Abstract
This paper presents the design and implementation of Adaptive Generalized Dynamic Inversion (AGDI) to track the position of a Linear Flexible Joint Cart (LFJC) system along with vibration suppression of the flexible joint. The proposed AGDI control law will be comprised of two control elements. The baseline (continuous) control law is based on principle of conventional GDI approach and is established by prescribing the constraint dynamics of controlled state variables that reflect the control objectives. The control law is realized by inverting the prescribed dynamics using dynamically scaled Moore-Penrose generalized inversion. To boost the robust attributes against system nonlinearities, parametric uncertainties and external perturbations, a discontinuous control law will be augmented which is based on the concept of sliding mode principle. In discontinuous control law, the sliding mode gain is made adaptive in order to achieve improved tracking performance and chattering reduction. The closed-loop stability of resultant control law is established by introducing a positive define Lyapunov candidate function such that semi-global asymptotic attitude tracking of LFJC system is guaranteed. Rigorous computer simulations followed by experimental investigation will be performed on Quanser's LFJC system to authenticate the feasibility of proposed control approach for its application to real world problems.
Highlights
1 Introduction This paper presents a controller design for position tracking of a classroom equipment for mass-damper-spring quadratic systems called Linear Flexible Joint Cart (LFJC) system supplied by [1]
The LFJC system is simulated based on the dynamic model given in (6–9) with the parameter’s value given in [1]
The superiority of Adaptive Generalized Dynamic Inversion (AGDI) over the other two controllers are further proven by comparing their Integral Time Absolute Error (ITAE) as shown in Tabs. 1 and 2
Summary
This paper presents a controller design for position tracking of a classroom equipment for mass-damper-spring quadratic systems called Linear Flexible Joint Cart (LFJC) system supplied by [1]. The usage of AI based technique in adaptive control is tempting as it generally provides a model free universal approximation. They were typically used together with classical controller to enhance their robustness, adaptivity to changes, and improve non-linear model approximation. An additional term based on Sliding Mode Controller (SMC) is included in the proposed controller as implemented in [19] In all these references, a constant sliding mode gain is used in the additional term for its application to rotary servo cart and inverted pendulum systems. In this article, the authors have extended the previous work by implementing the adaptive sliding mode gain in the discontinuous control which adapts itself with respect to the changing environment for chattering reduction and to achieve improved tracking performance.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
