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Active wrappers, 31 Aircraft example, 195, 204 Aligning compensator, AligningCompensator, 177 AligningCompensator, 177, 182 Amplitude behavior of compensator, MagnitudeFrequencyPlot, 142 Approximate commutative controller, 172 Characteristic equation, 170 Characteristic loci, and stability, 170 Characteristic locus, 170 Characteristic polynomial, 190 Characteristic values, 170 CharacteristicValuePlot, 173 Characteristic-direction vectors, 170 CharacteristicValuePlot, 173, 180, 183 Chemical reactor example, 119, 131, 179 CircleSpacing, 119 CircleStyle, 119, 124 Column dominance ratio, ColumnDominanceRatioPlot, 128 ColumnDominance, 17, 129 as value of GershgorinCircles, 115 ColumnDominanceRatioPlot, 128 Comparison matrix, 133 irreducible, 134 Compensator, 69, 109 aligning, 177 inverse, 122, 157 Compensator design, 15 ConsistentQ, 55 Continuous-time vs. discrete-time systems, 47 ContinuousTimeQ, 49 Control format, 21 Control objects, new in Polynomial Control Systems, 3 ControlInput, 189 Controllability, 57 and functional controllability, 70 functional, 57 Controllability indices, ControllabilityIndices, 203 Controllability matrix, 189 ControllabilityIndices, 203, 220 Controllable, 12, 67, 90, 94, 97 as value of TargetForm, 4 Controllable (f), 70 Controllable (l), 71 Controllable realizations, construction of, 4 ControllableCompanion, 4 ControllableSubsystem, 91 Controller, approximate commutative, 172 Controller design, 15, 103 Coprimeness, 57, 75 CountInputs, 55 CountOutputs, 55 CountStates, 55 D-contour, 109 Daly's algorithm, 206 Decoupling, 103 Decoupling zeros, 57, 84 removing, LeastOrderSystem, 13 DeleteSubsystem, 55 Determinantal divisors, 59 Diagonal dominance, 109 achieving, 133, 157 column, 109 for inverse systems, 110 measures of, 128 row, 109 DiscreteTimeQ, 49 Distillation column case study, 6 DropConstant, 143 Dyadic, 219-220 Dyadic algorithms and Ackermann's formula, 188 for output feedback, 217 for pole assignment, 188 Estimator, reduced-order, 208 Fan-in vector, 189, 191 Forward-path compensator, 17, 69, 109 Full-rank algorithm, 197 for output feedback, 226 FullRank, 14, 197, 226 Functional controllability, 57, 70, 103 and state controllability, 70 FunctionallyControllable, 71 FunctionallyControllable, 71 GCD, 75 Gershgorin circles, 17, 109 GershgorinCircles, 115 GershgorinCircles, 17, 115, 123, 129, 132, 137, 165 Hadamard product, 104 Input decoupling zeros, 85 InputDecouplingZeros, 87 removing, RemoveInputDecouplingZeros, 91 Input-output decoupling zeros, 87 Input-output pairing, 16 InputDecouplingZeros, 87-88, 91, 96 InputPermutations, 108 Installation, 2 Invariant polynomials, 58 Invariant zeros, InvariantZeros, 62 InvariantZeros, 62 Inverse systems, InverseSystem, 111 InverseSystem, 111, 119, 132, 139 Inverted pendulum example, 215 KNorm, 158 Laplace transform, 24 LCF, 75 Least-order system, LeastOrderSystem, 95 LeastOrderSystem, 82-83, 95, 97-98 Left coprime, LeftCoprime, 77 Left coprime factorization, 75 Left half-plane controllability, 71 LeftHalfPlaneControllable, 71 Left matrix GCD, LeftGCDDecomposition, 79 Left matrix-fraction, LeftMatrixFraction, 38 Left matrix-fraction model, of distillation column, 9 LeftCoprime, 9, 77, 80, 88, 98 LeftFraction, 42 as value of TargetForm, 33 LeftGCDDecomposition, 79, 88 LeftHalfPlaneControllable, 71 LeftMatrixFraction, 3, 9, 38 variable in, 26 LFT, 37 Linear-fraction transformation, 37 Luenberger controllable form, 201 LuenbergerControllableForm, 203 Luenberger observable form, 205 LuenbergerObservableForm, 206 Luenberger observer, 208 LuenbergerControllableForm, 203 LuenbergerObservableForm, 206, 215 MagnitudeFrequencyPlot, 142 Mapping, 190 Mapping algorithm, 189 Mass-spring system, 22 state-space model of, 23-24 system matrix of, 25 transfer-function of, 24 Matrix greatest common divisors, 75 Matrix-fraction descriptions, 37 McMillan degree, McMillanDegree, 66 McMillan form, 57 McMillanForm, 65 McMillanDegree, 4, 12, 66 McMillanForm, 65, 72 MFD, 37 Mixing tank example, 198 Monic polynomials, 