||Generalized Optimal Linear Quadratic Trackers and Their Applications to Control Systems
||Department of Electrical Engineering
Optimal linear quadratic tracker
Non-minimum phase systems
Optimal iterative learning control
Model predictive control
Ironmaking blast furnace
Generalized optimal linear quadratic trackers and their applications to control systems are investigated in this dissertation. With the deployment of the frequency-domain shaping on the time-domain performance index function, the frequency-domain design concept can be merged into the optimization methodology in the time domain. However, for the strictly proper system without having any extra input or output signal, inducing the frequency-domain proportional-integral-derivative (PID) weighting function on the item of time-domain output tracking performance is equivalent to augmenting PID filter at the output terminal of the given strictly proper plant, theoretically. Consequently, the augmented plant arises in a proper system model with extra input and output signals. Nevertheless, how to resolve the optimal tracking for this generic system model has not been properly addressed in literature. Specifically, if an arbitrary time-varying command signal with enormous variations at some isolated time instants is involved, the design methodology for the optimal tracking of this kind of system arises in more challenge. Nevertheless, in this dissertation we first derive generalized optimal linear quadratic analog and digital trackers for the deterministic continuous-time and discrete-time general system models, respectively. Then, some new applications of the generalized optimal linear quadratic trackers on control systems are investigated. These include: (i) A new approach for computing the control zeros of the given non-square systems, (ii) A new optimal PID filter-shaped proportional-plus-integral (PI) state-feedback linear quadratic design for non-square non-minimum phase system to achieve a minimum phase-like tracking performance. However, a square non-minimum plant is still non-minimum phase, even though through appending PID filter(s)/controller(s) at either the input terminal, output terminal, or both terminals. To solve for the above-mentioned issues, in this dissertation we have designed a new PI current-output observer-based optimal linear quadratic tracker for square non-minimum phase system with an unknown external disturbance, (iii) A new PI observer-based optimal linear quadratic tracker for the proper system, using PI observer to estimate the system state and the unknown external disturbance. Some illustrative examples are given to demonstrate the effectiveness of the proposed methodologies, and (iv) A one-learning-epoch optimal linear quadratic tracker with an input-constrained for the repetitive proper system with unknown process disturbance and unknown measurement noise.
For completeness, disturbance estimation and performance compensation of unknown stochastic system with disturbances and positive input constraint are presented in this dissertation. Its novelties and contributions include: (i) Developing an improved observer/Kalman filter identification (OKID) method, which uses the current output measurement to estimate the current state, (ii) Proposing a modelling of a delay-free linear model for the unknown nonlinear time-delay system, (iii) Constructing a well-performed system output estimation by utilizing the current output-based Kalman filter, (iv) Formulating a universal approach for constructing artificial system models, based the current output-based Kalman filter, (v) Conducting of quantitative analysis to determine the stochastic and deterministic components of the unknown system of interest, (vi) Presenting a mechanism for virtual measurement, which allows us to use the output of the constructed artificial system model as virtual measurement to replace those missing and/or abnormal output measurements during the phases of testing and/or practical operation, (vii) Developing a modified observer-based model predictive control (MPC) with input constraints for the unknown nonlinear time-delay stochastic system with positive input constraints, (viii) Developing a universal mechanism for creating simulator and tracker design for positive input-constrained unknown nonlinear input time-delay stochastic sampled-data systems, and (ix) Carrying out the closed-loop type long-time prediction of future input-output sets, along the associated virtual measurements of the proposed artificial system with the modified MPC. Finally, a case study on the real stochastic nonlinear input time-delay blast furnace temperature control is demonstrated to show the effectiveness of the proposed methodology.
