Real-time hybrid testing with equivalent force control method incorporating Kalman filter

The equivalent force control (EFC) method has been developed for real-time hybrid testing to replace the numerical iteration of implicit integration with a force-feedback control loop. With this control loop, the EFC method can also compensate for the time delay in real-time hybrid testing. However, the delay compensation effect of the EFC can be influenced by factors such as noises in the measured displacement. This paper discusses the influence of the measurement noises on real-time hybrid testing with the EFC. The Kalman filter is proposed to filter the noises in the measured actuator displacement for improved performance. A higher proportional gain in the PID controller, which improves the effect of time delay compensation of the EFC method, can be allowed without losing stability when incorporating the Kalman filter. A series of real-time hybrid tests were conducted, and the results validated that the EFC method with Kalman filter can effectively compensate for the time delay.