Immersion and invariance adaptive control for discrete‐time systems in strict‐feedback form with input delay and disturbances

Abstract

This work presents a new adaptive control algorithm for a class of discrete-time systems in strict feedback form with input delay and disturbances. The Immersion and Invariance formulation is employed to estimate the disturbances and to compensate the effect of the input delay, resulting in a recursive control law. The stability of the closed-loop system is studied employing Lyapunov functions and guidelines for tuning the controller parameters are presented. An explicit expression of the control law in case of multiple simultaneous disturbances is provided for the tracking problem of a pneumatic drive. The effectiveness of the control algorithm is demonstrated with numerical simulations considering disturbances and input delay representative of the application.

Robust balancing control of flexible inverted-pendulum systems

“…which holds true for all > 0, ∈ ℝ × and concludes the proof ∎ This result can be readily extended to state-dependent matched disturbances and to discrete-time systems [33,34]. A robust controller for underactuated rigid systems with variable disturbances was recently proposed in [35], while the extension to flexible mechanisms is part of our future work.…”

Position regulation in Cartesian space of a class of inextensible soft continuum manipulators with pneumatic actuation

“…Proof: The proof follows closely that of Proposition 1 thus the passages corresponding to (17) + 𝑅 0 ) modulates the ancillary control action, while 𝜃 ̂𝐴, 𝜃 ̂𝐵 are computed by (37). It must be noted that, differently from the adaptive observer (35) and (36), the TDC estimate does not change depending on the parameterization of the disturbances.…”

“…Instead, with controller (40) the 𝑥 coordinate is regulated with a smaller value of 𝑢 𝐴 , thus 𝑢 𝐵 increases until the 𝑦 coordinate reaches the prescribed value. This behaviour is due to the structure of controller (40) which accounts for the underlying system dynamics through the tip angles 𝜃 𝐴 and 𝜃 𝐵 , and which includes a coupling term in (37) and in the ancillary control action. The values of steady-state error, overshoot, and settling time corresponding to Figure 8 are reported in Table B5 (see Appendix B).…”

Discrete-Time IDA-PBC for Underactuated Mechanical Systems with Input-Delay and Matched Disturbances

“…If { }| | 2 ≥ | || / −1 | then ( + 1) ≤ ( ) proving the second claim □ Remark 1: For comparison purposes, considering the IDA-PBC (2) in closed-loop with system (1) and computing the corresponding Lyapunov increment (10) gives:…”