LPV Control of a 2-DOF Robot Using Parameter Reduction

Abstract

Abstract-This paper demonstrates the benefit of a new method for reducing the number of scheduling parameters of LPV controllers, by applying it to a robot manipulator. A full LPV representation of a planar two-link robot with ten scheduling parameters is considered. The number of parameters can be reduced by applying principal components analysis to typical scheduling trajectories. The proposed method enables a systematic trade-off between the number of reduced parameters and the desired accuracy of the model. The practicality of the approach is illustrated with a design example: an LPV controller, designed using a parameter reduced model, is shown in simulation studies to outperform a robust, fixed-gain controller designed to minimize the worst-case H 2 norm .

PCA-Based Parameter Set Mappings for LPV Models With Fewer Parameters and Less Overbounding

“…Therefore, the data set generated from is chosen for constructing an approximated model, and the full model is reduced by seven parameters to . Considering the parametrized (frozen) static gains and eigenvalues, the reduced model with approximates the original model satisfactorily, as illustrated in [12]. Note that this reduces the number of vertices of the polytopic model from to and with this the computational effort by much more than a factor of 128.…”

“…An advantage of this method is the possibility to trade modelling accuracy against the number of parameters. A conference version of this brief was presented in [12].…”

“…The comparison of and allows to assess the quality of the approximation, and-by choosing the number of scheduling variables-to trade accuracy of the model against complexity. The matrix represents a basis of the significant column space of the data matrix , and can be used to obtain a reduced mapping from to by computing (15) i.e., by applying the transformation and the scaling (12) to the mapping in (2). Note that the rows of represent the principal components of the data matrix , and that the approximate mappings , , , in (8) are related to (1) by (16) where (17) and denotes row-wise rescaling.…”

“…The rows of the data matrix need to be normalized by an affine law to achieve scaled, zero mean data (12) resulting in a normalized data matrix . Now, one applies the principle components analysis (PCA) [14] to the normalized data.…”

Model reduction for linear parameter-varying systems through parameter projection

“…Another method for parameter reduction is sensitivity analysis, which is similar to principal component analysis [17], [18]. This method evaluates how sensitive the outputs are to small changes in the parameter values.…”