Strictly positive real admittances for coupled stability

✍ Scribed by J. Edward Colgate

• Publisher: Elsevier Science
• Year: 1992
• Tongue: English
• Weight: 995 KB
• Volume: 329
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(92)90044-h

✦ Synopsis

This paper builds upon recent work that has addressed the stability ofa,jeedhackcontrolled robot coupled to a passice, dynamic erwironment. A new dejmition of a "strictly positire real" function is presented, and is used to procide necessary and sujficient conditions fbr the exponential stabilit)x of a coupled system comprising a I-port robot with a strictly positive real admittance. and a 1 -port environment with a positive real (but otherwise arhitravv) impedance. The distinction betbt'een the new definition and concentional dehnitions of'a strictly posit&e real,function is ,f&tnded in physical systems theory : the new definition relies upon distinct roles .for ej6ort.s and,fiows, and upon the concept qf an excess state. This definition will provide u useful design constraint,for the decelopment of robust robot controllers. Nomenclature (A, B, C, D) minimal realization of an impedance or admittance Acovplcd A-matrix of the coupled system B viscous damping coefficient D(s) denominator polynomial