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

Kaushik Halder, Saptarshi Das, Amitava Gupta

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)271–298
Number of pages28
Issue number2
Early online date14 May 2019
Publication statusPublished - 1 Feb 2020


  • Optimal control
  • Linear quadratic regulator (LQR)
  • PI/PID controller tuning
  • Dominant pole placement
  • Discrete time control
  • Stable–unstable-integrating test-bench


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