Modern Control Engineering

whereb 3 ,b 2 , and b 1 are determined as follows. By multiplying both sides of this last equation by (s+1)^3 , we have (B–2) Th ...

We thus obtain fort 0 Comments. For complicated functions with denominators involving higher-order polynomials, partial-fractio ...

For this function, num = [2 5 3 6] den = [1 6 11 6] The command [r,p,k] = residue(num,den) gives the following result: 872 Appen ...

EXAMPLE B–5 Expand the following B(s)/A(s)into partial fractions with MATLAB. For this function, we have num = [1 2 3] den = [1 ...

C 874 Appendix In this appendix we first review the determinant of a matrix, then we define the adjoint matrix, the inverse of a ...

This is because 6.The determinant of the product of two square matrices AandBis the product of determinants, or IfB=nmmatrix and ...

Note that =0. One of a number of largest submatrices whose determinant is not equal to zero is Hence, the rank of the matrix Ais ...

Note that the element of the jth row and ith column of the product A(adjA)is Hence,A(adjA)is a diagonal matrix with diagonal ele ...

and =17 Hence, the inverse of Ais In what follows, we give formulas for finding inverse matrices for the 2*2matrix and the 33mat ...

If and then If then If then Finally, we present the MATLAB approach to obtain the inverse of a square matrix. If all elements of ...

That is MATLAB Is Case Sensitive. It is important to note that MATLAB is case sen- sitive. That is, MATLAB distinguishes between ...

Differentiation of A^21 (t). If a matrix A(t)and its inverse A^1 (t)are differen- tiable with respect to t, then the derivative ...

R 882 References A–1 Anderson, B. D. O., and J. B. Moore,Linear Optimal Control. Upper Saddle River, NJ: Prentice Hall, 1971. A– ...

C–6 Coddington, E. A., and N. Levinson,Theory of Ordinary Differential Equations. New York: McGraw-Hill Book Company, 1955. C–7 ...

K–4 Kalman, R. E., “Canonical Structure of Linear Dynamical Systems,”Proc. Natl. Acad. Sci., USA, 48 (1962), pp. 596–600. K–5 Ka ...

O–6 Ogata, K.,MATLAB for Control Engineers.Upper Saddle River, NJ: Pearson Prentice Hall, 2008. P–1 Phillips, C. L., and R. D. H ...

I 886 Index A Absolute stability, 160 Ackermann’s formula: for observer gain matrix, 756–57 for pole placement, 730–31 Actuating ...

Index 887 C Canonical forms: controllable, 649 diagonal, 650 Jordan, 651, 653 observable, 650 Capacitance: of pressure system, 1 ...

E eAt: computation of, 670–71 Eigenvalue, 652 invariance of, 655 Electromagnetic valve, 23 Electronic controller, 77, 83 Enginee ...

Index 889 J Jet-pipe controller, 146–47 Jordan blocks, 679 Jordan canonical form, 651, 695, 706–07 K Kalman, R. E., 12, 675 Kirc ...