Page 11 - Practical Control Engineering a Guide for Engineers, Managers, and Practitioners

Contents xi

8-3-3 Moving Average Stochastic
Sequences . . . . . . . . . . . . . . . . . . . . . . . 220
8-3-4 Unstable Nonstationary Stochastic
Sequences . . . . . . . . . . . . . . . . . . . . . . . 223
8-3-5 Multidimensional Stochastic Processes
and the Covariance . . . . . . . . . . . . . . . 225
8-4 Populations, Realizations, Samples, Estimates,
and Expected Values . . . . . . . . . . . . . . . . . . . . 226
8-4-1 Realizations . . . . . . . . . . . . . . . . . . . . . 226
8-4-2 Expected Value . . . . . . . . . . . . . . . . . . 227
8-4-3 Ergodicity and Stationarity . . . . . . . . 228
8-4-4 Applying the Expectation
Operator . . . . . . . . . . . . . . . . . . . . . . . . 228
8-5 Comments on Stochastic Disturbances and
Difficulty of Control . . . . . . . . . . . . . . . . . . . . 230
8-5-1 White Noise . . . . . . . . . . . . . . . . . . . . . 230
8-5-2 Colored Noise . . . . . . . . . . . . . . . . . . . 231
8-6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
9 The Discrete Time Domain and the
Z-Transform • • • • • • • • • • • • • • • . . . . . • • • . . • . • • . • . 235
9-1 Discretizing the First-Order Model 236
9-2 Moving to the Z-Domain via the
Backshift Operator . . . . . . . . . . . . . . . . . . . . . . 238
9-3 Sampling and Zero-Holding . . . . . . . . . . . . . 239
9-4 Recognizing the First-Grder Model as a
Discrete Trme Filter . . . . . . . . . . . . . . . . . . . . . 243
9-5 Descretizing the FOWDT Model . . . . . . . . . . 244
9-6 The Proportional-Integral Control Equation
in the Discrete Time Domain . . . . . . . . . . . . . 244
9-7 Converting the Proportional-Integral Control
Algorithm to Z-Transforms . . . . . . . . . . . . . . 246
9-8 The PlfD Control Equation in the Discrete
Trme Domain . . . . . . . . . . . . . . . . . . . . . . . . . . 247
9-9 Using the Laplace Transform to Design
Control Algorithms-the Q Method . . . . . . . 249
9-9-1 Developing the Proportional-Integral
Control Algorithm . . . . . . . . . . . . . . . . 249
9-9-2 Developing a PID-Like Control
Algorithm . . . . . . . . . . . . . . . . . . . . . . . 252
9-10 Using the Z-Transform to Design Control
Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
9-11 Designing a Control Algorithm
for a Dead-Trme Process . . . . . . . . . . . . . . . . . 256
9-12 Moving to the Frequency Domain . . . . . . . . 259