1. 5 10 15 20 25 30 35 40 -2
2. 5 10 15 20 25 30 35 40 -1
3. Figures 5 through 16 show results with e-K-modification with the adaptation parameter settings summarized in Table 1. In Case 1, the adaptation gain is applied with zero stiffness gain. Figures 5 to 7 show that as the adaptation gain increases the roll angle oscillation and its frequency increase as well as the control effort. Case 2 introduces K-modification with k = 100 and T = 0.01 second. Figures 8 to 10 show that the roll angle oscillation and the control effort dramatically decrease. In Case 3, the stiffness gain is increased with fixed adaptation gain. Figures 11 to 13 show that as the stiffness gain increases the roll angle oscillation and its frequency decrease as well as the control effort decreases. Case 4 presents the effect that the value of T used in the weight update law in (9) has on performance with fixed adaptation and stiffness gain. Figures 14 to 16 show that the roll angle oscillation and its frequency as well as the control effort are significantly decreased for values of T in the range 0.01 - 0.1 seconds.
4. Instability analysis and improvement of robustness of adaptive control