59 Multivariable control systems, 1 NonlinearRegress, use in PerronFrobeniusCompensator, 141 NormalizedElement, 147 Nyquist array, 109 direct, 109, 113 inverse, 119 inverse-system, 110 NyquistArrayPlot, 113 of distillation column, 15 Nyquist contour, 109 Nyquist diagrams, generalized, 170 NyquistArrayPlot, 113, 119, 137 Observability, 57 Observability indices, ObservabilityIndices, 206 ObservabilityIndices, 206, 215, 220 Observable, 12, 67, 97 ObservableSubsystem, 91 Ostrowski circles, 111, 167 and Gershgorin circles, 111 OstrowskiCircleLoopGains, 123, 165 Output decoupling zeros, 86 OutputDecouplingZeros, 13, 87 removing, RemoveOutputDecouplingZeros, 91 Output feedback, 216 OutputDecouplingZeros, 87, 89-90, 96 OutputFeedbackCompensator, 219, 226 OutputFeedbackCompensatorDegree, 220 OutputResponse, 50 Permutation matrix, and input-output pairing, 105 Permutations of inputs and RelativeGainArrayNumberPlot, 108 and controller design, 108 and permutation matrix, 105 InputPermutations, 108 Perron-Frobenius eigenvalues, 133 eigenvectors, 134, 139 scaling, 118 Perron-Frobenius eigenvalue, PerronFrobeniusEigenvaluePlot, 135 Perron-Frobenius eigenvector, PerronFrobeniusEigenvectorPlot, 139 Perron-Frobenius scaling compensator constant, 133 dynamic, 139, 141, 152 PerronFrobeniusCompensator, 136 PerronFrobeniusCompensator, 136, 141, 147 PerronFrobeniusEigenvaluePlot, 135 PerronFrobeniusEigenvectorPlot, 139, 147 PI compensator, 126 Pole assignment, 188 full-rank algorithm for, 188 using dyadic algorithms, 188 using output feedback, 216 with state feedback, 13 Poles, of distillation column, 7 Precompensator design, 103 Pseudo-diagonalization, 157 PseudodiagonalizingCompensator, 158 Pseudo-diagonalizing compensator, PseudodiagonalizingCompensator, 19 PseudodiagonalizingCompensator, 19, 158 Pseudostates, 55 QNorm, 19, 158 RCF, 76 Reduced-order estimator, 208 ReducedOrderEstimator, 210 ReducedOrderEstimator, 210, 216 Relative gain array, RelativeGainArray, 104 Relative gain array number, RelativeGainArrayNumberPlot, 105 RelativeGainArray, 16 RelativeGainArrayNumberPlot, 105 Relatively left prime, 75 Relatively right prime, 76 RemoveInputDecouplingZeros, 89, 91, 94 and ControllableSubsystem, 91 RemoveOutputDecouplingZeros, 91 and ObservableSubsystem, 91 Responses, of distillation column, 7 Right coprime, RightCoprime, 77 Right coprime factorization, 76 Right matrix GCD, RightGCDDecomposition, 79 Right matrix-fraction, RightMatrixFraction, 37, 42 Right matrix-fraction model, of distillation column, 9 RightCoprime, 77, 83, 89-90 RightFraction, as value of TargetForm, 32 RightGCDDecomposition, 79 RightMatrixFraction, 3, 9, 42 variable in, 26 Row dominance ratio, RowDominanceRatioPlot, 128 RowDominance, 118, 123, 137, 165 as value of GershgorinCircles, 115 RowDominanceRatioPlot, 128, 138, 145 Schur product, 104 Separation principle, 213 Similarity transformations, SimilarityTransform, 99 SimilarityTransform, 99, 204, 207 and SystemMatrix, 99 SimulationPlot, 7, 18, 50 Smith form, 57 SmithForm, 60 SmithForm, 60, 78, 82-83 Spectral, 195 Spectral algorithm, 194 Stability, of distillation column, 7 State reconstruction, 208 State-space systems, 21 StateFeedbackConnect, 15 StateFeedbackGains, 14, 189, 195, 197 StateResponse, 50 Subsystem, 54 System equivalence, 35 System equivalence operations, 35 System matrix, 24 in polynomial form, 10, 25-26 in state-space form, 12, 25 SystemMatrix, 26 System requirements, 1 SystemEquivalentReduce, 35 SystemMatrix, 3, 9, 26 creating from other control objects, 30 left and right matrix-fraction forms of, 32 minimizing dimensions of, 35 variable in, 26 TargetForm, 4, 32-33, 42, 97 ToContinuousTime, 27 ToDiscreteTime, 4, 27, 48 Toeplitz matrix, 190 TraditionalForm, of control objects, 21 Transfer-function matrix, and system matrix, 25 TransformationMatrix use with LuenbergerControllableForm, 204 use with LuenbergerObservableForm, 207 Transmission zero, and stability, 69 Transmission zeros and McMillan form, 67 TransmissionZeros, 67 TransmissionZeros, 67-68, 117 Unimodular matrices, 58 |
