Optimization and evaluation of a proportional derivative controller for planar arm movement

Kathleen M. Jagodnik, Antonie J. van den Bogert

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


In most clinical applications of functional electrical stimulation (FES), the timing and amplitude of electrical stimuli have been controlled by open-loop pattern generators. The control of upper extremity reaching movements, however, will require feedback control to achieve the required precision. Here we present three controllers using proportional derivative (PD) feedback to stimulate six arm muscles, using two joint angle sensors. Controllers were first optimized and then evaluated on a computational arm model that includes musculoskeletal dynamics. Feedback gains were optimized by minimizing a weighted sum of position errors and muscle forces. Generalizability of the controllers was evaluated by performing movements for which the controller was not optimized, and robustness was tested via model simulations with randomly weakened muscles. Robustness was further evaluated by adding joint friction and doubling the arm mass. After optimization with a properly weighted cost function, all PD controllers performed fast, accurate, and robust reaching movements in simulation. Oscillatory behavior was seen after improper tuning. Performance improved slightly as the complexity of the feedback gain matrix increased.

Original languageEnglish
Pages (from-to)1086-1091
Number of pages6
JournalJournal of Biomechanics
Issue number6
StatePublished - 19 Apr 2010
Externally publishedYes

Bibliographical note

Funding Information:
This work was supported by the US National Institutes of Health through predoctoral fellowship 5F31HD049326, Grant 1R21HD049662 , and Contract N01HD53403. The authors thank Robert Kirsch for his assistance.


  • Neuromuscular stimulation
  • Optimal control
  • Simulation


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