Stability and bifurcation analysis of a non-rigid robotic arm controlled with a time-delayed acceleration feedback loop is addressed in this work. The study aims at revealing the dynamical mechanisms leading to the appearance of limit cycle oscillations existing in the stable region of the trivial solution of the system, which is related to the combined dynamics of the robot control and its structural nonlinearities. An analytical study of the bifurcations occurring at the loss of stability illustrates that, in general, hardening structural nonlinearities at the joint promote a subcritical character of the bifurcations. Consequently, limit cycle oscillations are generated within the stable region of the trivial solution. A nonlinear control force is then developed to enforce the supercriticality of the bifurcations. Results illustrate that this strategy enables to partially eliminate limit cycle oscillations coexisting with the stable trivial solution. The mechanical system is analysed in a collocated and a non-collocated configuration, depending on the position of the sensor.

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This study is interested in the stability of robots in machining. The goal is to improve the dynamic performance of robots using an additional acceleration signal fed back through the conventional built-in proportional-derivative controller provided by the manufacturer. The structure of the robot is modelled with a simple one degree of freedom lumped model and the control signals are fed back via a linear spring and damping. The time delays of feedback controllers are considered zero-order holds, which results in sawtooth-like time-periodic time delays. The resulting equation of motion is an advanced delay differential equation. The semidiscretization method is shown for such systems having multiple sampled digital delays and continuous delays. First, we establish the stable regions in the plane of the sampling delay and the gain of the acceleration signal without machining. Then we show the possibility to improve stability in turning and milling using the additional acceleration feedback controller compared to the cases without any controller or using only the built-in proportional-derivative controller.

This study investigates the lane-keeping control of autonomous vehicles with an emphasis on the digital delayed nature of the system. The vehicle dynamics are represented using a kinematic bicycle model, and a hierarchical lane-keeping controller is introduced with multiple delays in the feedback loop. An extension of the semidiscretization method is presented, in order to perform the stability analysis of the digitally controlled vehicle with multiple discrete time delays. The differences between the continuous approximation and the exact consideration of discrete time delays are highlighted. We show that in certain cases, neglecting the effects of quantization can lead to significant inaccuracies, especially when tuning the lower-level controller. The results are verified using a series of small-scale laboratory experiments.

This study investigates the stability of robots in machining. The goal is to improve the dynamic performance of robots using an additional acceleration signal fed back through the conventional built-in proportional-derivative controller provided by the manufacturer. The structure of the robot is modelled with a simple one degree-of-freedom lumped model. The control signals are fed back via a linear spring and damping. The time delays of feedback controllers are considered as zero-order holds, which results in sawtooth-like time-periodic time delays. The resulting equation of motion is an advanced delay differential equation. The semidiscretization method is shown for such systems with multiple sampled digital delays. First, we establish the stable regions in the plane of the sampling delay and the gain of the acceleration signal without machining. Then we show the possibility to improve stability in the simplest possible cutting case using the additional acceleration feedback controller compared to the cases without any controller or using only the proportional-derivative controller.