Michael Treuer

Brief paper: Swing-up of the double pendulum on a cart by feedforward and feedback control with experimental validation

The swing-up maneuver of the double pendulum on a cart serves to demonstrate a new approach of inversion-based feedforward control design introduced recently. The concept treats the transition task as a nonlinear two-point boundary value problem of the internal dynamics by providing free parameters in the desired output trajectory for the cart position. A feedback control is designed with linear methods to stabilize the swing-up maneuver. The emphasis of the paper is on the experimental realization of the double pendulum swing-up, which reveals the accuracy of the feedforward/feedback control scheme.

Fast Side-Stepping of the Triple Inverted Pendulum via Constrained Nonlinear Feedforward Control Design

The side-stepping of the triple inverted pendulum serves as a benchmark problem for the presentation of a new feedforward control design technique for finite-time transition problems under consideration of output constraints. The inversion-based design treats the transition task as a two-point boundary value problem (BVP) defined in the input-output coordinates of the pendulum. As a necessary condition for its solvability, a sufficient number of free parameters is provided in a set-up function for the cart acceleration. The new approach allows to directly incorporate output constraints of the pendulum within the BVP, which is solved by a standard MATLAB function. A linear LQR controller is used to stabilize the pendulum along the feedforward side-stepping trajectories. Experimental results for the triple inverted pendulum illustrate the accuracy and robustness of the proposed feedforward/feedback control scheme.

Flatness-Based Feedforward in a Two-Degree-of-Freedom Control of a Pumped Storage Power Plant

Pumped storage power plants are typically controlled using a two-degree-of-freedom control structure in which the feedforward part is static. For set point changes of the generator output, this control structure leads to pressure oscillations due to the non-minimum phase nature of pumped storage power plants. In order to improve the control performance, a flatness-based feedforward is developed as an add-on for the already existing two-degree-of-freedom control. Thereby a differentially flat dynamic model of a real power plant, derived on first principles, is used for both the design of a dynamic feedforward part and the design of consistent smooth trajectories for set point changes of the generator output. In view of trajectory planning, the effect of using different trajectory function types is addressed in detail. The improved control performance using the new control concept is shown in simulations, also in comparison with the widespread conventional two-degree-of-freedom control with static feedforward part.

Trajectory Planning for Flatness-based two-degree-of-freedom control of a pumped storage power station

Abstract A pumped storage plant is one of the fastest reacting types of power generating units within power systems. Typically, the desired value curves for the power output during set point changes are provided in form of non-smooth ramp shaped curves. These cannot be followed exactly by the plant process due to its physical limitations. Resulting oscillations of the water pressure with potentially high pressure peaks can cause severe damage to the plant. Therefore, the gradients of set point changes of the power output have to be carefully limited. In order to improve the control performance, a flatness-based two-degree-of-freedom control concept is applied: smooth trajectories for set point changes of the generator output are provided, which take the plant dynamics into account. The matter of trajectory planning is thereby addressed in detail. The improved control performance is shown by simulations, also in comparison with the widespread conventional PID control concept.