{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T09:56:03Z","timestamp":1777715763641,"version":"3.51.4"},"reference-count":22,"publisher":"SAGE Publications","issue":"8","license":[{"start":{"date-parts":[[2000,8,1]],"date-time":"2000-08-01T00:00:00Z","timestamp":965088000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["The International Journal of Robotics Research"],"published-print":{"date-parts":[[2000,8]]},"abstract":"<jats:p>Nonlinear PID (NPID) control is implemented by allowing the controller gains to vary as a function of system state. NPID control has been previously described and implemented, and recently a constructive Lyapunov stability proof has been given. The controllers arising with the constructive Lyapunov method will in general depend on knowledge of the full state vector. In the present work, NPID controllers that operate without knowledge of some state variables are demonstrated. A general but conservative design method is presented with an experimental demonstration. For a special case, complete necessary and sufficient conditions are established; for this case, simulation of a robotic force control application demonstrates well-damped control with no requirement for a force-rate signal. The extension to cases of partial state knowledge is important for NPID control, which is most practical when some state variables\u2014particularly rate variables\u2014are poorly known, confounding full-state feedback or other high-damping linear control designs. Extension of NPID control to MIMO systems and computed torque control is also shown.<\/jats:p>","DOI":"10.1177\/02783640022067120","type":"journal-article","created":{"date-parts":[[2003,7,19]],"date-time":"2003-07-19T02:59:46Z","timestamp":1058583586000},"page":"715-731","source":"Crossref","is-referenced-by-count":28,"title":["Nonlinear PID Control with Partial State Knowledge: Damping without Derivatives"],"prefix":"10.1177","volume":"19","author":[{"given":"Brian","family":"Armstrong","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering and Computer Science, and Center for                         Industrial Mathematics, UW-Milwaukee P.O. Box 784, Milwaukee, Wisconsin                         53201, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bruce A.","family":"Wade","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences and Center for Industrial                         Mathematics, UW-Milwaukee P.O. Box 413, Milwaukee, Wisconsin 53201, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2000,8,1]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"Armstrong, B. 1997a. A controls laboratory program with an accent on system identification . Proc. 1997 American Controls Conference, Albuquerque, NM, pp. 3166\u20133170 .","DOI":"10.1109\/ACC.1997.612043"},{"key":"atypb2","doi-asserted-by":"crossref","unstructured":"Armstrong, B. 1997b. Nonlinear PD control with incomplete state knowledge: Damping without derivatives . Proc. of SYROCO \u201897, Nantes, France, pp. 73\u201378 .","DOI":"10.1016\/S1474-6670(17)44246-7"},{"key":"atypb3","doi-asserted-by":"crossref","unstructured":"Armstrong, B. 1997c. Robustness of NPD control (preliminary results) . 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