Abstract
It is important to be able to assess the quality of control provided by PID controllers or indeed by any classical or advanced control method. Since many PID controllers are set up using intuition or empirical tuning rules, it is particularly important that PID designs can be benchmarked and the quality of control assessed. Furthermore, benchmarking methods can provide guidance for tuning controllers.
The most common performance measures used for PID control include step-response tracking performance, disturbance-rejection performance properties and the stochastic performance in regulating or tracking processes.
With respect to the regulating performance, assessment and benchmarking methods can mostly be considered part of the minimum variance or generalised minimum variance family of techniques. There are commercial tools which use such methods, but these are often based on rather simplistic strategies. One of the advances made in the last decade has been the development of so-called restricted structure benchmarking which provides a figure of merit which is much more representative of what might be achievable if the controller is tuned optimally.
With respect to step-input and disturbance rejection performance, the benchmarking should ideally determine how well the output of the system follows a step change in the system inputs (either a set-point or a disturbance change). This suggests a comparison with optimum tracking controllers, of which the most representative would be a model-based predictive controller. Thus, in the second part of this chapter the performance of a PID controller will be compared with the performance of a predictive controller.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ahmad, M., Benson, R.: Benchmarking in the process industries. In: IChemE. The Cromwell Press, Trowbridge (1999)
Anderson, B.D.O., Lin, Y.: Controller reduction concepts and approaches. IEEE Trans. Autom. Control 34, 802–812 (1989)
Andersen, B., Pettersen, P.G.: The Benchmarking Handbook. Chapman and Hall, New York (1996)
Calligaris, M., Johnson, M.A.: Power system studies and new benchmarking concepts. In: Proc. IASTED Int. Conf. on Control and Applications, Banff, Canada, pp. 211–216 (1999)
Calligaris, M., Johnson, M.A.: Benchmarking for hierarchical voltage control. In: IFAC Symp. on Power Plants and Power Systems Control 2000, Brussels, Belgium (2000)
Clarke, D.W., Hastings-James, R.: Design of digital controllers for randomly disturbed systems. Proc. IEEE 118(10), 1503–1506 (1971)
Codling, S.: Best Practice Benchmarking. Uniskill Ltd. (1992)
Desborough, L.D., Harris, T.J.: Performance assessment measures for univariate feedback control. Can. J. Chem. Eng. 70, 1186–1197 (1992)
Desborough, L.D., Harris, T.J.: Performance assessment measures for univariate feedback/feedforward control. Can. J. Chem. Eng. 71, 605–615 (1993)
Desborough, L.D., Harris, T.J.: Control performance assessment. Pulp Pap. Can. 95(11), 441–443 (1994)
Grimble, M.J.: Generalised minimum variance control law revisited. Optim. Control Appl. Methods 9, 63–77 (1988)
Grimble, M.J.: Restricted structure controller tuning and performance assessment. IEE Proc. Part D (1992)
Grimble, M.J.: Robust Industrial Control: Optimal Design Approach for Polynomial Systems. Prentice Hall, New York (1994)
Grimble, M.J.: Restricted structure feedforward stochastic optimal control. In: CDC 99, Phoenix, Arizona (1999)
Grimble, M.J.: Restricted structure LQG optimal control for continuous-time systems. IEE Proc. Control Theory Appl. 147(2), 185–195 (2000)
Grimble, M.J.: Industrial Control Systems Design. Wiley, Chichester (2000)
Grimble, M.J.: Restricted structure optimal linear pseudo-state filtering for discrete-time systems. In: American Control Conference, Chicago (2000)
