State Observer

State Observer for Intelligent Dynamical Systems

A state observer estimates the state of a dynamical system based on noisy sensor measurements and a system model. For the implementation of an intelligent control strategy, e.g. a self-optimizing control strategy, it is of high importance to design a state observer to estimate all required system states. The estimation quality of the state observer can be assessed by comparing the estimated and the real behavior of the system. With a converging behavior of the estimation error, a reliable state estimation can be achieved. In the research group Control Engineering and Mechatronics, different kinds of state observers are used to support the practical implementation of several challenging control strategies.

Extended Kalman Filter For A Double pendulum

The mathematical model of an ideal double pendulum undergoes chaotic behavior. This feature affects also the behavior of the real system. Even with small amount of disturbances or deviations from the nominal state trajectory, the swing-up and stabilization of the double pendulum to its upper equilibrium cannot be achieved. For more accurate knowledge of the full system state, a state observer must be designed.

The Extended Kalman Filter (EKF) is a state observer for nonlinear dynamical systems subjected to normally distributed disturbances (process noise and measurement noise). Applying the EKF for controlling the real double pendulum system, significantly better performance can be achieved. The deviation of the swing-up trajectory from the nominal state trajectory was notably smaller. The amplitude and frequency of the limit cycle by stabilizing the double pendulum at the upper equilibrium point was significantly reduced. To summarize, the application of EKF results in an improved system behavior and greatly supports the implementation of optimal control strategy.

Contact person: M.Sc. Ke Xu

Sliding-Mode Observer for an axle test rig

At the Heinz Nixdorf Institute of Paderborn University, a multi-axial axle test rig has been built up for real-time testing of complete vehicle axles. The main component is a controlled hydraulic hexapod used as an excitation unit for reconstructing the real road condition. The direct measurement of all required system states for such a parallel kinematic manipulator is a very difficult task. Thus, a state observer must be implemented.

The Sliding-Mode approach is applied to observe the required state. Comparing with the standard Luenberger observer or the Extended Kalman Filter, which uses continuous injection signals to reduce the estimation error, the Sliding-Mode observer applies discontinuous, i.e. switching signals. The usage of the switching signal results in the ability of the Sliding-Mode observer to generate a sliding motion on the error between the measured output and the output of the observer and provides a precise estimation of the system state. This approach is robust with respect to uncertainties in the system model and the system parameters. Moreover, the estimation error converges to zero in finite time.

With this Sliding-Mode observer, a reliable control strategy and a compensation of disturbances can be implemented in the multi-axial axle test rig. [FOT14]

Contact person: M.Sc. Simon Olma

event-based observer for cooperating robots

For cooperative ball juggling using Delta-Robots, the knowledge of the state of the ball, the state of the Delta-Robots and the striking time plays a vital role for the stability and duration of a long rally.

The continuous position of the ball during juggling is measured through a Kinect camera. The Kinect camera is of low cost, flexible and easy to implement even with limited knowledge of the hardware and computer vision algorithms. However, the measured signal has a low sampling frequency and there is computational delay resulting from the image processing.

An event-based observer is designed to remedy these problems. Each measurement of the position and velocity of the ball through the camera (30 FPS) triggers an event in the state observer to update its prediction of the striking time. In addition, the delay resulting from the image processing is also being considered. The preliminary model based simulations show successful results for using the event-based observer to control the cooperating Delta-Robots.

Contact person: Dr.-Ing. Julia Timmermann


Related publications:

  • [FOT14] Sarah Flottmeier, Simon Olma, Ansgar Tr├Ąchtler; Sliding Mode and Continuous Estimation Techniques for the Realization of Advanced Control Strategies for Parallel Kinematics; IFAC World Congress 2014