Index 887
C
Canonical forms:
controllable, 649
diagonal, 650
Jordan, 651, 653
observable, 650
Capacitance:
of pressure system, 107–09
of thermal system, 137
of water tank, 103
Cancellation of poles and zeros, 288
Cascaded system, 20
Cascaded transfer function, 20
Cauchy–Riemann conditions, 860–61
Cauchy’s theorem, 526
Cayley–Hamilton theorem, 668, 701
Characteristic equation, 652
Characteristic polynomial, 34
Characteristic roots, 652
Circular root locus, 282
Classical control theory, 2
Classification of control systems, 225
Closed-loop control system, 8
Closed-loop system, 20
Closed-loop frequency response, 477
Closed-loop frequency response curves:
desirable shapes of, 492
undesirable shapes of, 492
Closed-loop transfer function, 19–20
Cofactor, 876
Command compensation, 630
Compensation:
feedback, 308
parallel, 308
series, 308
Compensator:
lag, 323, 503–04
lag–lead, 332–34, 511–13
lead, 312–13, 495–96
Complete observability, 683–84
conditions for, 684–85
in the splane, 684
Complete output controllablility, 714
Complete state controllability, 676–81
in the splane, 680–81
Complex-conjugate poles:
cancellation of undesirable, 520
Complex function, 859
Complex impedence, 75
Complex variable, 859
Computational optimization approach to
design PID controller, 583–89
Conditional stability, 299–300, 510–11
Conditionally stable system, 299–300,
458, 510–11
Conduction heat transfer, 137
Conformal mapping, 447, 462–64
Conical water tank system, 152
Constant-gain loci, 302–03
Constant-magnitude loci (M circles),
478–79
Constant phase-angle loci (N circles),
480–81
Constantvnloci, 296
Constantzlines, 298
Constantzloci, 296
Control actions, 21
Control signal, 3
Controllability, 675–81
matrix, 677
output, 681
Controllable canonical form, 649, 688
Controlled variable, 3
Controller, 22
Convection heat transfer, 137
Conventional control theory, 29
Convolution, integral, 16
Corner frequency, 406
Critically damped system, 167
Cutoff frequency, 474
Cutoff rate, 475D
Damped natural frequency, 167
Damper, 64, 132
Damping ratio, 165
lines of constant, 296
Dashpot, 64, 132–33
Dead space, 43
Decade, 405
Decibel, 403
Delay time, 169–70
Derivative control action, 118–20, 222
Derivative gain, 84
Derivative time, 25, 61
Detectability, 688
Determinant, 874
Diagonal canonical form, 694
Diagonalization of n*nmatrix, 652
Differential amplifier, 78
Differential gap, 23, 24
Differentiating system, 231
Differentiation:
of inverse matrix, 881
of matrix, 880
of product of two matrices, 880
Differentiator:
approximate, 617
Direct transmission matrix, 31
Disturbance, 3, 26
Dominant closed-loop poles, 182
Duality, 754