List of Tables x
List of Figures xi
Chapter 1 Introduction 1
1.1 Motivation 1
1.1.1 Generalized optimal linear quadratic analog and digital trackers 1
1.1.2 Optimal PID filter-shaped PI state-feedback LQT designs for non-square non-minimum phase systems 2
1.1.3 Optimal LQDTs for the discrete-time systems with an unknown disturbance 4
1.1.4 One-learning-epoch input-constrained optimal LQT designs for the repetitive systems 4
1.1.5 Modelling and tracker design for unknown nonlinear stochastic delay systems with positive input constraints 4
1.2 Contributions 5
1.3 Organization 7
Chapter 2 Generalized Optimal Linear Quadratic Trackers for Proper Systems with Known System Disturbances 9
2.1 Overview 9
2.2 A generalized optimal linear quadratic analog tracker for continuous-time proper systems with known system disturbances 11
2.3 A generalized optimal linear quadratic digital tracker for the discrete-time proper system with known system disturbances 16
2.4 Illustrative examples 22
2.5 Summary 30
Chapter 3 Optimal PI State-Feedback Linear Quadratic Trackers for Non-Minimum Phase Systems 32
3.1 Overview 32
3.2 Control-zero computation of non-square systems 39
3.3 A new optimal PI state-feedback linear quadratic analog tracker for non-square non-minimum phase continuous-time systems 51
3.4 A new optimal PI state-feedback linear quadratic digital tracker for non-square non-minimum phase discrete-time systems 58
3.5 Illustrative examples 64
3.6 Summary 74
Chapter 4 Optimal Linear Quadratic Trackers for Discrete-Time Systems with an Unknown Disturbance 76
4.1 Overview 76
4.2 Current-output observer-based LQDT for square non-minimum phase strictly proper discrete-time system with an unknown disturbance 77
4.3 Observer-based optimal digital tracker for proper discrete-time system with an unknown disturbance 85
4.4 Illustrative examples 89
4.5 Summary 104
Chapter 5 One-Learning-Epoch Optimal Trackers with Input Constraint for Repetitive Proper Systems with Unknown Disturbances 106
5.1 Overview 106
5.2 A one-learning-epoch optimal LQAT with input constraint for the repetitive proper system with unknown disturbances 107
5.3 A one-learning-epoch optimal LQDT with input constraint for the repetitive proper system with unknown disturbances 112
5.4 Illustrative examples 117
5.5 Summary 126
Chapter 6 Modelling and Tracker Design for Unknown Nonlinear Stochastic Delay Systems with Positive Input Constraints: A Case Study on the Blast Furnace Temperature Control 127
6.1 Overview 128
6.2 An improved observer/Kalman filter identification 135
6.2.1 The proposed current output-based OKID method 136
6.2.2 Delay-free linear modelling of a nonlinear system with time-delay 142
6.3 A novel approach for formulating artificial system models 150
6.3.1 The unified state-space innovation form 151
6.3.2 The well-performed output estimator-based simulator 155
6.3.3 Quantification of the dynamic characteristic of the system between stochastic and deterministic 158
6.4 Improved OKID-based modified model predictive control 159
6.4.1 Model predictive control 159
6.4.2 Input-constrained model predictive control 161
6.4.3 Improved OKID-based modified observer-based model predictive control with input constraints 163
6.4.3-1 Improved OKID-based modified observer-based model predictive control 163
6.4.3-2 A new input constraint design method based on the modified observer-based model predictive control 165
6.5 A universal mechanism for creating simulator and tracker design for unknown nonlinear time-delay stochastic systems with input constraints 167
6.6 An Illustrative example 174
6.7 Summary 189
Chapter 7 Conclusion 191
7.1 Conclusions 191
7.2 Future work 192
Appendix A Mathematical Modeling of Non-Minimum Phase Plants and Related Systems 206
A.1 State-space model with input-to-output-feedthrough term  206
A.2 Non-minimum phase C-to-D and D-to-C model conversations  207
A.3 Non-minimum phase PWM systems  215
A.4 Non-minimum phase unmanned aerial vehicles  219
A.5 Non-minimum phase vertical take-off and landing aircraft  221
A.6 Non-minimum phase conventional take-off and landing aircraft  224
A.7 Non-minimum phase beam-ball systems  225
A.8 Non-minimum phase flexible one-link robots [86, 22] 227
A.9 Non-minimum phase behavior in a class of chemical reaction systems  233
Appendix B Proof of Theorem 6.1 237
Appendix C Auto-Correlation Matrix 242
Publication List 245
 Abdi, M.J., Cardinality Optimization Problems. Ph.D. thesis, College of Engineering, University of Birmingham, United Kingdom, 2013.
 Abidi, K., Xu, J.X., and Xinghuo, Y., “On the discrete-time integral sliding mode control,” IEEE Transactions on Automatic Control, vol. 52, no. 4, pp.709-715, 2007.
 Akanyeti, O., Rañó, I., Nehmzow, U., and Billings, S.A., “An application of Lyapunov stability analysis to improve the performance of NARMAX models,” Robotics and Autonomous Systems, vol. 58, no. 3, pp. 229-238, 2010.
 Al-Numay, M.S. and Taylor, D.G., “Digital tracking control for PWM systems with unacceptable zeros,” IEEE transactions on Circuits and Systems—I: Fundamental Theory and Applications, vol. 45, no. 4, pp. 397-407, 1998.
 Amann, N., Owens, D.H., and Rogers, E., “Iterative learning control for discrete-time systems with exponential rate of convergence,” IEE proceedings Control Theory and Applications, vol. 143, no. 2, pp. 217-224, 1996.
 Anderson, B.D.O. and Mingori, D.L., “Use of frequency dependence in linear quadratic problems to frequency shape robustness,” Journal of Guidance and Control, vol. 8, no. 3, pp. 397-401, 1985.
 Anderson, B.D.O. and Moore, J.B., Optimal Control: Linear Quadratic Methods. Englewood Cliffs, NJ: Prentice-Hall, 1989.
