Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Relay self-oscillations for second order, stable, nonminimum phase
  plants   We study a relay feedback system (RFS) having an ideal relay element and a
linear, time-invariant, second order plant. We model the relay element using an
ideal on-off switch. And we model the second order plant with a transfer
function that: (i) is Hurwitz stable, (ii) is proper, (iii) has a positive real
zero, and (iv) has a positive DC gain.
  We analyze this RFS using a state space description, with closed form
expressions for the state trajectory from one switching time to the next. We
prove that the state transformation from one switching time to the next: (a)
has a Schur stable linearization, (b) is a contraction mapping, and (c) maps
points of large magnitudes to points with lesser magnitudes. Then using the
Banach contraction mapping theorem, we prove that every trajectory of this RFS
converges asymptotically to an unique limit cycle. This limit cycle is
symmetric, and is unimodal as it has exactly two relay switches per period.
This result helps understand the behaviour of the relay autotuning method, when
applied to second order plants with no time delay.
  We also treat cases where the plant either has no finite zero, or has exactly
one zero and that is negative.

35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys