Underactuated systems are widely applied in industry, construction, manufacturing, etc., and the complex working environment puts forward higher demands for safety and transient performance. Hence, it is necessary to consider how to simultaneously ensure actuated and unactuated motion constraints by fewer control inputs, especially when systems suffer from model uncertainties, unavailable velocities, etc. Unfortunately, it is still a significant challenge to overcome in real applications and theoretical analysis. Additionally, most existing studies merely consider the specific control objects and few general methods are applicable to a class of underactuated systems. To this end, we design a new adaptive output-feedback controller for a class of uncertain underactuated systems. Compared with existing methods only handling actuated constraints, an important merit of this article is that by introducing the elaborately designed coupling term composed of actuated and unactuated constraints together, all state variables are kept within the preset time-variant ranges and converge to their desired values. Furthermore, a new Lyapunov function candidate is utilized to provide a theoretical guarantee. As far as we know, without the need of exact model knowledge and velocity feedback, this article provides the first solution to achieve accurate motion control and state constraints for both actuated and unactuated variables, which is meaningful both theoretically and practically. Meanwhile, the asymptotic stability of the equilibrium point for the closed-loop system is proven by utilizing Lyapunov techniques and Barbalat’s lemma. For verification, the presented controller is applied to underactuated overhead and rotary cranes, respectively, together with detailed theoretical analysis and experimental validations.

Tower crane systems exhibit high nonlinearity and underactuation, making the control issue challenging. Most reported methods utilize linearized models, and accurate plant parameters and full state feedback are usually required; moreover, most existing works only consider a part of the crane motions (not 5-DOF). However, tower cranes are practically influenced by uncertainties and disturbances, which may make linearized models ineffective; additionally, exact values of plant parameters may be difficult to obtain, and velocity signals are usually not directly measurable in practice. This paper proposes a control method for 5-DOF varying-cable-length tower cranes. As far as we know, the paper provides the first adaptive output feedback controller, designed and analyzed without linearizing the dynamic equations, which can simultaneously achieve cargo hoisting/lowering, jib slew, trolley translation, and swing suppression, by avoiding using velocity-related feedback signals. We provide rigorous stability analysis for the closed-loop system. Hardware experiment results are included for effectiveness/robustness verification.

Underactuated mechatronic systems are widely used in industrial production, where the control efforts and operation accuracy are both important aspects of performance evaluations. Hence, how to realize effective motion control, while reducing control efforts as much as possible, becomes an open problem for underactuated systems. Although some open loop approaches (e.g., trajectory planning) take energy optimization into account, they need linearization/approximation manipulations and exhibit weak robustness, which is prone to degrading practical control performance. To this end, this article proposes an adaptive tracking controller for uncertain multi-input-multi-output (MIMO) underactuated mechatronic systems, to fulfill accurate positioning/tracking control with saturated inputs and reduce control efforts as well. Particularly, by elaborately developing an auxiliary compensation term and a robust term, the proposed controller ensures asymptotic convergence of both actuated and unactuated variables. Meanwhile, the modified performance index function is approximated online and introduced into the Lyapunov function candidate to make the stability analysis process more concise. To the best of our knowledge, without the need of offline computation and the persistence of excitation (PE) condition, this article presents the first adaptive optimal controller to simultaneously achieve error elimination, control effort optimization, and actuator constraints for a class of underactuated systems. Finally, strict theoretical analysis and experimental validations show the effectiveness and robustness of the suggested controller.