 Arimoto, S., Kawamura, S., and Miyazaki, F., “Bettering operation of robots by learning,” Journal of Robotic Systems, vol. 1, no. 2, pp. 123-140, 1984.
 Astrom, K.J. and Wittenmark, G., Computer-Controlled System. Englewood Cliffs, NJ: Prentice-Hall, 1990.
 Astrom, K.J., Hagander, P., and Sternby, J., “Zeros of sampled systems,” Automatica, vol. 20, no. 1, pp. 31-38, 1984.
 Babaei, A., Mortazavi, M., and Moradi, M., “Fuzzy-genetic autopilot design for nonminimum phase and nonlinear unmanned aerial vehicles,” Journal of Aerospace Engineering, vol. 25, no. 1, pp. 1-9, 2012.
 Balas, M.J. and Frost, S.A., Adaptive control of non-minimum phase modal systems using residual mode filters: Part I, Advances in Aerospace Guidance, Navigation and Control, London: Springer. Retrieved from http://link.springer.com/chapter/10.1007% 2F978 -3-642-19817-5_17, 2011.
 Balas, M.J. and Frost, S.A., Adaptive control of non-minimum phase modal systems using residual mode filters: Part II, Advances in Aerospace Guidance, Navigation and Control, London: Springer, Retrieved from http://link.springer.com//chapter/10.1007% 2F978-3-642-19817-5_18#page-1, 2011.
 Bi, X., Torssell, K., and Wijk, O., “Prediction of the blast furnace by a mathematical model,” ISIJ International, vol. 32, no. 4, pp. 481-488, 1992.
 Bi, X., Torssell, K., and Wijk, O., “Simulation of the blast by a mathematical model,” ISIJ International, vol. 32, no. 4, pp. 470-480, 1992.
 Blakelock, J.H., Longitudinal Dynamics. Automatic Control of Aircraft and Missiles. New York, NY: Wiley, 1991.
 Breakwell, J.A., Control of Flexible Spacecraft. Ph.D. thesis, Department of Aeronautics and Astronautics, Stanford University, USA, 1980.
 Bristow, D.A., Tharayil, M., and Alleyne, A.G., “A survey of iterative learning control: A learning-based method for high-performance tracking control,” IEEE Control Systems, vol. 26, no. 3, pp. 96-114, 2006.
 Chang, J.L., “Applying discrete-time proportional integral observers for state and disturbance estimations,” IEEE Transactions on Automatic Control, vol. 51, no. 5, pp. 814-818, 2006.
 Chang, J.L., Ting, H.C. and Chen, Y.P., “Robust discrete-time output tracking controller design for non-minimum phase systems,” Journal of System Design and Dynamics, vol. 2, no. 4, pp. 950-961, 2008.
 Chang, W., Park, J.B., Lee, H.J., and Joo, Y.H., “LMI approach to digital redesign of linear time-invariant systems,” IEE Proceedings-Control Theory and Applications, vol. 149, no. 4, pp. 297-302, 2002.
 Chen B.S. and Yang, T.Y., “Robust optimal model matching control design for flexible manipulators,” Journal of Dynamic Systems, Measurement, and Control ,vol. 115, no. 1, pp. 173-178, 1993.
 Chen, F.M., Tsai, J.S. H., Liao, Y.T., Guo, S.M., Ho, M.C., Shaw, F.Z., and Shieh, L.S., “An improvement on the transient response of tracking for the sampled-data system based on an improved PD-type iterative learning control,” Journal of the Franklin Institute-Engineering and Applied Mathematics, vol. 35, no. 2, pp. 1130-1150, 2014.
 Chien, T.H., Tsai, J.S.H., Guo, S.M., and Li, J.S., “Low-order self-tuner for fault-tolerant control of a class of unknown nonlinear stochastic sampled-data systems,” Applied Mathematical Modelling, vol. 33, no. 2, pp. 706-723, 2009.
 Clarke, D.W., “Self-tuning control of non-minimum-phase systems,” Automatica, vol. 20, no. 5, pp. 501-517, 1984.
 Dahleh, M.A. and Pearson, J.Jr., “l1-optimal feedback controllers for MIMO discrete-time systems,” IEEE Transactions on Automatic Control, vol. 32, no. 4, pp. 314-322, 1987.
 Deolia, V.K., Purwar, S., and Sharma, T.N., “Stabilization of unknown nonlinear discrete-time delay systems based on neural network,” Intelligent Control and Automation, vol. 3, no. 4, pp. 337-345, 2012.
 Ding, F. and Chen, T., “Gradient based iterative algorithms for solving a class of matrix equation,” IEEE Transactions on Automatic Control, vol. 50, no. 8, pp. 216-1221, 2005.
 Doyle, J.C., Francis, B.A., and Tannenbaum, A.R., Feedback Control Theory. New York, NY: Macmillan, 1990.
