Use of a Simple Mechanical Analogy to Analytically Tune the PD Controller of a Flexible Manipulator System

Table 2

Three test cases with their optimal P and D gains.

		(Hz)	(Hz)	from Equation (17)	from Equation (12)	from Equation (13)	satisfying Equation (11)
0.3	2.92	8.19	8.26	12.082	0.358	0.316	0.313
0.5	2.06	7.21	7.37	6.022	0.259	0.215	0.211
	1.58	6.31	6.55	3.568	0.218	0.174	0.168

Note. Unlike the other terms, “” and “ satisfying Equation (11)” were numerically obtained. Here, “” was calculated from “ from Equation (17)” and “ satisfying Equation (11).” Units: (N·m/rad); (N·m·s/rad).