Research Papers

Linear Matrix Inequalities Approach to Input Covariance Constraint Control With Application to Electronic Throttle

[+] Author and Article Information
Ali Khudhair Al-Jiboory, Andrew White, Shupeng Zhang

Department of Mechanical Engineering,
Michigan State University,
East Lansing, MI 48824

Guoming Zhu, Jongeun Choi

Department of Mechanical Engineering,
Department of Electrical
and Computer Engineering,
Michigan State University,
East Lansing, MI 48824

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received October 17, 2014; final manuscript received March 24, 2015; published online June 24, 2015. Assoc. Editor: Ryozo Nagamune.

J. Dyn. Sys., Meas., Control 137(9), 091010 (Sep 01, 2015) (9 pages) Paper No: DS-14-1421; doi: 10.1115/1.4030525 History: Received October 17, 2014; Revised March 24, 2015; Online June 24, 2015

In this paper, the input covariance constraint (ICC) control problem is solved by convex optimization subject to linear matrix inequalities (LMIs) constraints. The ICC control problem is an optimal control problem that is concerned to obtain the best output performance subject to multiple constraints on the input covariance matrices. The contribution of this paper is the characterization of the control synthesis LMIs used to solve the ICC control problem. Both continuous- and discrete-time problems are considered. To validate our scheme in real-world systems, ICC control based on convex optimization approach was used to control the position of an electronic throttle plate. The controller performance compared experimentally with a well-tuned base-line proportional-integral-derivative (PID) controller. Comparison results showed that not only better performance has been achieved but also the required control energy for the ICC controller is lower than that of the base-line controller.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Zhu, G., Grigoriadis, K. M., and Skelton, R. E., 1995, “Covariance Control Design for Hubble Space Telescope,” J. Guid., Control, Dyn., 18(2), pp. 230–236. [CrossRef]
Christensen, R. S., and Geller, D., 2014, “Linear Covariance Techniques for Closed-Loop Guidance Navigation and Control System Design and Analysis,” J. Aerosp. Eng., 228(1), pp. 44–65. [CrossRef]
Kalandros, M., 2002, “Covariance Control for Multisensor Systems,” IEEE Trans. Aerosp. Electron. Syst., 38(4), pp. 1138–1157. [CrossRef]
Hotz, A., and Skelton, R. E., 1987, “Covariance Control Theory,” Int. J. Control, 46(1), pp. 13–32. [CrossRef]
Grigoriadis, K. M., and Skelton, R. E., 1997, “Minimum-Energy Covariance Controllers,” Automatica, 33(4), pp. 569–578. [CrossRef]
Xu, J., and Skelton, R., 1992, “Robust Covariance Control,” Robust Control of Lecture Notes in Control and Information Sciences, Vol. 183, Springer, Berlin, pp. 98–105.
Chen, X., Wang, Z., Xu, G., Guo, Z., and Feng, Z., 1995, “Eigenstructure Assignment in State Covariance Control,” Syst. Control Lett., 26(3), pp. 157–162. [CrossRef]
Khaloozadeh, H., and Baromand, S., 2010, “State Covariance Assignment Problem,” IET Control Theory Appl., 4(3), pp. 391–402. [CrossRef]
Sreeram, V., Liu, W. Q., and Diab, M., 1996, “Theory of State Covariance Assignment for Linear Single-Input Systems,” IEEE Proc. Control Theory Appl., 143(3), pp. 289–295. [CrossRef]
Hsieh, C., Skelton, R. E., and Damra, F. M., 1989, “Minimum Energy Controllers With Inequality Constraints on Output Variances,” Optim. Control Appl. Methods, 10(4), pp. 347–366. [CrossRef]
Zhu, G., Rotea, M., and Skelton, R. E., 1997, “A Convergent Algorithm for the Output Covariance Constraint Control Problem,” SIAM J. Control Optim., 35(1), pp. 341–361. [CrossRef]