 Du, Y.Y., Tsai, J.S.H., Patil, H., Shieh, L.S., and Chen, Y., “Indirect identification of continuous-time delay systems from step responses,” Applied Mathematical Modelling, vol. 35no. 2, pp. 594-611, 2011.
 Emami-Naeini, A. and Dooren, P.V., “Computation of zeros of linear multivariable systems,” Automatica, vol. 18, no. 4, pp. 425-430, 1982.
 Fiagbedzi, Y.A. and Pearson, A.E., “Feedback stabilization of linear autonomous time lag system,” IEEE Transactions on Automatic Control, vol. 31, no. 9, pp. 847-855, 1986.
 Gangsaas, D., Bruce, K.R., Blight, D.J., and Ly, U-.L., “Application of modern synthesis to aircraft control: Three case studies,” IEEE Transactions on Automatic Control, vol. 31, no. 11, pp. 995-1014, 1986.
 Gao, Z., Breikin, T., and Wang, H., “Discrete-time proportional-integral observer and observer-based controller for systems with unknown disturbances,” In European Control Conference. Kos, Greece, pp. 5248-5253, 2007.
 Geerdes, M., Toxopeus, H., Vliet, Cvd., Chaigneau, R., and Vander, T., Modern Blast Furnace Ironmaking: An Introduction. IOS Press, 2009.
 Guo, S.M., Shieh, L.S., Chen, G., Lin, C.F., and Chandra, J., “State-space self-tuning control for nonlinear stochastic and chaotic hybrid system,” International Journal of Bifurcation Chaos, vol. 11, no. 4, pp. 1079-1113, 2001.
 Guo, S.M., Shieh, L.S., Chen, G.R., and Lin, C.F., “Effective chaotic orbit tracker: A prediction-based digital redesign approach,” IEEE Transactions on Circuits and Systems I-Fundamental Theory and Applications, vol. 47, no. 11, pp. 1557-1570, 2000.
 Gupta, N.K., “Frequency-shaped loop functionals: Extensions of linear-quadratic-Gaussian design methods,” Journal of Guidance and Control, vol. 3, no. 6, pp. 529-535, 1980.
 Hauser, J., Sastry, S., and Meyer, G., “Nonlinear control design for slightly non-minimum phase systems: application to V/STOL aircraft,” Automatica, vol. 28, no. 4, pp. 665-679, 1992.
 Huang, Y.J. and Wang, Y-.J., “Robust PID controller design for non-minimum phase time delay systems,” ISA Transactions, vol. 40, no. 1, pp. 31-39, 2001.
 Huliehel, F. and Ben-Yaakov, S., “Low-frequency sampled-data models of switched mode DC–DC converters,” IEEE Transactions on Power Electronics., vol. 6, no. 1, pp. 55-61, 1991.
 Jemaa, L.B. and Davison, E., “Performance limitations in the robust servomechanism problem for discrete-time LTI systems,” IEEE Transactions on Automatic Control, vol. 48, no. 8, pp. 1299-1311, 2003.
 Jiménez, J., Mochón, J., Ayala, JSde., and Obeso, F., “Blast furnace hot metal temperature prediction through neural networks-based models,” The Iron and Steel Institute of Japan International, vol. 44, no. 3, pp. 573-580, 2004.
 Johnson, M.A. and Moradi, M.H., PID Control: New Identification and Design Methods. London: Springer, 2005.
 Joshi, V.V., Xie, L.B., Park, J.J., Shieh, L.S., Chen, Y.H., Grigoriadis, K., and Tsai, J.S.H., “Digital modeling and control of multiple time-delayed distributed power grid,” Applied Mathematical Modelling, vol. 36, no. 9, pp. 4118-4134, 2012.
 Juang, J.N., Applied System Identification. Englewood Cliffs, NJ: Prentice-Hall, 1994.
 Kaneko, N., Matsuzaki, S., Ito, M., Oogai, H., and Uchida, K., “Application of improved local models of large scale database-based online modeling to prediction of molten iron temperature of blast furnace,” The Iron and Steel Institute of Japan International, vol. 50, no. 7, pp. 939-945, 2010.
 Kapoor, N. and Daoutidis, P., “An observer-based anti-windup scheme for non-linear systems with input constraints,” International Journal of Control, vol. 72, no. 1, pp. 18-29, 1999.
 Kassakian, J.G., Schlecht, M.F., and Verghese, G.C., Principles of Power Electronics. Addison-Wesley, Reading, Massachusetts, 1991.
 Katebi, M. and Moradi, M., “Predictive PID controllers,” IEE Proceedings-Control Theory and Applications, vol. 148, no. 6, pp. 478-487, 2001.
 Koo, G.B., Park, J.B., and Joo, Y.H., “Decentralized control for large-scale sampled-data systems: digital redesign approach,” International Journal of Control, vol. 88, no. 11, pp. 2181-2193, 2015.
