17,081 research outputs found
Synthesis of Minimal Error Control Software
Software implementations of controllers for physical systems are at the core
of many embedded systems. The design of controllers uses the theory of
dynamical systems to construct a mathematical control law that ensures that the
controlled system has certain properties, such as asymptotic convergence to an
equilibrium point, while optimizing some performance criteria. However, owing
to quantization errors arising from the use of fixed-point arithmetic, the
implementation of this control law can only guarantee practical stability:
under the actions of the implementation, the trajectories of the controlled
system converge to a bounded set around the equilibrium point, and the size of
the bounded set is proportional to the error in the implementation. The problem
of verifying whether a controller implementation achieves practical stability
for a given bounded set has been studied before. In this paper, we change the
emphasis from verification to automatic synthesis. Using synthesis, the need
for formal verification can be considerably reduced thereby reducing the design
time as well as design cost of embedded control software.
We give a methodology and a tool to synthesize embedded control software that
is Pareto optimal w.r.t. both performance criteria and practical stability
regions. Our technique is a combination of static analysis to estimate
quantization errors for specific controller implementations and stochastic
local search over the space of possible controllers using particle swarm
optimization. The effectiveness of our technique is illustrated using examples
of various standard control systems: in most examples, we achieve controllers
with close LQR-LQG performance but with implementation errors, hence regions of
practical stability, several times as small.Comment: 18 pages, 2 figure
Angular velocity nonlinear observer from single vector measurements
The paper proposes a technique to estimate the angular velocity of a rigid
body from single vector measurements. Compared to the approaches presented in
the literature, it does not use attitude information nor rate gyros as inputs.
Instead, vector measurements are directly filtered through a nonlinear observer
estimating the angular velocity. Convergence is established using a detailed
analysis of a linear-time varying dynamics appearing in the estimation error
equation. This equation stems from the classic Euler equations and measurement
equations. As is proven, the case of free-rotation allows one to relax the
persistence of excitation assumption. Simulation results are provided to
illustrate the method.Comment: 10 pages, 8 figures. arXiv admin note: substantial text overlap with
arXiv:1503.0287
- …