Zhu, G., 1992, “L2 and L∞Multiobjective Control for Linear Systems,” Ph.D. thesis, Purdue University, West Lafayette, IN.
Collins, E. G., Jr., and Selekwa, M. F., 2002, “A Fuzzy Logic Approach to LQG Design With Variance Constraints,” IEEE Trans. Control Syst. Technol., 10(1), pp. 32–42. [CrossRef]
Conway, R., and Horowitz, R., 2008, “A Quasi-Newton Algorithm for LQG Controller Design With Variance Constraints,” ASME Paper No. DSCC2008-2239. [CrossRef]
White, A., Zhu, G., and Choi, J., 2012, “A Linear Matrix Inequality Solution to the Output Covariance Constraint Control Problem,” ASME Paper No. DSCC2012-MOVIC2012-8799. [CrossRef]
Al-Jiboory, A. K., Zhu, G., and Sultan, C., 2014, “LMI Control Design With Input Covariance Constraint for a Tensegrity Simplex Structure,” ASME Paper No. DSCC2014-6122. [CrossRef]
Nesterov, Y., Nemirovskii, A., and Ye, Y., 1994, Interior-Point Polynomial Algorithms in Convex Programming, Vol. 13, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.
Rotea, M. A., 1993, “The Generalized H2Control Problem,” Automatica, 29(2), pp. 373–385. [CrossRef]
De Oliveira, M. C., Geromel, J. C., and Bernussou, J., 2002, “Extended H2 and H∞ Norm Characterizations and Controller Parameterizations for Discrete-Time Systems,” Int. J. Control, 75(9), pp. 666–679. [CrossRef]
Scherer, C., Gahinet, P., and Chilali, M., 1997, “Multiobjective Output-Feedback Control Via LMI Optimization,” IEEE Trans. Autom. Control, 42(7), pp. 896–911. [CrossRef]
Chilali, M., and Gahinet, P., 1996, “H∞ Design With Pole Placement Constraints: An LMI Approach,” IEEE Trans. Autom. Control, 41(3), pp. 358–367. [CrossRef]
Masubuchi, I., Ohara, A., and Suda, N., 1998, “LMI-Based Controller Synthesis: A Unified Formulation and Solution,” Int. J. Rob. Nonlinear Control, 8(8), pp. 669–686. [CrossRef]
De Oliveira, M. C., Bernussou, J., and Geromel, J., 1999, “A New Discrete-Time Robust Stability Condition,” Syst. Control Lett., 37(4), pp. 261–265. [CrossRef]
Grepl, R., and Lee, B., 2010, “Model Based Controller Design for Automotive Electronic Throttle,” Recent Advances in Mechatronics, Springer, Berlin, pp. 209–214.
Zhang, S., Yang, J. J., and Zhu, G. G., 2014, “LPV Modeling and Mixed Constrained H2/H∞ Control of an Electronic Throttle,” IEEE/ASME Trans. Mechatronics, PP(99), pp. 1–13. [CrossRef]
Löfberg, J., 2004, “YALMIP: A Toolbox for Modeling and Optimization in MATLAB,” IEEE International Symposium on Computer Aided Control Systems Design (CACSD), Taipei, Sept. 4, pp. 284–289. [CrossRef]
Sturm, J., 1999, “Using SeDuMi 1.02, a MATLAB Toolbox for Optimization Over Symmetric Cones,” Optim. Methods Software, 11(1), pp. 625–653. [CrossRef]
Keel, L., Rego, J., and Bhattacharyya, S., 2003, “A New Approach to Digital PID Controller Design,” IEEE Trans. Autom. Control, 48(4), pp. 687–692. [CrossRef]


Grahic Jump Location
Fig. 1

An electronic throttle system

Grahic Jump Location
Fig. 2

Experiment test bench setup and block diagram

Grahic Jump Location
Fig. 3

Experimental tracking and signals of throttle the ICC control

Grahic Jump Location
Fig. 4

Tracking experiment for different throttle angles

Grahic Jump Location
Fig. 5

Experiment and simulation tracking (raising edge)

Grahic Jump Location
Fig. 6

Experiment and simulation tracking (falling edge)

Grahic Jump Location
Fig. 7

Performance comparison between ICC and PID controllers

Grahic Jump Location
Fig. 8

Performance versus control energy



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In