 Korda, M. and Cigler, J., “On 1-norm stochastic optimal control with bounded control inputs,” In American Control Conference (ACC). San Francisco, CA, pp. 60-65, 2011.
 Kravaris, C., Daoutidis, P., and Wright R.A., “Output feedback control of non-minimum phase nonlinear processes,” Chemical Engineering Science, vol. 49, no. 13, J, pp. 2107-2122, 1994.
 Kwon, B.H. and Youn, M.J., “Optimal regulators using time-weighted quadratic performance index with prescribed closed-loop eigenvalues,” IEEE Transactions on Automatic Control, vol. AC-31, no. 5, pp. 449-451, 1986.
 Latawiec, K., Banka, S., and Tokarzewski, J., “Control zeros and non-minimum phase LTI MIMO systems,” Annual reviews in Control, vol. 24, no. 1, pp. 105-112, 2000.
 Latawiec, K., Contributions to Advanced Control and Estimation for Linear Discrete-Time MIMO Systems. Technical University of Opole Press, Opole, Poland, 1998.
 Lee, D.H., Joo, Y.H., and Kim, S.K., “H-infinity digital redesign for LTI systems,” International Journal of Control, Automation, and Systems, vol. 13, no. 3, pp. 603-610, 2015.
 Lee, F.C., Iwens, R.P., Yu, Y., and Triner, J.E., “Generalized computer aided discrete time-domain modeling and analysis of DC–DC converters,” IEEE Transactions on Industrial Electronics and Control Instrumentation, vol. IECI-26, no. 2, pp. 58-69, 1979.
 Lee, H.J., Shieh, L.S., and Kim, D.W., “Digital control of nonlinear systems: Optimal linearization-based digital redesign approach,” IET Control Theory and Applications, vol. 2, no. 4, pp. 337-351, 2008.
 Lee, Y.Y., Tsai, J.S.H., Shieh, L.S., and Chen, G., “Equivalent linear observer-based tracker for stochastic chaotic system with delays and disturbances,” IMA Journal of Mathematical Control and Information, vol. 22, no. 3, pp. 266-284, 2005.
 Lewis, F.L., Applied Optimal Control and Estimation. Englewood Cliffs, NJ: Prentice-Hall, 1992.
 Lewis, F.L. and Syrmos, V.L., Optimal Control. New York, NJ: John Wiley & Sons, 1995.
 Lin, F.J., Chen, S.Y., and Huang, M.S., “Intelligent double integral sliding-mode control for five-degree-of-freedom active magnetic bearing system,” IET Control Theory and Applications, vol. 5, no. 11, pp. 1287-1303, 2011.
 Liu, Y., Yin, Y. and Liu, F., “Continuous gain scheduled H-infinity observer for uncertain nonlinear system with time-delay and actuator saturation,” International Journal of Innovative Computing, Information and Control, vol. 8, no. 12, pp. 1349-4198, 2012.
 Li, Y., Chen, Y.Q., and Ahn, H.S., “Fractional-order iterative learning control for fractional-order linear systems,” Asian Journal of Control, vol. 1, no. 13, pp. 54-63, 2011.
 MacFariance, A.G.J., and Karcanias, N., “Poles and zeros of linear multivariable systems: A survey of the algebraic, geometric and complex variable theory,” International Journal of Control, vol. 24, no. 1, pp. 33-74, 1976.
 Madsen, J.M., Shieh, L.S., and Guo, S.M., “State-space digital PID controller design for multivariable analog systems with multiple time delays,” Asia Journal of Control, vol. 8, no. 2, pp. 161-173, 2006.
 Martensson, B., Zeros of Sampled Systems. Report CODEN LUTFD2/(TF,RT-5266/1-022/(1982). Department of Automatic Control, Lund Institute of Technology, Lund, Sweden, 1982.
 Matausek, M.R., Micić, A.D., and Dacić, D.B., “Modified internal model control approach to the design and tuning of linear digital controllers,” International Journal of Systems Science, vol. 33, no. 1, pp. 67-79, 2002.
 McDonnell Aircraft Company, AV-8B NATOPS Flight Manual. McDonnell Aircraft Company, 1983.
 Miller, R.M., Shah, S.L., Wood, R.K., and Kwok, E.K., “Predictive PID,” ISA Transactions, vol. 38, no. 1, pp. 11-23, 1999.
 Mirkin, L., Rivlin, E., and Rotstein, H., “On static feedback for the l1 and other optimal control problems,” International Journal of Control, vol. 76, no. 5, pp. 453-458, 2003.
 Moore, J.B., Glover, K., and Telford, A., “All stabilizing controllers as frequency shaped state estimate feedback,” IEEE Transactions on Automatic Control, vol. 35, no. 2, pp. 203-208, 1990.
