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Sysquake LE On The Web

Sysquake LE is a free version of Sysquake. Sysquake brings life to boring static figures. With it, you can not only display graphics, but interact with them thanks to your mouse. You will immediately understand the effect of parameters, how to make a system perform better, or what an obscure mathematical theorem is about. Sysquake LE is much safer than Sysquake when it is used with files downloaded from the World Wide Web, because it does not support program-level stealth access to files on your hard disk.

Sysquake LE replaces Sysquake Viewer.

Installation

 Once you've installed Sysquake LE, you'll be a single click away from the live graphics listed below! To install Sysquake LE on your own computer (Mac or PC), please follow these simple instructions (the current version is 1.3 for Macintosh and Windows (12 Sept. 00) and Sysquake Viewer 1.2 PR5 for Linux Intel and PowerPC (3 Feb. 00); please download it if you've got a previous version). Then come back and try the SQ files below! We will add new files in the next weeks and months; come back often!

Mathematics

SQ FileDateDescriptionRef.
triangle.sq 04.10.99 Triangle, medians, perpendicular bisectors and bisectors, and circumscribed and inscribed circles (you can drag the corners of the triangle).
bezier3.sq 29.11.99 Bezier curve of order 3 (you can drag the control points, displayed as red circles).
moebius.sq 28.12.99 Möbius transformation (you can drag the two fixed points, displayed as red circles, and one point of the figure; hold down the Shift key to constrain the transformation to an elliptic or hyperbolic transformation instead of the more general loxodromic transformation). [6]
convExp.sq 31.07.99 Convolution of two exponential functions (you can shift one of the operands and see how the integral is defined). [4]
cor.sq 12.08.99 Correlation to find the position of a square in a noisy signal (you can shift the square and see how the correlation integral is defined).
taylor.sq 31.07.99 Taylor approximation of a sine (you can change the polynomial order and the point where the derivatives are evaluated).
cheb.sq 06.08.99 Chebyshev approximation of a sine (you can change the polynomial order and the region where the error is made as small as possible). [7]
gibbs.sq 22.11.99 Gibbs effect; the Fourier serie of a sawtooth signal does not converge to the approximated signal (you can change the number of terms of the approximation).
lissajou.sq 25.08.99 Lissajou figure (you can change the phase between x and y).
triang.sq 04.10.99 Triangulation (you can move the points).
voronoi.sq 26.10.99 Voronoi diagram (you can move the points).
cvoronoi.sq 26.10.99 Color Voronoi diagram and triangulation; each Voronoi region is colored in one of four colors, taking advantage of the four-color theorem (you can move the points).

Physics

SQ FileDateDescription
potlines.sq 05.08.99 Potential lines in a electrostatic field created by three charges (you can drag the charges).
pendulum.sq 23.11.99 Simulation of a pendulum, in the phase plane and as a function of time (you can change the initial angle and velocity, represented by a red circle in the phase plane).

Demography

SQ FileDateDescription
dem_evol.sq 05.08.99 Evolution of the Swiss population (you can simulate the evolution of the pyramid by dragging it up, or dragging the green line in the population evolution graphic).
dem_ret.sq 05.08.99 Evolution of the ratio between active and retired people (you can change the age limits of the groups by dragging the green lines in the pyramid).

Automatic Control

SQ FileDateDescriptionRef.
step2ndo.sq 27.10.00 Continuous-time step response of a 2nd-order transfer function (you can shape the step response and drag the poles). [4]
zpstep.sq 03.07.00 Continuous-time step response of a 3rd-order transfer function with a zero (you can drag the poles and the zero, and observe the effect of a non-minimum-phase zero: the step response has an undershoot when you move the zero to the right of the imaginary axis). [4]
rloc_dt.sq 04.08.99 Synthesis of a PD controller in the rlocus (you can drag the open-loop zero of the controller (red circle) and the closed-loop poles (triangles) along the root locus (black line)). [1]
PI_sat.sq 04.08.99 PI-controlled system with input saturation (you can change the saturation (red line) and the frequency of the set-point (blue signal)). [2]
PI_s_ARW.sq 04.08.99 PI-controlled system with input saturation and Anti-Reset Windup (you can change the saturation (red line) and the frequency of the set-point (blue signal)). [2]
pp_dt.sq 04.08.99 Pole placement design of a discrete-time RST controller (you can drag the closed-loop poles and observe the step response, Nyquist diagram and sensitivity). [2]
relay2.sq 11.08.99 Relay controller for a second-ordem continuous-time system (you can drag the hysteresis and observe the time response and the phase plane). [5]
relay3.sq 11.08.99 Relay controller for a third-order continuous-time system (you can drag the hysteresis and observe the time response and the phase plane). [5]
GPC_c.sq 18.08.99 GPC (Generalized Predictive Control) (you can drag the prediction (blue) and control (red) horizons). [3]

Signal Processing

SQ FileDateDescriptionRef.
minphase.sq 07.08.99 Comparison between minimum-phase (MP) and non-minimum-phase (NMP) systems (you can drag the poles and zeros of a continuous-time transfer function and compare the frequency and step responses of the MP and NMP systems). [4]
samplZOH.sq 05.08.99 Conversion of a continuous-time model (black) to a discrete-time model (red) using a sampler and a zero-order hold (you can drag the Nyquist frequency (green), the sample frequency (blue) or one of the samples (red circle)). [2]
cmp_c2d.sq 19.08.99 Comparison of different methods (zero-order hold, bilinear, backward difference, and forward difference) for converting a system from continuous time to discrete time (you can drag the Nyquist frequency (vertical line), and the continuous-time poles).
butterw.sq 23.09.99 Digital low-pass Butterworth filter, with the frequency response magnitude and the poles in the complex plane (you can drag the cut-off frequency (vertical line)). [8]
chebfltr.sq 09.11.99 Digital high-pass Chebyshev filter, with the frequency response magnitude and the poles in the complex plane (you can drag the cut-off frequency (vertical line) and the ripple lower limit (horizontal line)). [8]

Miscellaneous Demonstrations

SQ FileDateDescription
salesman.sq 04.08.99 Shortest path of a salesman (you can drag around the towns and the river).
cells.sq 23.09.99 Cellular automata; at each step of the animation, cells are born, survive, or die depending on the number of neighbors (no interactivity).
clock.sq 23.08.99 Clock with date to permit you to check whether the date given to Sysquake by the operating system is Y2K-compliant (no interactivity, but you can still zoom in and out).

References

 [1] J. Ackermann, Sampled-Data Control Systems, Springer-Verlag, Berlin, 1985. [2] K.J. Åström and B. Wittenmark, Computer-Controlled Systems, Theory and Design, 2nd ed., Prentice Hall International, Englewood Cliffs, NJ, 1990. [3] D.W. Clarke and C. Mohtadi, 1989, "Properties of Generalized Predictive Control", Automatica vol. 25 no 6 pp. 859-875. [4] R.C. Dorf and R.H. Bishop, Modern Control Systems, 8th ed. Addison Wesley Longman, Menlo Park, CA, 1998. [5] A. Gelb and W.E. Vander Velde, Multiple-Input Describing Functions and Non-Linear System Design, McGraw-Hill, New York, 1968. [6] M. Henle, Modern Geometries, the Analytic Approach, Prentice Hall, Upper Saddle River, NJ, 1997. [7] J.H. Mathews, Numerical Methods for Mathematics, Science, and Engineering, 2nd ed., Prentice Hall International, Englewood Cliffs, NJ, 1992. [8] T.W. Parks and C.S. Burrus, Digital Filter Design, John Wiley & Sons, New York, 1987.