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Revision as of 14:47, 9 May 2014
Description
The nonlinear RC-ladder is an electronic test circuit introduced in[1][2]. This nonlinear first-order system models a resistor-capacitor network that exhibits a distinct nonlinear behaviour caused by the nonlinear resistors consisting of a parallel connected resistor with a diode.
Model
The underlying model is given by a (SISO) gradient system of the form[3]:
where the nonlinearity is given by:
Input
As external input several alternatives are presented in[4], which are listed next. A simple step function is given by:
an exponential decaying input is provided by:
Additional input sources are given by conjunction of sine waves with different periods:
Data
A sample MATLAB implementation is given by:
g = @(x) exp(40.0*x)+x-1;
A1 = spdiags(ones(N-1,1),-1,N,N)-speye(N);
A2 = spdiags([ones(N-1,1);0],0,N,N)-spdiags(ones(N,1),1,N,N);
xdot = @(x,u) g(A1*x)-g(A2*x) + [u;sparse(N-1,1)];
y = @(x) x(1);
References
- ↑ Y. Chen, "Model Reduction for Nonlinear Systems", Master Thesis, 1999.
- ↑ Y. Chen and J. White, "A quadratic method for nonlinear model order reduction", Int. conference on modelling and simulation of Microsystems semiconductors, sensors and actuators, 2000.
- ↑ M. Condon and R. Ivanov, "Empirical balanced truncation for nonlinear systems", Journal of Nonlinear Science 14(5):405--414, 2004.
- ↑ M. Condon and R. Ivanov, "Model Reduction of Nonlinear Systems", COMPEL 23(2): 547--557, 2004