448 research outputs found
Rapid-convergent nonlinear differentiator
A nonlinear differentiator being fit for rapid convergence is presented,
which is based on singular perturbation technique. The differentiator design
can not only sufficiently reduce the chattering phenomenon of derivative
estimation by introducing a continuous power function, but the dynamical
performances are also improved by adding linear correction terms to the
nonlinear ones. Moreover, strong robustness ability is obtained by integrating
nonlinear items and the linear filter. The merits of the rapid-convergent
differentiator include the excellent dynamical performances, restraining noises
sufficiently, avoiding the chattering phenomenon and being not based on system
model. The theoretical results are confirmed by computer simulations and an
experiment.Comment: 26 pages, 15 figure
Design and analysis of continuous hybrid differentiator
In this paper, a continuous hybrid differentiator is presented based on a
strong Lyapunov function. The differentiator design can not only reduce
sufficiently chattering phenomenon of derivative estimation by introducing a
perturbation parameter, but also the dynamical performances are improved by
adding linear correction terms to the nonlinear ones. Moreover, strong
robustness ability is obtained by integrating sliding mode items and the linear
filter. Frequency analysis is applied to compare the hybrid continuous
differentiator with sliding mode differentiator. The merits of the continuous
hybrid differentiator include the excellent dynamical performances, restraining
noises sufficiently, and avoiding the chattering phenomenon
Robust Synchronization of Master-Slave Chaotic Systems Using Approximate Model:An Experimental Study
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
Fractional Calculus Guidance Algorithm in a Hypersonic Pursuit-Evasion Game
Aiming at intercepting a hypersonic weapon in a hypersonic pursuit-evasion game, this paper presents a fractional calculus guidance algorithm based on a nonlinear proportional and differential guidance law. First, under the premise of without increasing the complexity degree of the guidance system against a hypersonic manoeuvering target, the principle that the differential signal of the line-of-sight rate is more sensitive to the target manoeuver than the line-of-sight rate is employed as the guidelines to design the guidance law. A nonlinear proportional and differential guidance law (NPDG) is designed by using the differential derivative of the line-of-sight rate from a nonlinear tracking differentiator. By using the differential definition of fractional calculus, on the basis of the NPDG, a fractional calculus guidance law (FCG) is proposed. According to relative motions between the interceptor and target, the guidance system stability condition with the FCG is given and quantitative values are also proposed for the parameters of the FCG. Under different target manoeuver conditions and noisy conditions, the interception accuracy and robustness of these two guidance laws are analysed. Numerical experimental results demonstrate that the proposed guidance algorithms effectively reduce the miss distance against target manoeuvers. Compared with the NPDG, a stronger robustness of the FCG is shown under noisy condition
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