 Moradi, M.H., Katebi, M.R., and Johnson, M.A., “Predictive PID control: A new algorithm,” In Industrial Electronics Society 2001. IECON '01: The 27th Annual Conference of the IEEE. Denver, CO, pp. 764-769, 2001.
 Morari, M. and Zafiriou, E., Robust Process Control. Englewood Cliffs, NJ: Prentice Hall, 1989.
 Nasiri, M.R., “An optimal iterative learning control for continuous time system,” In IECON 2006-32nd Annual Conference on IEEE Industrial Electronics. Paris, pp. 114-119, 2006.
 Noura, H., Sauter, D., Hamelin, F., and Theilliol, D., “Fault-tolerant control in dynamic systems: Application to a winding machine,” IEEE Control Systems Magazine, vol. 20, no. 1, pp. 33-49, 2000.
 Ogata, K., Discrete-time Control Systems. Englewood Cliffs, NJ: Prentice-Hall, 1995.
 Ogunnaike, B.A., Lemaire, J.P., Morari, M., and Ray, W.H., “Advanced multivariable control of a pilot-plant distillation column,” AIChE Journal, vol. 29, no. 4, pp. 632-640, 1983.
 Otsuka, K., Matoba, Y., Kajiwara, Y., and Yoshida, M., “A hybrid expert system combined with a mathematical model for blast furnace operation,” ISIJ International, vol. 30, no. 2, pp. 118-127, 1990.
 Owens, D.H., Freeman, C.T., and Dinh, V.T., “Norm optimal iterative learning control with intermediate point weighting: Theory, algorithms and experimental evaluation,” IEEE Transactions on Control Systems Technology, vol. 21, no. 3, pp. 999-1007, 2013.
 Patel, R.V. and Misra, P., “Transmission zero assignment in linear multivariable systems; Part II: The general case,” In American Control Conference. Chicago, IL, pp. 644-648, 1992.
 Patel, R.V., “On zeros of multivariable systems,” International Journal of Control, vol. 21, no. 4, pp. 599-608, 1975.
 Rahrooh, A. and Shepard, S., “Identification of nonlinear systems using NARMAX model,” Nonlinear Analysis: Theory, Methods and Applications, vol. 71, no. 12, pp. e1198-e1202, 2009.
 Rauw, M., FDC 1.4—A SIMULINK toolbox for flight dynamics and control analysis, Retrieved from http://www.dutchroll.com, 2005.
 Robert, H. and Canon, Jr. and Schmitz, E., “Initial Experiments on the End-Point Control of a Flexible One-Link Robot,” The International Journal of Robotics Research, vol. 3, no. 3, pp. 62-75, 1984.
 Rodrigues, M., Theilliol, D., Aberkane, S., and Sauter, D., “Fault tolerant control design for polytopic LPV system,” International Journal of Applied Mathematics and Computer Science, vol. 17, no. 1, pp. 27-38, 2007.
 Rosenbrock, H.H., State-Space and Multivariable Theory. New York, NY: Nelson-Wiley, 1970.
 Roskam, J., Airplane Design Part VI: Preliminary Calculation of Aerodynamic Thrust and Power Characteristics. Lawrence: Kansas, 1990.
 Sage, A.P. and White, C.C., Optimum System Control. Englewood Cliffs, NJ: Prentice-Hall, 1977.
 Sato, T., “Design of a GPC-based PID controller for controlling a weigh feeder,” Control Engineering Practice, vol. 18, no. 2, pp. 105-113, 2010.
 Schrader, C.B. and Sain, M.K., “Research on system zeros: A survey,” International Journal of Control, vol. 50, no. 4, pp. 1407-1433, 1989.
 Sebakhy, O.A., Singaby, M.EL., and Arabawy, I.F.EL., “Zero placement and squaring problem: A state space approach,” International Journal of Systems Science, vol. 17, no. 12, pp. 1741-1750, 1986.
 She, J.H., Fang, M., Ohyama, Y., Hashimoto, H., and Wu, M., “Improving disturbance-rejection performance based on an equivalent-input-disturbance approach,” IEEE Transactions on Industrial Electronics, vol. 55, no. 1, pp. 380-389, 2008.
 She, J.H., Xin, X., and Pan, Y., “Equivalent-input-disturbance approach-Analysis and application to disturbance rejection in dual-stage feed drive control system,” IEEE/ASME Transactions on Mechatronics, vol. 16, no. 2, pp. 330-340, 2011.
 Shieh, L.S., Hani, M.D., and Sekar, G., “Continuous-time quadratic regulators and pseudo-continuous-time quadratic regulators with pole placement in a specific region,” IEE Proceedings-Control Theory and Applications, vol. 134, no. 5, pp. 338-346, 1987.
