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1. Hybrid feedback for global asymptotic stabilization on a compact manifold

   https://doi.org/10.1109/CDC.2017.8263998  

   Casau, Pedro; Cunha, Rita; Sanfelice, Ricardo G.; Silvestre, Carlos (December 2017, Proceedings of 2017 IEEE 56th Annual Conference on Decision and Control (CDC 2017))

   In this paper, we employ a hybrid feedback control strategy to globally asymptotically stabilize a setpoint on a smooth compact manifold without boundary satisfying the following: there exists a finite maximal atlas such that the desired setpoint belongs to each chart of the atlas. The proposed hybrid controller includes a proportional-derivative (PD) action during flows and, at jumps, uses hysteresis to switch between local coordinate charts to stabilize the desired setpoint robustly with respect to exogenous disturbances. We show that the proposed controller can be used for attitude stabilization of a rigid body and we illustrate the behavior of the closed-loop system via simulation results. 

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2. Analytical and experimental nonzero-sum differential game-based control of a 7-DOF robotic manipulator

   https://doi.org/https://doi.org/10.1177/1077546320982447  

   Bagheri, Mostafa; Naseradinmousavi, Peiman (January 2021, Journal of vibration and control)

   null (Ed.)

   We formulate a Nash-based feedback control law for an Euler–Lagrange system to yield a solution to noncooperative differential game. The robot manipulators are broadly used in industrial units on the account of their reliable, fast, and precise motions, while consuming a significant lumped amount of energy. Therefore, an optimal control strategy needs to be implemented in addressing efficiency issues, while delivering accuracy obligation. As a case study, we here focus on a 7-DOF robot manipulator through formulating a two-player feedback nonzero-sum differential game. First, coupled Euler–Lagrangian dynamic equations of the manipulator are briefly presented. Then, we formulate the feedback Nash equilibrium solution to achieve perfect trajectory tracking. Finally, the performance of the Nash-based feedback controller is analytically and experimentally examined. Simulation and experimental results reveal that the control law yields almost perfect tracking and achieves closed-loop stability. 

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3. Experimental and Analytical Nonzero-Sum Differential Game-Based Control of a 7-DOF Robotic Manipulator

   https://doi.org/10.1115/DSCC2020-3114  

   Bagheri, Mostafa; Bertino, Alexander; Naseradinmousavi, Peiman (January 2021, Proceedings of the ASME Dynamic Systems and Control Conference)

   null (Ed.)

   We formulate a Nash-based feedback control law for an Euler-Lagrange system to yield a solution to non-cooperative differential game. The robot manipulators are broadly utilized in industrial units on the account of their reliable, fast, and precise motions, while consuming a significant lumped amount of energy. Therefore, an optimal control strategy needs to be implemented in addressing efficiency issues, while delivering accuracy obligation. As a case study, we here focus on a 7-DOF robot manipulator through formulating a two-player feedback nonzero-sum differential game. First, coupled Euler-Lagrangian dynamic equations of the manipulator are briefly presented. Then, we formulate the feedback Nash equilibrium solution in order to achieve perfect trajectory tracking. Finally, the performance of the Nash-based feedback controller is analytically and experimentally examined. Simulation and experimental results reveal that the control law yields almost perfect tracking and achieves closed-loop stability. 

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4. Stable nullspace adaptive parameter identification of 6 degree-of-freedom plant and actuator models for underactuated vehicles: Theory and experimental evaluation

   https://doi.org/10.1177/02783649231191184  

   Harris, Zachary J.; Mao, Annie M.; Paine, Tyler M.; Whitcomb, Louis L. (November 2023, The International Journal of Robotics Research)

   Model-based approaches to navigation, control, and fault detection that utilize precise nonlinear models of vehicle plant dynamics will enable more accurate control and navigation, assured autonomy, and more complex missions for such vehicles. This paper reports novel theoretical and experimental results addressing the problem of parameter estimation of plant and actuator models for underactuated underwater vehicles operating in 6 degrees-of-freedom (DOF) whose dynamics are modeled by finite-dimensional Newton-Euler equations. This paper reports the first theoretical approach and experimental validation to identify simultaneously plant-model parameters (parameters such as mass, added mass, hydrodynamic drag, and buoyancy) and control-actuator parameters (control-surface models and thruster models) in 6-DOF. Most previously reported studies on parameter identification assume that the control-actuator parameters are known a priori. Moreover, this paper reports the first proof of convergence of the parameter estimates to the true set of parameters for this class of vehicles under a persistence of excitation condition. The reported adaptive identification (AID) algorithm does not require instrumentation of 6-DOF vehicle acceleration, which is required by conventional approaches to parameter estimation such as least squares. Additionally, the reported AID algorithm is applicable under any arbitrary open-loop or closed-loop control law. We report simulation and experimental results for identifying the plant-model and control-actuator parameters for an L3 OceanServer Iver3 autonomous underwater vehicle. We believe this general approach to AID could be extended to apply to other classes of machines and other classes of marine, land, aerial, and space vehicles. 

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5. Proportional Integral Derivative Control in Spark Plasma Sintering Simulations

   https://doi.org/10.3390/ma14071779  

   Jiang, Runjian; Torresani, Elisa; Cui, Guodong; Olevsky, Eugene A. (April 2021, Materials)

   null (Ed.)

   The prediction of microstructure evolution and densification behavior during the spark plasma sintering (SPS) process largely depends on accurate temperature regulation. A loop feedback control algorithm called proportional integral derivative (PID) control is a practical simulation tool, but its coefficients are often determined by an inefficient “trial and error” method. This paper is devoted to proposing a numerical method based on the principles of variable coefficients to construct an optimal linear PID controller in SPS electro-thermal simulations. Different types of temperature profiles were applied to evaluate the feasibility of the proposed method. Simulation results showed that, for temperature profiles conventionally used in SPS cycles, the PID output keeps pace with the desired profile. Characterized by an imperfect time delay and overshoot/undershoot, the constructed PID controller needs further advancement to provide a more satisfactory temperature regulation for non-continuous temperature profiles. The first step towards a numerical rule for the optimal PID controller design was undertaken in this work. It is expected to provide a valuable reference for the advanced electro-thermal modeling of SPS. 

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