Hangstrup, M., Ordys, A.W., Grimble, M.J.: Dynamic algorithm of LQGPC predictive control. In: 4th International Symposium on Methods and Models in Automation and Robotics, Miedzyzdroje, August 1997
Harris, T.: Assessment of closed loop performance. Can. J. Chem. Eng. 67, 856–861 (1989)
Huang, B., Shah, S.L., Kwok, E.K.: Good, bad or optimal, Performance assessment of multivariable processes. Automatica 33(6), 1175–1183 (1997)
Huang, B., Shah, S.L.: Performance Assessment of Control Loops: Theory and Applications. Springer, London (1999)
Hyland, D.C., Bernstein, D.A.: The optimal projection equations for model reduction and the relationships among the methods of Wilson, Skelton and Moore. IEEE Trans. Autom. Control 30, 1201–1211 (1985)
Levine, W.S. (ed.): The Control Handbook. CRC Press, Boca Raton (1996), Chap. 62
Moden, P.E., Soderstrom, T.: On the achievable accuracy in stochastic control. In: 17th IEEE Conf on Decision and Control, pp. 490–495 (1978)
Ordys, A.W.: Model-system parameters mismatch in GPC control. Int. J. Adapt. Control Signal Process. 7, 239–253 (1993)
Ordys, A.W., Clarke, D.W.: A state-space description for GPC controllers. Int. J. Syst. Sci. 24(9) (1993)
Ordys, A.W., Uduehi, D., Johnson, M.: Process Control Performance Assessment. From Theory to Implementation. Monograph Series: Advances in Industrial Control. Springer, London (2007). ISBN 978-1-84628-623-0
Rivera, D.E., Morari, M.: Control relevant model reduction problems for SISO H2, H∞ and μ controller synthesis. Int. J. Control 46(2), 505–527 (1987)
Rivera, D.E., Morari, M.: Low order SISO controller tuning methods for the H2, H∞ and μ objective functions. Automatica 26(2), 361–369 (1990)
Rolstadas, A.: Benchmarking—Theory and Practice. Chapman and Hall, London (1995)
Saeki, M., Kimura, J.: Design method of robust PID controller and CAD system. In: 11th IFAC Symposium on System Identification, vol. 3, pp. 1587–1593 (1997)
Saeki, M., Aimoto, K.: PID controller optimization for H∞ control by linear programming. Int. J. Robust Nonlinear Control 10, 83–99 (2000)
Shakouri, P., Ordys, A., Askari, M., Laila, D.S.: Longitudinal vehicle dynamics using Simulink/Matlab. In: UKACC International Conference CONTROL 2010, Coventry, 7–10 September 2010
Shakouri, P., Ordys, A., Laila, D.S., Askari, M.: Adaptive cruise control system: Comparing gain-scheduling PI and LQ controllers. In: IFAC Word Congress, Milano, 28 August–2 September 2011
Stanfelj, N., Marlin, T.E., MacGregor, J.F.: Monitoring and diagnosing process control performance: the single loop case. Ind. Eng. Chem. Res. 32, 301–314 (1993)
Thornhill, N.F., Oettinger, M., Fedenczuk, P.: Refinery-wide control loop performance assessment. J. Process Control 9, 109–124 (1999)
Uduehi, D., Ordys, A.: Multivariable PID controller design using online generalised predictive control optimisation. In: IEEE Conference on Control Applications & IEEE Conference on Computer Aided Control Systems Design, Glasgow, 17–20 September 2002
Uduehi, D., Ordys, A., Grimble, M.: A generalised predictive control benchmark index for SISO systems. In: IEEE Control and Decision Conference, Las Vegas, December 2002
Acknowledgements
The authors would like to thank Payman Shakouri for a help in numerical examples related to the Adaptive Cruise Control system.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag London Limited
About this chapter
Cite this chapter
Ordys, A.W., Grimble, M.J. (2012). Benchmarking and Tuning PID Controllers. In: Vilanova, R., Visioli, A. (eds) PID Control in the Third Millennium. Advances in Industrial Control. Springer, London. https://doi.org/10.1007/978-1-4471-2425-2_13
Download citation
DOI: https://doi.org/10.1007/978-1-4471-2425-2_13
Publisher Name: Springer, London
Print ISBN: 978-1-4471-2424-5
Online ISBN: 978-1-4471-2425-2
eBook Packages: EngineeringEngineering (R0)