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9 Index 2-norm measure of impulse response coefficients, 197 AIC criterion, 51 Algorithm for estimating minimum variance benchmark directly from input-output data, 188 ARIMAX model, 117 ARMAX mode, 16 ARX model, 15 ARX-prediction based closed-loop subspace identification, 60 Backshift operator, 11 Bayes rule, 172 Bayesian network for diagnosis, 171 Benchmark problem for closed-loop subspace identification, 72 Box-Jenkins model, 17 Block-Hankel matrices, 37 Block-Toeplitz matrices, 39 Canonical variables, 49 Closed-loop estimation of dynamic matrices, 79, 81, 84 Closed-loop estimation of noise model, 85 Closed-loop identification of EIV systems, 71 Closed-loop Markov parameter matrices, 202 Closed-loop potential, 166, 198 Closed-loop SIMPCA, CSIMPCA, 69 Closed-loop SOPIM, CSOPIM, 69 Closed-loop subspace identification algorithm, 85 Closed-loop subspace matrices in relation to open-loop subspace matrices, 182 Consistent estimation, 25 Constrained DMC, 115 Constraints, 107, 128 Control horizon, 107, 108 Control-loop performance assessment: conventional approach, 145 Controller performance index, 188 Controller subspace, 69 Conventional MIMO control performance assessment algorithm, 151 Conventional SISO feedback control performance assessment algorithm, 149 Covariance of the prediction error, 197 CVA, 48, 49 Data-driven subspace algorithms to calculate multi-step optimal prediction errors, 202 Decision making in performance diagnosis, 173 Delay-free transfer function, 146 Designed vs. achieved benchmark, 161 Determination of model order, 51 Diophantine equations, 118, 146 Direct closed-loop identification method, 27 Discrete transfer function, 12 Disturbance model, 105 DMC prediction equation, 109 Dynamic Bayesian network, 175 Dynamic matrix, 110, 115

10 238 Index Dynamic matrix control, 108 Economic objective function, 168 Economic optimization, 116 Economic performance assessment and tuning, 167 Economic performance index, 170 EIV, 63 EIV state space model, 52 EIV subspace identification, 51 Estimation of multi-step optimal prediction errors, 202 Estimation of MVC Benchmark from Input/Output Data, 183 Estimation of subspace matrices, 180 Exact discretization, 10 Feedback control invariance property, 148, 151 Feedback control invariant, 145 Feedforward control, 127 Finite step response model, 109 Forced response, 106 Free response, 106, 118 Frobenius norm, 42 Fundamentals of MPC, 103 Generalized likelihood ratio test, 164 Generalized predictive control, GPC, 117 Generalized singular value, 50 GPC control law, 118 Graphic model, 171 Guidelines for closed-loop estimation of dynamic matrix, 86 Handling Disturbances in DMC, 112 Historical benchmark, 161 Historical covariance benchmark, 161 Impulse response curvature for performance monitoring, 165 Impulse response model, 104 Indirect closed-loop identification, 28 Innovation estimation approach, 61 Innovation form of state space model, 179 Instrument variable, 52, 67, 68 Instrument-variable methods, 51 Integral action, 125 Integrated white noise, 125 Interactor-matrix free methods for control performance assessment, 196 Joint input-output closed-loop identification, 29 Kalman filter states, 69 Least squares, 70, 181 Linear matrix inequality (LMI) for MPC economic performance analysis (LMIPA), 167 Local approach for model validation, 162 LQG benchmark, 159 LQG benchmark from closed-loop data: subspace approach, 214 LQG benchmark tradeoff curve, 217, 219 LQG benchmark variances of inputs, 216 LQG benchmark variances of outputs, 216 LQG benchmark with measured disturbances, 217 LQG benchmark: data-driven subspace approach, 213 LQG performance indices, 219, 220 LQG-benchmark based controller performance analysis, 219 Markov chain approach for performance monitoring, 166 Matrix inversion lemma, 84 Maximum likelihood, 50 Maximum likelihood ratio test, 164 Measured disturbances, 87 MIMO DMC problem formulation, 115 MIMO dynamic matrix, 115 MIMO feedback control performance assessment: conventional approach, 150 Minimum variance benchmark in subspace, 186 Minimum variance control, 145 Minimum variance control benchmark, 158 Minimum variance control law, 147 Minimum variance term, 151 MISO model for DMC, 114 MISO PEM model, 18 Model free approach for performance monitoring, 165

11 Index 239 Model predictive control, 101 Model structure selection, 15 Model-based simulation for control performance monitoring, 160 MOESP, 46, 48 Monte-Carlo simulations, 72 MPC performance assessment: prediction error approach, 195 MPC performance monitoring, 157 MPC performance monitoring through model validation, 162 MPC performance monitoring: modelbased approach, 158 MPC relevant model validation, 165 MPC solutions, 108 MPC tradeoff curve, 159 Multi-step optimal prediction errors: subspace algorithm, 201 Multivariate dynamic matrix control, 113 Multivariate performance assessment, 146 MVC benchmark from subspace matrices, 181 N4SID, 46, 48, 63 Noise model estimation from closed-loop data, 81 Noise model tuning, 130 Normalized multivariate impulse response (NMIR) curve, 166 Normalized residual, 164 Objective function, 107 Optimal ith step prediction, 197 Optimal prediction, 21 Optimal prediction for general linear models, 23 Order of interactor matrix, 151 Orthogonal complement, 47 Orthogonal-projection based identification, 63 Out of control index (OCI), 167 Output error model, 17 Output variance under minimum variance control expressed in subspace, 183 Penalizing control action, 111 Persistent excitation, 13 Petrochemical distillation column simulation example, 206 Prediction error approach to control performance assessment, 196 Prediction error method, 24 Prediction error method: algorithm, 25 Prediction error model, 15 Prediction horizon, 103 Prediction model for DMC, 109 Prediction-error approach for performance monitoring, 166 Predictions for MIMO DMC, 115 Primary residual, 163 Probabilistic inferencing for diagnosis of MPC performance, 171 Process model subspace, 69 QR decomposition, 48, 184 QR decomposition for projections, 66 Quadratic objective function, 117, 122 Rank determination, 65 Receding horizon, 103 Recurrence relation, 10 Reference closed-loop potential, 198 Reference trajectory, 107 Relative closed-loop potential index, 198 Riccati equation, 23 SISO feedback control performance assessment: conventional approach, 146 Solution of open-loop subspace identification by projection approach, 46 State space model of closed-loop system, 182 State space models, 105 Static Bayesian network, 174 Statistical approach, 49 Step response model, 104 Subspace approach for MIMO feedback control performance assessment, 177 Subspace expression of feedback control invariance property, 186 Subspace identification method via PCA, SIMPCA, 65 Subspace orthogonal projection identification method via the state estimation for model extraction, SOPIM-S, 70

12 240 Index Subspace orthogonal projection identification method, SOPIM, 65 Subspace predictive controller, SPC, 124 SVD, 48, 65 Theoretical economic index, 170 Time-delays, 12 Total least squares, 63 Tradeoff curve, 159 Transfer function model, 104 Transition tendency index (TTI), 167 Unconstrained DMC, 111 Unified approach to subspace algorithms, 48 Unitary interactor matrix, 151 Univariate performance assessment, 146 White noise, 32

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