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1. Cadence Tracking for Switched FES-Cycling With Unknown Time-Varying Input Delay

   https://doi.org/10.1115/DSCC2019-9078  

   Allen, B. ; Cousin, C. ; Rouse, C. ; Dixon, W. ( October 2019 , ASME 2019 Dynamic Systems and Control Conference)

   Functional electrical stimulation (FES) induced exercise, such as motorized FES-cycling, is commonly used in rehabilitation for lower limb movement disorders. A challenge in closed-loop FES control is the presence of an input delay between the application (and removal) of the electrical stimulus and the production of muscle force. Moreover, switching between motor control and FES control of various muscle groups can be destabilizing. This paper examines the development of a control method and state-dependent trigger condition to account for the time-varying input delayed response. Uniformly ultimately bounded tracking for a switched uncertain nonlinear dynamic system with input delays is achieved.
2. Saturated Control of a Switched FES-Cycle with an Unknown Time-Varying Input Delay

   Allen, B. C. ; Stubbs, K. J. ; Dixon, W. E. ( December 2020 , IFAC Conference on Cyber-Physical Human-Systems)

   A common rehabilitation for those with lower limb movement disorders is motorized functional electrical stimulation (FES) induced cycling. Motorized FES-cycling is a switched system with uncertain dynamics, unknown disturbances, and there exists an unknown time-varying input delay between the application/removal of stimulation and the onset/removal of muscle force. This is further complicated by the fact that each participant has varying levels of sensitivity to the FES input, and the stimulation must be bounded to ensure comfort and safety. In this paper, saturated FES and motor controllers are developed for an FES-cycle that ensure safety and comfort of the participant, while likewise being robust to uncertain parameters in the dynamics, unknown disturbances, and an unknown time-varying input delay. A Lyapunov-based stability analysis is performed to ensure uniformly ultimately bounded cadence tracking.
3. Optimal Selection of Basis Functions for Robust Tracking Control of Uncertain Linear Systems—With Application to Three-Dimensional Printing

   https://doi.org/10.1115/1.4051097  

   Ramani, Keval S. ; Okwudire, Chinedum E. ( October 2021 , Journal of Dynamic Systems, Measurement, and Control)

   Abstract There is growing interest in the use of the filtered basis functions (FBF) approach to track linear systems, especially nonminimum phase (NMP) plants, because of its distinct advantages compared to other tracking control methods in the literature. The FBF approach expresses the control input to the plant as a linear combination of basis functions with unknown coefficients. The basis functions are forward filtered through the plant dynamics, and the coefficients are selected such that tracking error is minimized. Similar to other feedforward control methods, the tracking accuracy of the FBF approach deteriorates in the presence of uncertainties. However, unlike other methods, the FBF approach presents flexibility in terms of the choice of the basis functions, which can be used to improve its accuracy. This paper analyzes the effect of the choice of the basis functions on the tracking accuracy of FBF, in the presence of uncertainties, using the Frobenius norm of the lifted system representation (LSR) of FBF's error dynamics. Based on the analysis, a methodology for optimal selection of basis functions to maximize robustness is proposed, together with an approach to avoid large control effort when it is applied to NMP systems. The basis functions resulting from thismore »process are called robust basis functions. Applied experimentally to a desktop three-dimensional (3D) printer with uncertain NMP dynamics, up to 48% improvement in tracking accuracy is achieved using the proposed robust basis functions compared to B-splines, while utilizing much less control effort.« less
4. Optimal fractional-order proportional–integral–derivative control enabling full actuation of decomposed rotary inverted pendulum system

   https://doi.org/10.1177/01423312221146606  

   Yang, Yi ; Zhang, Haiyan H. ; Voyles, Richard M. ( January 2023 , Transactions of the Institute of Measurement and Control)

   Allowing for a “virtual” full actuation of a rotary inverted pendulum (RIP) system with only a single physical actuator has been a challenging problem. In this paper, a hybrid control scheme that involves a pole-placement feedback controller and an optimal proportional–integral–derivative (PID) or fractional-order PID (FOPID) controller is proposed to simultaneously enable the tracking control of the rotary arm and the stabilization of the pendulum arm in an input–output feedback linearized RIP system. The PID controller is optimized first with the particle swarm optimization (PSO) to obtain three optimal gains, and then the other two parameters of the FOPID controller are optimized with the PSO. Compared to the optimized PID controller, the optimized FOPID controller improves the tracking and stabilizing accuracy by 53% and 29%, respectively, and demonstrates better adaptability for tracking different reference signals. Moreover, the hybrid FOPID controller exhibits 74.8% and 53% higher tracking accuracy than previous optimized model reference adaptive control PID (MRAC-PID) and linear–quadratic regulator (LQR) controllers, respectively. The proposed hybrid controllers are also digitized with different rules and sampling times, showing a closer performance between the discrete-time and continuous-time hybrid controllers under smaller sampling times.
5. Robust Analysis of Linear Systems with Uncertain Delays using PIEs

   https://doi.org/10.1016/j.ifacol.2021.11.133  

   Wu, S. ; Peet, M. ; Sun, F. ; Hua, C. ( January 2021 , IFACPapersOnLine)

   Appeared in the proceedings of the 2021 IFAC Workshop on Time-Delay Systems This paper establishes a PIE (Partial Integral Equation)-based technique for the robust stability and H∞ performance analysis of linear systems with interval delays. The delays considered are time-invariant but uncertain, residing within a bounded interval excluding zero. We first propose a structured class of PIE systems with parametric uncertainty, then propose a Linear PI Inequality (LPI) for robust stability and H∞ performance of PIEs with polytopic uncertainty. Next, we consider the problem of robust stability and H∞ performance of multidelay systems with interval uncertainty in the delay parameters and show this problem is equivalent to robust stability and performance of a given PIE with parametric uncertainty. The robust stability and H∞ performance of the uncertain time-delay system are then solved using the LPI solver in the MATLAB PIETOOLS toolbox. Numerical examples are given to prove the effectiveness and accuracy of the method. This paper adds to the expanding field of PIE approach and can be extended to linear partial differential equations.