 Shieh, L.S., Wang, C.T., and Tsay, Y.T., “Fast suboptimal state-space self-tuner for linear stochastic multivariable systems,” IEE Proceedings-Control Theory and Applications, vol. 130, no. 4, pp. 143-154, 1983.
 Siddarth, A. and Valaseky, J., “Output tracking of non-minimum phase dynamics,” In A.I.A.A. Guidance, Navigation, and Control Conference. Portland, Oregon, 2011.
 Sirisena, H.R. and Teng, F.C., “Multivariable pole-zero placement self-tuning controller,” International Journal of Systems Science, vol. 17, no. 2, pp. 345-352, 1986.
 Skogestad, S. and Postlethwaite, I., Multivariable Feedback Control: Analysis and Design. New York, NY: John Wiley & Sons, 2005.
 Smagina, Y., “Zero Assignment in Multivariable System Using Pole Assignment Method,” Retrieved from arXiv:math/0207094v1 [math.DS], 2002.
 Stanislaw, H.Z., Systems and Control. New York, NY: Oxford University Press, In Tech, 2003.
 Strassburger, J.H., Blast Furnace–Theory and Practice. New York, NY: Gordon and Breach Science,,969.
 Syrmos, V.L. and Lewis, F.L., “Transmission zero assignment using semistate descriptions,” In American Control Conference. Chicago, IL, pp. 791-795, 1992.
 Tan, K.K., Huang, S.N., and Lee, T.H., “Development of a GPC-based PID controller for unstable systems with dead-time,” ISA Transactions, vol. 39, no. 1, pp. 57-70, 2000.
 Tan, K.K., Lee, T.H., and Leu, F.M., “Predictive PI versus Smith control for dead-time compensation,” ISA Transactions, vol. 40, no. 1, pp. 17-29, 2001.
 Theilliol, D., Join, C., and Zhang, Y., “Actuator fault tolerant control design based on a reconfigurable reference input,” International Journal of Applied Mathematics and Computer Science, vol. 18, no. 4, pp. 553-560, 2008.
 Theilliol, D., Noura, H., and Ponsart, J.C., “Fault diagnosis and accommodation of a three-tank system based on analytical redundancy,” ISA Transactions, vol. 41, no. 3, pp. 365-382, 2002.
 Thompson, C.M., Coleman, E.E., and Blight, J.D., “Integral LQG controller design for a fighter aircraft,” In A.I.A.A. Guidance, Navigation and Control Conference. Monterey, CA, pp. 87-2452, 1987.
 Tibaldi, M. and Capitani, G., “Duality between frequency–shaped LQ regulation and coloured noise estimation,” International Journal of Systems Science, vol. 21no. 7, pp. 1289-1296, 1990.
 Tomizuka, M., “Zero phase error tracking algorithm for digital contro1,” Journal of Dynamic Systems, Measurement and Control, vol. 109, no. 1, pp. 65-68, 1987.
 Torfs, D., Swevers, J., and Schutter, J.D., “Quasi-perfect tracking control of non-minimal phase systems,” In Proceeding of the 30th Conference on Decision and Control. Brighton, pp. 241-244, 1991.
 Tsai, J.S.H., Dua, Y.Y., Huanga, P.H., Guo, S.M., Shieh, L.S., and Chen, Y., “Iterative learning-based decentralized adaptive tracker for large-scale systems: A digital redesign approach,” ISA Transactions, vol. 50, no. 3, pp. 344-356, 2011.
 Tsai, J.S.H., Du, Y.Y., Zhuang, W.Z., Guo, S.M., Chen, C.W., and Shieh, L.S., “Optimal anti-windup digital redesign of MIMO control systems under input constraints,” IET Control Theory and Applications, vol. 5, no. 3, pp. 447-464, 2011.
 Tsai, J.S.H., Hsu, W.T., Lin, L.G., Guo, S.M., and Tan, J.W., “A modified NARMAX model-based self-tuner with fault tolerance for unknown nonlinear stochastic hybrid systems with an input-output direct feed-through term,” ISA Transactions, vol. 53, no. 1, pp. 56-75, 2014.
 Tsai, J.S.H., Hsu, W.T., Tsai, T.J., Lin, K., Guo, S.M., and Shieh, L.S., “Realization of causal current output-based optimal full/reduced-order observer and tracker for the linear sampled-data system with a direct transmission term,” Optimal Control Application and Methods, vol. 34, no. 6, pp. 729-749, 2015.
 Tsai, J.S.H., Hsu, W.T., Wei, C.L., Guo, S.M., and Shieh, L.S., “Universal prediction-based adaptive fault estimator applied to secure communication,” Applied Mathematical Modelling, vol. 38no. 19–20, pp. 4717-4732, 2014.
 Tsai, J.S.H., Huang, C.C., Guo, S.M., and Shieh, L.S., “Continuous to discrete model conversion for the system with a singular system matrix based on matrix sign function,” Applied Mathematical Modelling, vol. 35, no. 8, pp. 3893-3904, 2011.
