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54 Adaptive Identification and Control of Uncertain Systems with Non-smooth Dynamics

that compared with PID control, the proposed DSC with ESN and fric-
tion compensation can retain better tracking performance (e.g., the tracking
error is smaller and strictly within prescribed bound), and the torsional vi-
bration is damped (Fig. 3.8C).

3.5 CONCLUSION

This chapter proposes a modified DSC design with friction compensa-
tion for two-inertia systems with elastic couplings. The system is first
reformulated and the unmeasured system states are estimated by using a
Luenberger observer. The non-linear frictions are molded by using the
LuGre model, which is incorporated into ESN to address the lumped non-
linearities. Then HGDTs are incorporated into DSC control designs to
achieve improved convergence response. The PPFs are used in the control
implementation to guarantee both the transient and steady-state conver-
gence of the tracking error within a prescribed bound. The stability of the
closed-loop system is ensured by Lyapunov method. Simulation and exper-
iment results are conducted to illustrate the effectiveness of the proposed
control methods.

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