Limit Cycle Predictions of Nonlinear Multivariable Feedback Control Systems with Large Transportation Lags

Table 1

Calculated results of a stable (Point 𝑄₁) and a unstable limit cycle (Point 𝑄₃).

Point	𝑁1(𝑎1)	𝑁2(𝑎2)	𝜔	𝐴1	𝐴2	𝜕𝑁1(𝑎1)/𝜕𝐴1	𝜕𝑁2(𝑎2)/𝜕𝐴2	𝜃2{9}	𝜃2{11}	𝑀𝜃2
𝑄1	0.5719	0.5691	0.7888	1.904	1.889	−0.185	-0.1849	−70.39°	−70.39°	0.93
				1.175	1.179	+0.788	+0.762	−70.39°	−70.39°	0.92
𝑄3	0.6366	0.5313	0.8002	1.414	1.136	0	+1.149	−88.49°	−88.49°	1.12
				1.414	2.112	0	−0.179	−88.49°	−88.49°	0.61