 Tsai, J.S.H., Lin, J.Y., Shieh, L.S., Chandra, J., and Guo, S.M., “Self-tuning fault-tolerant digital PID controller for MIMO analog systems with partial actuator and system component failures,” IMA Journal of Mathematical Control and Information, vol. 25, no. 2, pp. 221-238, 2008.
 Tsai, J.S.H., Wang, C.T., Kuang, C.C., Guo, S.M., Shieh, L.S., Chen, C.W., “A NARMAX model-based state-space self-tuning control for nonlinear stochastic hybrid systems,” Applied Mathematical Modelling, vol. 34, no. 10, pp. 3030-3054, 2010.
 Tsay, Y.T. and Shieh, L.S., “State-space approach for self-tuning feedback control with pole assignment,” IEE Proceedings D-Control Theory and Applications, 128, no. 3, 93-101, 1981.
 Uren, K. and Schoor, G.V., Predictive PID control of non-minimum phase systems, Advances in PID Control, Valery, D., and Yurkevich (Ed.)., Advances in PID Control. Rijeka: In Tech, Retrieved from http://www.intechopen.com/books/advances-in-pid- control/predictive-pid-control-of-non minimum-phase-systems, 2011.
 Valery, D. and Yurkevich, (Ed.), Advances in PID Control. In Tech, Croatia, 2011.
 Verghese, G.C., Elbuluk, M.E., and Kassakian, J.G., “A general approach to sampled-data modeling for power electronic circuits,” IEEE Transactions on Power Electron., vol. PE-1, no. 2, pp. 76-89, 1986.
 Wang, H.P., Tsai, J.S.H., Yi, Y.I., and Shieh, L.S., “Lifted digital redesign of observer-based tracker for sampled-data system,” International Journal of Systems Science, vol. 35, no. 4, pp. 255-271, 2004.
 Wang, J.H., Tsai, J.S.H., Huang, J.S., Guo, S.M., Shieh, L.S., “A low-order active fault-tolerant state space self-tuner for the unknown sampled-data nonlinear singular system using OKID and modified ARMAX model-based system identification,” Applied Mathematical Modelling, vol. 37, no. 3, pp. 1242-1274, 2013.
 Wang, L.P., Model Predictive Control System Design and Implementation using MATLAB. London: Springer, 2009.
 Wang, M.H., Wang, B.P., and Hui, Z.G., “Process control and expert system for blast furnace,” Heilongjiang Yejin, vol. 4, pp. 7-12, 2004 (in Chinese).
 Wang, W., Control of a Ball and Beam System. Submitted for the degree of Advanced Master on the 5 June, 2007, School of Mechanical Engineering, The University of Adelaide, South Australia 5005, Australia, 2007.
 Wang, Y.J., “Determination of all feasible robust PID controllers for open-loop unstable plus time delay processes with gain margin and phase margin specifications,” ISA Transactions, vol. 53, no. 2, pp. 628-646, 2014.
 Warwick, K., “Self-tuning regulators-a state-space approach,” International Journal of Control, vol. 33, pp. 839-858, 1981.
 Wellstead, P.E., Edmunds, J.M., Prager, D., and Zanker, P., “Self-tuning pole/zero assignment regulators,” International Journal of Control, vol. 30, no. 1, pp. 1-26, 1979.
 Wellstead, P.E., Prager, D., and Zanker, P., “Pole assignment self-tuning regulator,” IEE Proceedings-Control and Science, vol. 126, no. 8, pp. 781-787, 1979.
 Wiberg, D.M., Theory and Problems of State Space and Linear Systems. New York, NY: McGraw-Hill, 1971.
 Wu, C.Y., Tsai, J.S.H., Guo, S.M., Shieh, L.S., Canelon, J.I., Ebrahimzadeh, F., and Wang, L., “A novel on-line observer/Kalman filter identification method and its application to input-constrained active fault-tolerant tracker design for unknown stochastic systems,” Journal of the Franklin Institute-Engineering and Applied Mathematics, vol. 352, no. 3, pp. 1119-1151, 2015.
 Xu, J.X., “A survey on iterative learning control for nonlinear systems,” International Journal of Control, vol. 84(7), pp. 1275-1294, 2011.
 Zhang, Y., Shieh, L.S., Liu, C.R., and Guo, S.M., “Digital PID controller design for multivariable analogue systems with computational input-delay,” IMA Journal of Mathematical Control and Information, vol. 21, no. 4, pp. 433-456, 2004.
 Zhou, H.Q., Shieh, L.S., Liu, C.R., and Wang, Q.G., “State-space digital PI controller design for linear stochastic multivariable systems with input delays,” The Canadian Journal of Chemical Engineering, vol. 84, no. 2, pp. 230-238, 2006