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Transformation of LQR Weights for Discretization Invariant Performance of PI/PID Dominant Pole Placement Controllers

Published online by Cambridge University Press:  14 May 2019

Kaushik Halder ,
Saptarshi Das Open the ORCID record for Saptarshi Das [Opens in a new window]  and
Amitava Gupta
Kaushik Halder
Affiliation:
Department of Power Engineering, Jadavpur University, Salt Lake Campus, LB-8, Sector 3, Kolkata 700098, India. E-mails: [email protected], [email protected]
Saptarshi Das*
Affiliation:
Department of Mathematics, College of Engineering, Mathematics and Physical Sciences, University of Exeter, Penryn Campus, Penryn TR10 9FE, United Kingdom
Amitava Gupta
Affiliation:
Department of Power Engineering, Jadavpur University, Salt Lake Campus, LB-8, Sector 3, Kolkata 700098, India. E-mails: [email protected], [email protected]
*
*Corresponding author. E-mails: [email protected], [email protected]
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Summary

Linear quadratic regulator (LQR), a popular technique for designing optimal state feedback controller, is used to derive a mapping between continuous and discrete time inverse optimal equivalence of proportional integral derivative (PID) control problem via dominant pole placement. The aim is to derive transformation of the LQR weighting matrix for fixed weighting factor, using the discrete algebraic Riccati equation (DARE) to design a discrete time optimal PID controller producing similar time response to its continuous time counterpart. Continuous time LQR-based PID controller can be transformed to discrete time by establishing a relation between the respective LQR weighting matrices that will produce similar closed loop response, independent of the chosen sampling time. Simulation examples of first/second order and first-order integrating processes exhibiting stable/unstable and marginally stable open loop dynamics are provided, using the transformation of LQR weights. Time responses for set-point and disturbance inputs are compared for different sampling times as fraction of the desired closed loop time constant.

Keywords

Optimal controlLinear quadratic regulator (LQR)PI/PID controller tuningDominant pole placementDiscrete time controlStable–unstable-integrating test-bench
Type
Articles
Information
Robotica , Volume 38 , Issue 2 , February 2020 , pp. 271 - 298
Copyright
© Cambridge University Press 2019 

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