A Toolbox for Input-Output System Inversion

  • Antonio Visioli University of Brescia Dipartimento di Elettronica per l’Automazione Via Branze 38, I-25123 Brescia, Italy
  • Aurelio Piazzi University of Parma Dipartimento di Ingegneria dell’Informazione Parco Area delle Scienze 181A, I-43100 Parma, Italy


In this paper a Matlab-based toolbox for the input-output system inversion of linear systems is presented. Different methods, based either on analytical or numerical approaches, are implemented. The toolbox can be exploited in the design of a feedforward action for control systems in different contexts in order to improve performances in the set-point regulation. The use of a pre-actuation and a post-actuation time can be easily analyzed as well as the role played by the choice of the desired output function.


[1] B. C. Kuo, Automatic Control Systems, Prentice Hall, Englewood Cliffs (NJ), 1995.

[2] A. Wallen, K. J. Åström, Pulse-step control, Preprints of the 15th IFAC World Congress on Automatic Control, Barcelona (Spain), 2002.

[3] A. Visioli, A new design for a PID plus feedforward controller, Journal of Process Control, Vol. 14, No. 4, pp. 455-461, 2004.

[4] H. Perez, S. Devasia, Optimal output transitions for linear systems, Automatica, Vol. 39, pp. 181-192, 2003.

[5] Q. Zou, S. Devasia, Preview-based optimal inversion for output tracking: application to scanning tunneling microscopy, Proceedings IEEE International Conference on Decision and Control, Las Vegas (USA), pp. 79-85, 2002.

[6] D. Iamratanakul, H. Perez, S. Devasia, Feedforward trajectory design for output transitions in discrete-time systems: disk-drive example, Proceedings of the American Control Conference, Denver (USA), pp. 3142-3147, 2003.

[7] A. Piazzi, A. Visioli, Minimum-time system-inversion-based motion planning for residual vibration reduction, IEEE/ASME Transactions on Mechatronics, Vol. 5, No. 1, pp. 12-22, 2000.

[8] A. Piazzi, A.Visioli, Optimal inversion-based control fo the set-point regulation of nonminimumphase uncertain scalar systems, IEEE Transactions on Automatic Control, Vol. 46, No. 10, pp. 1654- 1659, 2001.

[9] M. Benosman, G. Le Vey, Stable inversion of SISO nonminimum phase linear systems through output planning: an experimental application to the one-link flexible manipulator, IEEE Transactions on Control Systems Technology, Vol. 11, No. 4, pp. 588-597, 2003.

[10] C. Guarino Lo Bianco, A. Piazzi, A servo control system design using dynamic inversion, Control Engineering Practice, Vol. 10, No, 8, pp. 847-855, 2002.

[11] A. Piazzi, A. Visioli, Optimal dynamic inversion based control of an overhead crane, IEE Proceedings - Control Theory and Applications, Vol. 149, No. 5, pp. 405-411, 2002.

[12] A. Visioli, A. Piazzi, Improving set-point following performance of industrial controllers with a fast dynamic inversion algorithm, Industrial Engineering and Chemistry Research, Vol. 42, pp. 1357- 1362, 2003.

[13] A. Piazzi, A. Visioli, A noncausal approach for PID control, Journal of Process Control, Vol. 16, pp. 831-843, 2006.

[14] J. W. Polderman, J. C. Willems, Introduction to Mathematical Systems Theory, Springer-Verlag, New York, 1998.

[15] D. Pallastrelli, A. Piazzi, Stable dynamic inversion of nonminimum-phase scalar linear systems, Preprints of the 16th IFAC World Congress on Automatic Control, Prague (CZ), 2005.

[16] Q. Zou, S. Devasia, Preview-based inversion of nonlinear nonminimum-phase systems: VTOL example, Proceedings of the IEEE International Conference on Decision and Control, Paradise Island (The Bahamas), pp. 4350-4356, 2004.

[17] A. Piazzi, A. Visioli, Optimal noncausal set-point regulation of scalar systems, Automatica, Vol. 37, No. 1, pp. 121-127, 2001.

[18] A. Piazzi, A. Visioli, Using stable input-output inversion for minimum-time feedforward constrained regulation of scalar systems, Automatica, Vol. 41, No. 2, pp. 305-313, 2005.

[19] E. Hansen, G.W.Walster, Global optimization using interval analysis - 2nd edition, Marcel Dekker, 2003.
How to Cite
VISIOLI, Antonio; PIAZZI, Aurelio. A Toolbox for Input-Output System Inversion. INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL, [S.l.], v. 2, n. 4, p. 388-402, dec. 2007. ISSN 1841-9844. Available at: <http://univagora.ro/jour/index.php/ijccc/article/view/2369>. Date accessed: 02 mar. 2021. doi: https://doi.org/10.15837/ijccc.2007.4.2369.


CACSD, input-output inversion, feedforward, set-point regulation, optimization