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Abstract

In this paper, linear time-invariant square systems are considered. A procedure to design infinitely many proportional–integral–derivative controllers, all of them assigning closed-loop poles (or closed-loop eigenvalues), at desired locations fixed in the open left half plane of the complex plane is presented. The formulation accommodates partial pole placement features. The state-space realization of the linear system incorporated with a proportional–integral–derivative controller boils down to the generalized eigenvalue problem. The generalized eigenvalue-eigenvector constraint is transformed into a system of underdetermined linear homogenous set of equations whose unknowns include proportional–integral–derivative parameters. Hence, the proportional–integral–derivative solution sets are infinitely many for the chosen closed-loop eigenvalues in the eigenvalue-eigenvector constraint. The solution set is also useful to reduce the tracking errors and improve the performance. Three examples are illustrated.

Keywords

Linear systems proportional–integral–derivative controller family pole placement state-space model design parameters

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References

Ashokkumar CR and York WPG. Trajectory transcriptions for potential autonomy features in UAV maneuvers. In: Proceedings of the AIAA guidance, navigation, and control conference, San Diego, USA, January 2016, AIAA 2016-0380.

Ashokkumar CR and York WPG. UAV control and simulation using trajectory transcriptions. In: Proceedings of the AIAA modeling and simulation technologies, San Diego, USA, January 2016, AIAA 2016-0944.

Burken JJ, Lu P and Wu Z. Reconfigurable flight control designs with application to the X-33 vehicle. NASA Dryden Flight Research Center, CA, August 1999, NASA Technical Memorandum, 206582.

Christopher MC and Burken JJ. Reconfigurable control design for full X-33 flight envelope. NASA Dryden Flight Research Center, CA, August 2001, NASA Technical Memorandum, 210396.

Hess

Cama

. Flight control system design for inherent damage tolerance. J Aircraft 2008; 45: 2024–2035.

Steinberg

. Historical overview of research in reconfigurable flight control. Proc IMechE, Part G: J Aerospace Engineering 2005; 219: 263–275.

Psonis

Nikolakopoulas

Mitronikas

. Design of a PID controller for a linearized magnetic bearing. Int J Rotat Mach 2015. 2015: Article ID 656749, pp. 12.

Sinlapakun V and Assawinchaichote W. Optimized PID controller design for electric furnace temperature systems with Nelder Mead algorithm. In: 12^th IEEE international conference on electrical engineering/electronics, computer, telecommunications and information technology, Hua Hin, Thailand, 2015, pp.1–4.

Deniz FN, Alagoz BB and Tan N. PID controller design based on second order model approximation by using stability boundary locus fitting. In: 9^th international conference on electrical and electronics engineering, 2015, pp.827–831.

10.

Ghiglino P, Forshaw JL and Lappas VJ. Online PID tuning using an evolutionary swarm algorithm with experimental quadrotor flight results. In: AIAA guidance, navigation, and control and co-located conferences, Boston, MA, USA, 19–22 August 2013, AIAA 2013-5098.

11.

Zhuang

Atherton

. Automatic tuning of optimum PID controllers. IEE Proc D – Control Theory Appl 1993; 140: 216–224.

12.

Nishiyama T, Suzuki S, Sato M, et al. Simple adaptive control with PID for MIMO fault tolerant flight control design. In: AIAA SciTech, San Diego, CA, USA, 4–8 January 2016, AIAA Infotech@Aerospace, AIAA 2016-0132.

13.

Wellstead

Prager

Zanker

. Pole assignment self-tuning regulator. Proc Intn Electr Engrs 1979; 126: 781–787.

14.

Prager

Wellstead

. Multivariable pole assignment self-tuning regulators. IEE Proc D – Control Theory Appl 1981; 128: 9–18.

15.

Elliott

Wolovich

Das

. Arbitrary adaptive pole placement for linear multivariable systems. IEEE Trans Autom Control 1984; 29: 221–229.

16.

Gundes AN and Chang TS. PID controller synthesis with shifted axis pole assignment for a class of MIMO systems. In: American control conference, St Lois, MO, USA, 10–12 June 2009, pp.1849–1854.

17.

Seraji H. Design of discrete PID controllers for pole placement. In: 23^rd IEEE conference on decision and control, Las Vegas, NV, USA, 12–14 December 1984, pp.1721–1722.

18.

Sujitjorn

Wiboonjaroen

. State PID feedback for pole placement of LTI systems. Math Prob Eng 2011. 2011: Article ID 929430, pp. 20.

19.

Ashokkumar

. Active self-healing mechanisms for discrete dynamic structures. Struct Control Health Monitor 2014; 21: 721–740.

20.

Ashokkumar

Iyengar

NGR

. Partial eigenvalue assignment for structural damage mitigation. J Sound Vib 2011; 330: 9–16.

Proportional–integral–derivative controller family for pole placement

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