Adaptive IDA‐PBC for underactuated mechanical systems with constant disturbances

Abstract

This work investigates the control of nonlinear underactuated mechanical systems with matched and unmatched constant disturbances. To this end, a new control strategy is proposed, which builds upon the interconnection-anddamping-assignment passivity-based control, augmenting it with an additional term for the purpose of disturbance compensation. In particular, the disturbances are estimated adaptively and then accounted for in the control law employing a new matching condition of algebraic nature. Stability conditions are discussed, and for comparison purposes, an alternative controller based on partial feedback linearization is presented. The effectiveness of the proposed approach is demonstrated with numerical simulations for three motivating examples: the inertia wheel pendulum, the disk-on-disk system, and the pendulum-on-cart system. KEYWORDS adaptive control, matched and unmatched disturbances, nonlinear control, underactuated mechanical systems Int J Adapt Control Signal Process. 2019;33:1-15.wileyonlinelibrary.com/journal/acs

Energy Shaping Control for Robotic Needle Insertion

“…The controller (11)- (17) has been implemented with the following tuning parameters: > 10; Q 3, D 1. Since very large deflections were registered for the baseline controller (23) with the same values, the following parameters have been used to provide a meaningful comparison: > 2; Q 15. The desired insertion depth * 0.1 m is reached within 30 seconds in all the simulations, which is representative of percutaneous interventions [1], [2].…”

Energy-based design of elastic joints for inverted pendulum systems with input saturation

“…Clearly, for a given and 0 there exist some 0 < < 1 that satisfies (13). Additionally, it follows form (12) that ′ ∈ ℒ ∞ hence ∈ ℒ ∞ on all closed-loop trajectories of (1)- (11).…”

“…In particular, energy-shaping control enforces a minimum of the closed-loop potential energy at the desired equilibrium, and is applicable to a wide range of underactuated mechanisms [8]. A further advantage of energy-shaping control is its robustness to disturbances, which has been the focus of recent research [9]- [13]. Nevertheless, the presence of control input saturation, which is often encountered in engineering practice, represents an obstacle to the energy shaping procedure.…”

Robust dynamic state feedback for underactuated systems with linearly parameterized disturbances

“…Taking advantage of this structure, different definitions of algebraic solution of the matching equations can be employed. The proposed method is also applicable to the conventional IDA‐PBC design that relies on the classical solution of the PDE, and it represents an extension of References 26,35 for multiple additive variable disturbances. In any case, the terms F 1 ( x ), F 0 contained in u * are computed from (22), which does not include any PDE.…”

“…The case of nonconstant inertia matrix and variable but bounded disturbances was considered in Reference . In addition, the adaptive compensation of constant disturbances within energy shaping control was attempted in References 26,27: while the former still requires solving the PDE, the latter is confined to a limited class of mechanical systems. Besides energy shaping, a sliding mode control for a class of underactuated systems with dry friction was presented in Reference , while an active disturbance rejection control was proposed for systems with bounded uncertainties and applied to the inertia‐wheel‐pendulum in Reference .…”