0000000000432537
AUTHOR
Johann Reger
Comparison of Fractional-Order and Integer-Order H-infinity Control of a Non-Collocated Two-Mass Oscillator
We consider the robust control of a two-mass oscillator with a dominant input delay. Our aim is to compare a fractional-order tuning approach including the partial compensation of non-minimum phase zeros with a classical H∞ loop-shaping design, since both these designs lead to a relatively high controller order. First of all a detailed physical model is derived and validated using measurement data. Based on the line arized model both controllers are designed to be comparable, i.e. they show a similar crossover frequency in the open loop and the final controller order is reduced to the same range for both designs. The major differences between both are the different methods how the feed-forw…
Fractional-Order Partial Cancellation of Integer-Order Poles and Zeros
The key idea of this contribution is the partial compensation of non-minimum phase zeros or unstable poles. Therefore the integer-order zero/pole is split into a product of fractional-order pseudo zeros/poles. The amplitude and phase response of these fractional-order terms is derived to include these compensators into the loop-shaping design. Such compensators can be generalized to conjugate complex zeros/poles, and also implicit fractional-order terms can be applied. In the case of the non-minimum phase zero, its compensation leads to a higher phase margin and a steeper open-loop amplitude response around the crossover frequency resulting in a reduced undershooting in the step-response, a…
A Fractional-Order Control Approach to Ramp Tracking with Memory-Efficient Implementation
We investigate the fractional-order (FO) control of arbitrary order LTI systems. We show that, for ramp tracking or input disturbance rejection, it is advantageous to include an FO integrator to the open-loop if we have to increase the order of integration further than one. With the lower phase-loss of the FO integrator it is easier to guarantee a desired phase margin. Furthermore the flat phase response around the crossover-frequency (iso-damping property) can be achieved for a wider frequency range such that the closed-loop is more robust wrt. amplitude and phase margins. The drawback of the FO approach is the increased implementation effort and the algebraic decay, which slows down the t…
Fractional-Order System Identification of Viscoelastic Behavior: A Frequency Domain Based Experimental Study
In this work, the fractional-order modeling of viscoelastic behavior is investigated based on measurement data in the frequency domain. For the results of two different test setups we apply existing parameter estimation algorithms designed for fractional-order transfer functions. These algorithms require a priori knowledge of the system structure including the commensurate order of differentiation. An iterative procedure is used to evaluate the influence of the unknown structure. The measured polymer samples show a viscoelastic stress response. We can show that integer-order models are not capable of capturing this behavior. For a set of predefined structures, the best obtained fractional-o…