The use of digital twins to remotely update feedback controllers for the motion control of nonlinear dynamic systems
Yoav Vered, Stephen N. Elliott
Abstract
• A digital twin is employed to ensure the stability of a mechanical system with an uncertain nonlinear sandwiched backlash. • A time-varying backlash is modelled and used in the simulation to represent wear processes. • A PID controller with a dead zone switching law is used to avoid limit cycles and restabilize the system. • Asynchronous communication and buffers are utilized to ensure constant sampling time and reduce the controller complexity. The use of a digital twin to update a feedback controller is considered, and this is illustrated using simulations of a position-controlled dynamical system with a time-varying nonlinear element. The feedback control system consists of a dc motor driving the displacement of a three degree of freedom structure through a lead screw that is subject to backlash, whose gap angle changes over time due to wear for example. The backlash is shown to destabilise the feedback loop when using a PID controller designed for the linear system. However, stability can then be re-established by including a dead zone within the controller. The design of the dead zone depends on the extent of the gap angle in the backlash and is a trade-off between stabilising the system and avoiding excessive steady-state errors and undesired transient behaviour. When the backlash gap angle changes significantly from the one used to design the dead zone, both performance and stability are affected. Therefore, a digital twin of the system is used to estimate the backlash gap angle as it changes with time and this estimate is used to re-design the dead zone, which is then communicated back to update the controller. The digital twin and controller-design process can be implemented offline and remotely from the physical twin and the real-time controller via an asynchronous link with variable time delays. As a result of combining the feedback loop and digital twin, good performance and stability are maintained at all times.