Damping Analysis of Reset Control Systems: an Analytical Approach
M. Vanderbroeck (TU Delft - Mechanical Engineering)
N. Karbasizadeh Esfahani – Mentor (TU Delft - Mechanical Engineering)
S.H. Hossein Nia Kani – Graduation committee member (TU Delft - Mechanical Engineering)
D. Boskos – Graduation committee member (TU Delft - Mechanical Engineering)
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Abstract
The high-tech industry continuously pushes the boundaries of controller performance to achieve faster and more precise machines. Currently, linear control is the standard in the industry. These controllers suffer from the waterbed effect and Bode's phase/gain relation, which impose inherent limitations on the precision and robustness of the system. Reset control is a popular strategy to get around these limitations and improve performance. The damping in reset control systems is not only determined by the phase margin of the system but is also dependent on the exact controller element sequence. Currently, finding the optimal controller sequence is done through simulation of the step response. However, this fails to provide insight into the underlying cause of the additional damping achieved by specific controller configurations. This thesis proposes an analytical approach to analyze the damping of the transient response reset control systems. The analytical analysis provides a better understanding of sequence-dependent damping and assists in controller design. First, the analytical expressions of the step response and states of the system are derived, which are used to define the system's energy. The step response and energy equations are used to characterize the damping in a reset control system. To show the value of the proposed method, the damping in a reset control system is assessed as an illustrative example. It is found that when a lead is in front of a reset element, the reset controller can provide more damping because it reduces the oscillatory content in the step response.