Set-point filter design for a two-degree-of-freedom fractional control system

This paper focuses on a new approach to design U+0028 possibly fractional U+0029 set-point filters for fractional control systems. After designing a smooth and monotonic desired output signal, the necessary command signal is obtained via fractional input-output inversion. Then, a set-point filter is determined based on the synthesized command signal. The filter is computed by minimizing the 2-norm of the difference between the command signal and the filter step response. The proposed methodology allows the designer to synthesize both integer and fractional set-point filters. The pros and cons of both solutions are discussed in details. This approach is suitable for the design of two degree-of-freedom controllers capable to make the set-point tracking performance almost independent from the feedback part of the controller. Simulation results show the effectiveness of the proposed methodology.

[1]  Aurelio Piazzi,et al.  A noncausal approach for PID Control , 2006 .

[2]  Aurelio Piazzi,et al.  Optimal inversion-based control for the set-point regulation of nonminimum-phase uncertain scalar systems , 2001, IEEE Trans. Autom. Control..

[3]  YangQuan Chen,et al.  Fractional order control - A tutorial , 2009, 2009 American Control Conference.

[4]  Luigi Fortuna,et al.  New results on the synthesis of FO-PID controllers , 2010 .

[5]  Antonio Visioli,et al.  Optimal tuning rules for proportional-integral-derivative and fractional-order proportional-integral-derivative controllers for integral and unstable processes , 2012 .

[6]  O. Agrawal,et al.  Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering , 2007 .

[7]  Alessandro Pisano,et al.  Sliding mode control approaches to the robust regulation of linear multivariable fractional‐order dynamics , 2010 .

[8]  Antonio Visioli,et al.  Inversion-based set-point filter design for fractional control systems , 2014, ICFDA'14 International Conference on Fractional Differentiation and Its Applications 2014.

[9]  Aurelio Piazzi,et al.  Optimal noncausal set-point regulation of scalar systems , 2001, Autom..

[10]  Duarte Valério,et al.  Introduction to single-input, single-output fractional control , 2011 .

[11]  YangQuan Chen,et al.  Fractional-order systems and control : fundamentals and applications , 2010 .

[12]  Aurelio Piazzi,et al.  Robust set-point constrained regulation via dynamic inversion† , 2001 .

[13]  Alain Oustaloup,et al.  Frequency-band complex noninteger differentiator: characterization and synthesis , 2000 .

[14]  Antonio Visioli,et al.  Set‐point weight tuning rules for fractional‐order PID controllers , 2013 .

[15]  Alain Oustaloup,et al.  Fractional Motion Control: Application to an XY Cutting Table , 2002 .

[16]  Nabil Derbel,et al.  Robust path tracking by preshaping approach designed for third generation CRONE control , 2012, Int. J. Model. Identif. Control..

[18]  Mathieu Moze,et al.  LMI stability conditions for fractional order systems , 2010, Comput. Math. Appl..

[19]  Antonio Visioli,et al.  Inversion-based feedforward and reference signal design for fractional constrained control systems , 2014, Autom..

[20]  I. Podlubny.  Fractional differential equations , 1998 .

[21]  Alain Oustaloup,et al.  Flatness control for linear fractional {MIMO} systems: thermal application , 2008 .

[22]  Guido Maione,et al.  Continued fractions approximation of the impulse response of fractional-order dynamic systems , 2008 .

[23]  Antonio Visioli,et al.  H∞ model matching PID design for fractional FOPDT systems , 2012, 2012 American Control Conference (ACC).

[24]  Antonio Visioli,et al.  Practical PID Control , 2006 .

[25]  Manuel Duarte Ortigueira,et al.  A new look into the discrete-time fractional calculus: transform and linear systems , 2013 .