Robust Smith Predictor Design for Time-Delay Systems with H∞ Performance

A new method for robust fixed-order H∞ controller design for uncertain time-delay systems is presented. It is shown that the H∞ robust performance condition can be represented by a set of convex constraints with respect to the parameters of a linearly parameterized primary controller in the Smith predictor structure. Therefore, the parameters of the primary controller can be obtained by convex optimization. The proposed method can be applied to stable SISO and MIMO models with uncertain dead-time and with multimodel and frequency-dependent uncertainty. It is also shown that how the design method can be extended to unstable SISO models. The design of robust gain-scheduled dead-time compensators is also investigated. The performance of the method is illustrated for both SISO and MIMO systems by simulation examples

Robustness analysis of discrete predictor-based controllers for input-delay systems

In this article, robustness to model uncertainties are analysed in the context of discrete predictor-based state-feedback controllers for discrete-time input-delay systems with time-varying delay, in an LMI framework. The goal is comparing robustness of predictor-based strategies with respect to other (sub)optimal state feedback ones. A numerical example illustrates that improvements in tolerance to modelling errors can be achieved by using the predictor framework.The authors are grateful for grant nos. DPI2008-06737-C02-01, DPI2008-06731-C02-01, DPI2011-27845-C02-01 and PROMETEO/2008/088 from the Spanish and Valencian governments.González Sorribes, A.; Sala, A.; García Gil, PJ.; Albertos Pérez, P. (2013). Robustness analysis of discrete predictor-based controllers for input-delay systems. International Journal of Systems Science. 44(2):232-239. https://doi.org/10.1080/00207721.2011.600469S232239442Boukas, E.-K. (2006). Discrete-time systems with time-varying time delay: Stability and stabilizability. Mathematical Problems in Engineering, 2006, 1-10. doi:10.1155/mpe/2006/42489Du, D., Jiang, B., & Zhou, S. (2008). Delay-dependent robust stabilisation of uncertain discrete-time switched systems with time-varying state delay. International Journal of Systems Science, 39(3), 305-313. doi:10.1080/00207720701805982El Ghaoui, L., Oustry, F., & AitRami, M. (1997). A cone complementarity linearization algorithm for static output-feedback and related problems. IEEE Transactions on Automatic Control, 42(8), 1171-1176. doi:10.1109/9.618250Gao, H., & Chen, T. (2007). New Results on Stability of Discrete-Time Systems With Time-Varying State Delay. IEEE Transactions on Automatic Control, 52(2), 328-334. doi:10.1109/tac.2006.890320Gao, H., Wang, C., Lam, J., & Wang, Y. (2004). Delay-dependent output-feedback stabilisation of discrete-time systems with time-varying state delay. IEE Proceedings - Control Theory and Applications, 151(6), 691-698. doi:10.1049/ip-cta:20040822Gao, H., Chen, T., & Lam, J. (2008). A new delay system approach to network-based control. Automatica, 44(1), 39-52. doi:10.1016/j.automatica.2007.04.020Garcia , P , Castillo , P , Lozano , R and Albertos , P . 2006 . Robustness with Respect to Delay Uncertainties of a Predictor Observer Based Discrete-time Controller . Proceeding of the 45th IEEE Conference on Decision and Control . 2006 . pp. 199 – 204 .Guo , Y and Li , S . 2009 . New Stability Criterion for Discrete-time Systems with Interval Time-varying State Delay . Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference . 2009 . pp. 1342 – 1347 .Hägglund, T. (1996). An industrial dead-time compensating PI controller. Control Engineering Practice, 4(6), 749-756. doi:10.1016/0967-0661(96)00065-2V.J.S. Leite, and Miranda, M.F. (2008), ‘Robust Stabilization of Discrete-time Systems with Time-varying Delay: An LMI Approach’,Mathematical Problems in Engineering, 2008, 15 pages (doi:10.1155/2008/875609)Liu, X. G., Tang, M. L., Martin, R. R., & Wu, M. (2006). Delay-dependent robust stabilisation of discrete-time systems with time-varying delay. IEE Proceedings - Control Theory and Applications, 153(6), 689-702. doi:10.1049/ip-cta:20050223Lozano, R., Castillo, P., Garcia, P., & Dzul, A. (2004). Robust prediction-based control for unstable delay systems: Application to the yaw control of a mini-helicopter. Automatica, 40(4), 603-612. doi:10.1016/j.automatica.2003.10.007Manitius, A., & Olbrot, A. (1979). Finite spectrum assignment problem for systems with delays. IEEE Transactions on Automatic Control, 24(4), 541-552. doi:10.1109/tac.1979.1102124Michiels, W., & Niculescu, S.-I. (2003). On the delay sensitivity of Smith Predictors. International Journal of Systems Science, 34(8-9), 543-551. doi:10.1080/00207720310001609057Palmor, Z.J. (1996), ‘Time-delay Compensation – Smith Predictor and Its Modifications’, inThe Control Handbook, ed. W.S. Levine, Boca Raton: CRC Press, pp. 224–237Pan, Y.-J., Marquez, H. J., & Chen, T. (2006). Stabilization of remote control systems with unknown time varying delays by LMI techniques. International Journal of Control, 79(7), 752-763. doi:10.1080/00207170600654554Richard, J.-P. (2003). Time-delay systems: an overview of some recent advances and open problems. Automatica, 39(10), 1667-1694. doi:10.1016/s0005-1098(03)00167-5Wang, Q.-G., Lee, T. H., & Tan, K. K. (1999). Finite-Spectrum Assignment for Time-Delay Systems. Lecture Notes in Control and Information Sciences. doi:10.1007/978-1-84628-531-8He, Y., Wu, M., Han, Q.-L., & She, J.-H. (2008). Delay-dependentH∞control of linear discrete-time systems with an interval-like time-varying delay. International Journal of Systems Science, 39(4), 427-436. doi:10.1080/00207720701832531Yue, D., & Han, Q.-L. (2005). Delayed feedback control of uncertain systems with time-varying input delay. Automatica, 41(2), 233-240. doi:10.1016/j.automatica.2004.09.006Zhang, B., Xu, S., & Zou, Y. (2008). Improved stability criterion and its applications in delayed controller design for discrete-time systems. Automatica, 44(11), 2963-2967. doi:10.1016/j.automatica.2008.04.01

