By Jer-Nan Juang
By Minh Q. Phan
Publisher: Cambridge University Press
Print Publication Year: 2001
Online Publication Date:September 2009
Online ISBN:9780511547119
Hardback ISBN:9780521783552
Paperback ISBN:9780521031905
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511547119.003
Subjects: Engineering design, kinematics, and robotics, Computational Science
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Introduction
In the previous chapter, we paid attention to the solution of a scalar ODE. A scalar ODE describes the dynamics of a single-input single output (SISO) dynamic system. In general, a system can have several inputs and several outputs. Such a multi-input multi-output (MIMO) dynamic system can be described by a set of coupled ODEs involving several input and output variables. We must solve these equations simultaneously to obtain the dynamic response of the system. We can find such a solution by using matrix theory, which conveniently rearranges the set of coupled equations in a compact form. Instead of having several coupled scalar ODEs, we now have one single matrix ODE. Matrix operations can be performed on the matrix differential equations, and the final solution can be expressed in a simple form. It is important to realize that applying such matrix operations is equivalent to operating on the scalar ODEs individually, although with the scalar approach it is very easy to miss the general picture. Thus, matrix theory is one fine example in which one gains by simply rewriting an old problem in a new form that can be analyzed more effectively. Another reason why the matrix formulations are so useful is that a set of coupled differential equations of any order can be rewritten as a single matrix differential equation of first order. The same statement applies for a single scalar ODE of any order as well.
pp. i-vi
pp. vii-xii
pp. xiii-xvi
1 - Ordinary Differential Equations : Read PDF
pp. 1-13
2 - Elementary Matrix Algebra : Read PDF
pp. 14-44
3 - Modeling Techniques : Read PDF
pp. 45-79
4 - Finite-Element Method : Read PDF
pp. 80-119
5 - Response of Dynamic Systems : Read PDF
pp. 120-144
6 - Virtual Passive Controllers : Read PDF
pp. 145-163
7 - Stateâ€“Space Models : Read PDF
pp. 164-183
8 - State-Feedback Control : Read PDF
pp. 184-216
9 - Dynamic Feedback Controller : Read PDF
pp. 217-255
10 - System Identification : Read PDF
pp. 256-294
11 - Predictive Control : Read PDF
pp. 295-332
pp. 333-334