Delta-Modulation Coding Redesign for Feedback-Controlled Systems

This paper investigates the closed-loop properties of the differential coding scheme known as delta-modulation (Delta-M) when used in feedback loops within the context of feedback controlled systems. We propose a new modified scheme of the original form of the Delta-M algorithm which is better suited for applications where the sensed information is used in feedback. A state feedback controller is implemented with the state estimated by a predictor based differential decoder. Stability of the resulting closed-loop system (controller-coder-decoder) is studied. These properties (stability and performance) depend on the quantization parameter Delta, which is assumed constant in the first part of this paper. In a further step, parameter Delta is made adaptive, by defining an adaptation law exclusively in terms of information available at both the transmitter and receiver side. With this approach both stability and performance is improved.

[1]  M. Alamir,et al.  Remote stabilization via time-varying communication network delays: application to TCP networks , 2004, Proceedings of the 2004 IEEE International Conference on Control Applications, 2004..

[2]  Mo-Yuen Chow,et al.  Gain scheduler middleware: a methodology to enable existing controllers for networked control and teleoperation - part I: networked control , 2004, IEEE Transactions on Industrial Electronics.

[3]  Nicola Elia,et al.  Stabilization of linear systems with limited information , 2001, IEEE Trans. Autom. Control..

[4]  Y. Fujimoto,et al.  Control System With High-Speed and Real-Time Communication Links , 2008, IEEE Transactions on Industrial Electronics.

[5]  Sekhar Tatikonda,et al.  Control under communication constraints , 2004, IEEE Transactions on Automatic Control.

[6]  Carlos Canudas-de-Wit,et al.  Non uniform sampling coding in networked controlled linear systems , 2007 .

[7]  C. Canudas-de-Wit,et al.  Differential coding in networked controlled linear systems , 2006, 2006 American Control Conference.

[8]  Yasutaka Fujimoto,et al.  A control system with high speed and real time communication links , 2006, 9th IEEE International Workshop on Advanced Motion Control, 2006..

[9]  Manel Velasco,et al.  Managing quality-of-control in network-based control systems by controller and message scheduling co-design , 2004, IEEE Transactions on Industrial Electronics.

[10]  Umr Cnrs,et al.  Compensation Schemes for a Delta-Modulation-Based NCS , 2008 .

[11]  Ann C. Mertens,et al.  Voltage and current sensing in power electronic converters using sigma-delta A/D conversion , 1996, IAS '96. Conference Record of the 1996 IEEE Industry Applications Conference Thirty-First IAS Annual Meeting.

[12]  Gerhard Wachutka,et al.  Sensitivity enhancement of MEMS inertial sensors using negative springs and active control , 2002 .

[13]  M. Lemmon,et al.  Control system performance under dynamic quantization: the scalar case , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[14]  John S. Baras,et al.  Numerical study on joint quantization and control under block-coding , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[15]  John G. Proakis,et al.  Digital Communications , 1983 .

[16]  Tamer Basar,et al.  Remote control of LTI systems over networks with state quantization , 2005, Syst. Control. Lett..

[17]  Luis Angel Barragan,et al.  FPGA-Based Power Measuring for Induction Heating Appliances Using Sigma–Delta A/D Conversion , 2007, IEEE Transactions on Industrial Electronics.

[18]  Carlos Canudas de Wit,et al.  Energy-aware 3-level coding and control co-design for sensor network systems , 2007 .

[19]  Daniel Liberzon,et al.  Quantized feedback stabilization of linear systems , 2000, IEEE Trans. Autom. Control..

[20]  Michael Kraft.  Closed loop digital accelerometer employing oversampling conversion , 1997 .

[21]  J. Hespanha,et al.  Towards the Control of Linear Systems with Minimum Bit-Rate , 2002 .

[22]  Carlos Canudas-de-Wit,et al.  Energy-aware 3-level coding design for sensor network controlled systems , 2007, 2007 IEEE International Conference on Control Applications.

[23]  Carlos Canudas-de-Wit,et al.  Adaptive Delta-modulation Coding for Networked Controlled Systems , 2007, 2007 American Control Conference.

[24]  Carlos Canudas-de-Wit,et al.  Delta modulation for multivariable centralized linear networked controlled systems , 2008, 2008 47th IEEE Conference on Decision and Control.

[25]  Grenoble,et al.  Energy-aware 3-level coding and control co-design for sensor network systems , 2007 .

[26]  Daniel Liberzon,et al.  On stabilization of linear systems with limited information , 2003, IEEE Trans. Autom. Control..

[27]  Mo-Yuen Chow,et al.  Gain scheduler middleware: a methodology to enable existing controllers for networked control and teleoperation-part II: teleoperation , 2004, IEEE Transactions on Industrial Electronics.

[28]  C. Canudas de Wit,et al.  Gain-scheduling multi-bit Delta-Modulator for Networked Controlled System , 2007, 2007 European Control Conference (ECC).

[29]  Roberto Horowitz,et al.  Adaptive control for the conventional mode of operation of MEMS gyroscopes , 2002 .

[30]  John Baillieul,et al.  Robust quantization for digital finite communication bandwidth (DFCB) control , 2004, IEEE Transactions on Automatic Control.

[31]  Carlos Canudas-de-Wit.  Energy-aware 3-level coding and control co-design for sensor network systems , 2007 .