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Parameter Space Optimization Towards Constrained Controller Design With Application to Tray Indexing
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DOI：10.1109/TIE.2019.2935982.png)
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Abstract
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Tray indexing driven by timing belt actuator is widely used in the industry, where high-precision profile tracking is essential to guarantee good production quality. To avoid humming sound and chip dislodged, an autonomous S-curve trajectory is used as the reference profile and the jerk resulting from the control input chattering needs to be well controlled. To implement the optimal tracking control with respect to an S-curve profile and maintain a guaranteed adequate level of performance towards the perturbation, the composite system is constructed by augmenting the S-curve trajectory with the system model and an H-2 guaranteed cost optimization problem is formulated. The system performance in terms of tracking accuracy and jerk minimization is quantified as the H-2-norm, and it aims to minimize the upper bound to the H-2-norm over the uncertain domain. However, due to structural constraints on the composite gain matrix as well as robustness requirement, the algebraic Riccati equations cannot be used. This article presents the theoretical results where all the stabilizing constrained gain matrices can be parameterized over an extended matrical set. Efficient numerical procedures are developed to obtain the epsilon-optimum with guaranteed robustness by linear programming and outer linearization in an iterative framework. Numerical optimization and experiments are conducted to validate the theoretical results and the practical appeal of the proposed approach.
Keywords:
Constrained optimization
convex optimization
jerk control
linear programming
outer linearization
robust control
epsilon-optimum
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