Page 12 - Practical Control Engineering a Guide for Engineers, Managers, and Practitioners

xii Contents

9-12-1 The First-Order Process Model . . . . 260
9-12-2 The Ripple . . . . . . . . . . . . . . . . . . . . . . 261
9-12-3 Sampling and Replication . . . . . . . . 262
9-13 Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
9-13-1 Autogressive Filters . . . . . . . . . . . . . . 263
9-13-2 Moving Average Filters . . . . . . . . . . . 265
9-13-3 A Double-Pass Filter . . . . . . . . . . . . . 267
9-13-4 High-Pass Filters . . . . . . . . . . . . . . . . 269
9-14 Frequency Domain Filtering . . . . . . . . . . . . . 271
9-15 The Discrete Trme State-Space Equation . . . 273
9-16 Determining Model Parameters from
Experimental Data . . . . . . . . . . . . . . . . . . . . . . 274
9-16-1 First-Order Models . . . . . . . . . . . . . . 274
9-16-2 Third-Order Models . . . . . . . . . . . . . 276
9-16-3 A Practical Method . . . . . . . . . . . . . . 278
9-17 Process Identification with White
Noise mputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
9-18 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
10 Estimating the State and Using It for Control . . . . 285
10-1 An Elementary Presentation of the
Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . 286
10-1-1 The Process Model . . . . . . . . . . . . . . . 286
10-1-2 The Premeasurement and
Postmeasurement Equations . . . . . . 287
10-1-3 The Scalar Case . . . . . . . . . . . . . . . . . 288
10-1-4 A Two-Dimensional Example 288
10-1-5 The Propagation of the Covariances . . . 289
10-1-6 The Kalman Filter Gain . . . . . . . . . . . 290
10-2 Estimating the Underdamped Process
State ................................... 291
10-3 The Dynamics of the Kalman Filter and an
Alternative Way to Find the Gain . . . . . . . . . 296
10-3-1 The Dynamics of a Predictor
Estimator . . . . . . . . . . . . . . . . . . . . . . . 298
10-4 Using the Kalman Filter for Control . . . . . . . 299
10-4-1 A Little Detour to Find the
Integral Gain . . . . . . . . . . . . . . . . . . . . 300
10-5 Feeding Back the State for Control . . . . . . . . 301
10-5-1 Integral Control . . . . . . . . . . . . . . . . . 302
10-5-2 Duals . . . . . . . . . . . . . . . . . . . . . . . . . . 302
10-6 Integral and Multidimensional Control . . . . 303
10-6-1 Setting Up the Example Process and
Posing the Control Problem . . . . . . . 303
10-6-2 Developing the Discrete Trme
Version . . . . . . . . . . . . . . . . . . . . . . . . . 304