Control of nonlinear underactuated systems

In this paper we introduce a new method to design control laws for non-linear underactuated systems. Our method produces an infinite dimensional family of control laws, whereas most control techniques only produce a finite dimensional family. These control laws each come with a natural Lyapunov function. The inverted pendulum cart is used as an example. In addition, we construct an abstract system which is open loop unstable and cannot be stabilized using any linear control law, and demonstrate that our method produces a stabilizing control law.Comment: 17 page

Secular variability in the baroclinic structure of the interior North Pacific from 1950-1970

Recently White (1975) found significant year to year changes in the baroclinic transport of the Subtropical Gyre in the North Pacific. To determine the spatial variability in the general circulation associated with this change in bulk transport, the baroclinic potential energy (BPE) in the mid-latitude interior from 20-50N, 145E-130W is mapped (using the methods of optimum interpolation) onto a regular 5 degree latitude/ 10 degree longitude grid each year from 1950-1970...

Westward propagation of short-term climatic anomalies in the western North Pacific Ocean from 1964-1974

Short-term climatic anomalies in the surface dynamic height (O/400 db) structure of the western North Pacific from 1964-1974 are investigated on a seasonal basis for propagational character. From the equator to 32.5N, negative dynamic height anomalies occurred in 1965, 1969 and 1972, approximately every three years, associated with E1 Nino events in the eastern tropical Pacific (Wyrtki, 1977). The decorrelation time scale of these short-term climatic anomalies was independent of latitude (i.e., 6-9 months), but the decorrelation longitude scale decreased poleward; i.e., from 10° longitude at 7.5N to 5° longitude at 32.5N. Time/longitude correlation studies find these anomalies to have propagated westward at the speed of baroclinic long (Rossby) waves; i.e., 14 ± 4 cm/sec to the west at 7.5N and 1.5 ± .5 cm/sec to the west at 32.5N, with intermediate speeds in between

Secular variability in the large-scale baroclinic transport of the North Pacific from 1950–1970

A time sequence of meridional baroclinic transport (0/1000 db) across the Subtropical gyre of the North Pacific is constructed, based upon available hydrographic data collected from 1950-1970. This time sequence displays significant variability, with a maximum possible range ± 25 % about the long-term mean and a principal time scale of approximately six years. A comparison of this time sequence with that of the Kuroshio (Nitani, 1972) shows good correlation in both amplitude and phase...

Matching, linear systems, and the ball and beam

A recent approach to the control of underactuated systems is to look for control laws which will induce some specified structure on the closed loop system. This basic idea is used in several papers already. In this paper, we will describe one matching condition and an approach for finding all control laws that fit the condition. After an analysis of the resulting control laws for linear systems, we will present the results from an experiment on a ball and beam system.Comment: An image of the apparatus may be downloaded from http://www.math.ksu.edu/~dav

Interannual variability in the baroclinic gyre structure of the western North Pacific from 1954-1974

In the western North Pacific from 0-35N 130-180E, the vertical and horizontal thermal structure of the baroclinic gyre systems in the region from 0-400 m depth has been mapped on a yearly basis from 1954-1974. From this measure of the baroclinic field of mass, the dynamic height (0/400 db) has been computed for each year, yielding geostrophic current indices of the major zonal currents...