Adaptive hierarchical sliding mode controller for tower cranes based on finite time disturbance observer

Abstract

Summary A finite time disturbance observer (FTDO) based adaptive hierarchical sliding mode control (AHSMC) is proposed for 4‐DOF tower crane systems with unknown external disturbances. More specifically, to overcome the unknown disturbances, an FTDO combined with the designed adaptive observation error is presented to estimate both matched and unmatched disturbances. Then a new error dynamics taking into account the unmatched disturbances is defined, based on which, a novel nonsingular fast terminal sliding mode (FTSM) surfaces is designed to improve the convergence of system states. Finally, in order to ensure the stability of each subsystem, an AHSMC law incorporating the suggested FTSM‐type reaching law is presented to realize the anti‐sway and positioning control of tower crane system. The finite‐time stability analysis of the closed‐loop system is derived by Lyapunov technique, and simulation results verify the effectiveness of the presented control strategy.

Fixed time robust control for tower cranes with unmatched disturbances and input saturation

“…$$ Therefore, the hierarchical sliding mode surface () can converge to zero when $$$ t\ge \max \left\{{T}_o,{T}_{\mathrm{r}}\right\} $$$. According to Reference 12, one can conclude that the subsystem surfaces can also converge to the equilibrium in fixed time. Then, Equation () becomes $$$$ {\boldsymbol{y}}_{2(i)}=-{\phi}_1\left(\left|{\boldsymbol{y}}_{1(i)}\right|\right)\mathrm{si}{\mathrm{g}}^{\kappa_1\left(\left|{\boldsymbol{y}}_{1(i)}\right|\right)}\left({\boldsymbol{y}}_{1(i)}\right)-{\phi}_2\left(\left|{\boldsymbol{y}}_{1(i)}\right|\right)\mathrm{si}{\mathrm{g}}^{\kappa_2\left(\left|{\boldsymbol{y}}_{1(i)}\right|\right)}\left({\boldsymbol{y}}_{1(i)}\right)\kern1em i=1,2,3,4.$$…”

“…In this section, according to the geometric model shown in Figure 1 and using the Euler–Lagrange function, a dynamic model of a tower crane can be described as follows 12 : $$$$ {\displaystyle \begin{array}{ll}& \left({M}_{\mathrm{t}}+{m}_{\mathrm{p}}\right)\ddot{d}...$$…”

“…Therefore, the dynamic model of the tower crane is transformed into the following integral chain form: $$$$ \left\{\begin{array}{l}\dot{\boldsymbol{q}}={\dot{\boldsymbol{q}}}_{\mathrm{m}}+{\boldsymbol{D}}_1\\ {}\ddot{\boldsymbol{q}}=\boldsymbol{G}\left(\boldsymbol{q}\right)\boldsymbol{u}+\boldsymbol{H}\left(\boldsymbol{q},\dot{\boldsymbol{q}}\right)+{\boldsymbol{D}}_2,\end{array}\right. $$$$ where $$$ {\boldsymbol{q}}_{\mathrm{m}} $$$ represents the measured velocity signal vector, $$$ {\boldsymbol{D}}_1\in {\mathbf{R}}^{4\times 1} $$$ stands for the unmatched disturbance vector, mainly refer to the measurement uncertainties caused by the sensor drift 12 …”

“…In Reference 22, to suppress the frictions of input channel and lumped disturbances, a robust adaptive sliding mode control is proposed for tower cranes with unknown payload mass, while the nonlinear variable gains are designed for high robustness. Unfortunately, unmatched disturbances (the input and disturbances are in different channels 23 ) caused by measurement uncertainties frequently happen during the practical tower crane operation 12 . Since there is no control input directly reacted on them, these disturbances can greatly degrade the control precision and even lead to system instability.…”

“…Typically, a generalized extended state observer is suggested to overcome the unmatched disturbances, with estimated disturbances used as the feedforward compensation 26 . In order to further improve the transient performances of the disturbance observer, Gu et al present a finite‐time disturbance observer based composite controller for tower cranes to resist the unmatched uncertainties 12 . In Reference 27, a novel finite‐time disturbance observer based fractional‐order nonsingular terminal sliding mode controller is presented for mismatched uncertain nonlinear systems.…”