander), which may have been related to global changes in plate motion, large igneous province eruptions, and a shift in magnetic field polarity state.

Abstract: An H-inifinity control law design is presented for a benchmark problem consisting of an undamped pair of spring-coupled masses with a sensor and actuator that are not collocated. This simple mechanical system captures many of the salient features of more complex aircraft and space structure vibration control problems. The H-infinity problem formulation enables the issue of stability robustness in the face of large mass and spring constant variation to be directly addressed. Constraints on closed-loop dominant pole locations and settling time are accommodated via a simple s-plane bilinear transform. The transform parameter can give direct control of closed-loop disturbance settling time and controller open-loop pole-zero locations. A four-state H-infinity minimum phase controller was found to meet the given specifications of each design. Detailed analysis on the tradeoffs of sensor noise vs control energy are also presented.

Abstract: A method is put forward for the pole allocation of linear multivariable systems using output feedback. The necessary and sufficient conditions for pole allocation are established and a method is given for calculating the output feedback matrix for attainable poles. The analysis, which is based on frequency-domain techniques, employs an equivalent single-input system to treat the multi-input system. A feature of the method is that the tightness of the feedbacks can be weighted relative to each other, although this may reduce the attainable set of closed-loop poles. The method is readily computerised, and an algorithm is established which generates a near attainable set of poles when the specified set is unattainable.