By Rush D. Robinett III, John Feddema, G. Richard Eisler, Clark Dohrmann, Gordon G. Parker, David G. Wilson, Dennis Stokes
This booklet is the results of over ten (10) years of study and improvement in versatile robots and buildings at Sandia nationwide Laboratories. The authors de cided to assemble this wealth of information right into a set of viewgraphs as a way to educate a graduate type in versatile robotic Dynamics and Controls in the Mechanical En gineering division on the collage of latest Mexico (UNM). those viewgraphs, encouragement from numerous scholars, and lots of overdue nights have produced a publication that are meant to supply an upper-level undergraduate and graduate textbook and a reference for knowledgeable pros. The content material of this publication spans a number of disciplines together with structural dynam ics, procedure id, optimization, and linear, electronic, and nonlinear keep an eye on thought that are constructed from a number of issues of view together with electric, me chanical, and aerospace engineering in addition to engineering mechanics. accordingly, the authors think that this publication demonstrates the worth of sturdy utilized idea while constructing ideas to genuine international difficulties. The reader will locate many genuine global functions during this ebook and may be proven the applicability of those suggestions past versatile constructions which, in flip, indicates the worth of mul tidisciplinary schooling and teaming.
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Extra info for Flexible Robot Dynamics and Controls
4. 31 Digital Systems Any control system that one designs for a flexible robot will be implemented on an embedded computer. As a result, the control system must be directly written in digital form and/or transformed from continuous time to discrete time. In this section, a few topics regarding sampled data systems are covered. Specifically, digital integration methods for simulating linear and nonlinear systems. To this end, the Z-transform and the unit impulse response function (the discrete analog of the impulse response function) are introduced.
1. p(A) = n. This implies that v(A) x=O. = O. 2. p(A) < n. This implies that v(A) > O. Therefore, 3 a nontrivial solution to Ax = O. This test is useful when determining eigenvalues as will be necessary in subsequent sections and chapters. An interesting property of square matrices is that their rank is invariant with respect to pre or post multiplication by nonsingular square matrices. That is, if A E Rnxn, then p(A) = p(AB) = p(BA). Although the rank of B is n (since it is nonsingular), the rank of A can be less than B.
Next, several Runge-Kutta methods will be presented with a brief discussion regarding real-time compatibility. In short, an integration method is real-time compatible if the algorithm does not require Un+l to calculate Xn+J' This is important for simulating real-time systems where the input is the result of a closed-loop control law. Typically, the control law is a function of the current state and physically is not available until the new state information has been calculated. Note, the number of passes determines the order of the routing.