Robust predictive control strategy applied for propofol dosing using BIS as a controlled variable during anesthesia

This paper presents the application of predictive control to drug dosing during anesthesia in patients undergoing surgery. The performance of a generic predictive control strategy in drug dosing control, with a previously reported anesthesia-specific control algorithm, has been evaluated. The robustness properties of the predictive controller are evaluated with respect to inter- and intrapatient variability. A single-input (propofol) single-output (bispectral index, BIS) model of the patient has been assumed for prediction as well as for simulation. A set of 12 patient models were studied and interpatient variability and disturbances are used to assess robustness of the controller. Furthermore, the controller guarantees the stability in a desired range. The applicability of the predictive controller in a real-life environment via simulation studies has been assessed

Adaptive digital PID control of first‐order‐lag‐plus‐dead‐time dynamics with sensor, actuator, and feedback nonlinearities

Proportional‐integral‐derivative (PID) control is one of the most widely used feedback control strategies because of its ability to follow step commands and reject constant disturbances with zero asymptotic error, as well as the ease of tuning. This paper presents an adaptive digital PID controller for sampled‐data systems with sensor, actuator, and feedback nonlinearities. The linear continuous‐time dynamics are assumed to be first‐order lag with dead time (ie, delay). The plant gain is assumed to have known sign but unknown magnitude, and the dead time is assumed to be unknown. The sensor and actuator nonlinearities are assumed to be monotonic, with known trend but are otherwise unknown, and the feedback nonlinearity is assumed to be monotonic, but is otherwise unknown. A numerical investigation is presented to support a simulation‐based conjecture, which concerns closed‐loop stability and performance. Numerical examples illustrate the effect of initialization on the rate of adaptation and investigate failure modes in cases where the assumptions of the simulation‐based conjecture are violated. This paper presents an adaptive digital PID controller for sampled‐data systems with sensor, actuator, and feedback nonlinearities as well as linear continuous‐time dynamics that are first‐order lag with dead time (ie, delay). A numerical investigation is presented to support a simulation‐based conjecture on closed‐loop stability and performance. Numerical examples illustrate the effect of initialization on the rate of adaptation and investigate failure modes in cases where the assumptions of the simulation‐based conjecture are violated.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/153185/1/adc220.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/153185/2/adc220_am.pd