Minimum-time feedforward technique for PID control

This study deals with the determination of the (reference) command input to be applied to a closed-loop control system in order to achieve a minimum-time output transition subject to constraints on both the control variable and the system output. In particular, the authors consider the important practical case of a process described by a first-order-plus-dead-time transfer function with a proportional-integral-derivative feedback controller. The optimal command input is determined by suitably approximating the state variables and the input signal by means of Chebyshev series and by subsequently solving a constrained optimisation problem. Simulation as well as experimental results demonstrate the effectiveness of the methodology.

[1]  John McPhee,et al.  Determination of Minimum-Time Maneuvers for a Robotic Manipulator Using Numerical Optimization Methods∗ , 1999 .

[2]  A. Quarteroni,et al.  Numerical Approximation of Partial Differential Equations , 2008 .

[3]  Chang-Chieh Hang,et al.  Improvement of transient response by means of variable set point weighting , 1996, IEEE Trans. Ind. Electron..

[4]  Anders Wallén,et al.  Tools for Autonomous Process Control , 2000 .

[5]  Luca Consolini,et al.  Generalized bang-bang control for feedforward constrained regulation , 2006, CDC.

[6]  Luca Bascetta,et al.  FIR based causal design of 2-d.o.f. controllers for optimal set point tracking , 2008 .

[7]  A. Piazzi,et al.  Minimum-time feedforward control with input and output constraints , 2006, 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control.

[8]  António E. Ruano,et al.  Hands-on PID autotuning: a guide to better utilisation , 2002 .

[9]  Gamal N. Elnagar.  State-control spectral Chebyshev parameterization for linearly constrained quadratic optimal control problems , 1997 .

[10]  Benjamin C. Kuo,et al.  AUTOMATIC CONTROL SYSTEMS , 1962, Universum:Technical sciences.

[11]  Antonio Visioli.  A new design for a PID plus feedforward controller , 2004 .

[12]  Gamal N. Elnagar,et al.  Pseudospectral Chebyshev Optimal Control of Constrained Nonlinear Dynamical Systems , 1998, Comput. Optim. Appl..

[13]  Tore Hägglund,et al.  Advanced PID Control , 2005 .

[14]  Antonio Visioli,et al.  Fuzzy logic based set-point weight tuning of PID controllers , 1999, IEEE Trans. Syst. Man Cybern. Part A.

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

[16]  M. S. Salim,et al.  A Chebyshev approximation for solving optimal control problems , 1995 .

[17]  Hussein Jaddu,et al.  Computation of optimal control trajectories using chebyshev polynomials : Parameterization, and quadratic programming , 1999 .

[18]  George E. Collins.  Fundamental Numerical Methods and Data Analysis , 1990 .

[19]  Aidan O'Dwyer,et al.  Handbook of PI and PID controller tuning rules , 2003 .

[20]  L. Fox,et al.  Chebyshev polynomials in numerical analysis , 1970 .

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

[22]  Luca Bascetta,et al.  Designing the feedforward part of 2-d.o.f. industrial controllers for optimal tracking , 2007 .

[23]  Thomas F. Coleman,et al.  Optimization Toolbox User's Guide , 1998 .