Design and implementation of periodic digital controllers
Abstract
Three control problems, related to the design and the implementation of digital controllers, are studied. The overall objective is to develop efficient methods for the computation of solutions. The approach relies on translating the control problems into optimization problems with linear matrix inequality constraints—which can be solved efficiently. The problems and the contributions are summarized next. A digital controller is connected to an analog plant through analog-to-digital and digital-to-analog converters. In practice, these converters have finite range and finite precision. Finite precision causes quantization errors and finite range leads to signal saturation. The controller scaling problem consists in the computation of scaling matrices to guarantee that the input and output signals of the controller do not saturate and to ensure that the performance degradation due to quantization errors is minimized. Traditionally, these scaling matrices are computed only to guarantee that the controller signals do not saturate, and in this case, diagonal matrices suffice. However, diagonal scaling matrices do not necessarily minimize the performance degradation. A method to efficiently compute full matrices in order to prevent signal saturation and to minimize the performance degradation is described. It is shown that full scaling matrices perform better than diagonal scaling matrices. Multirate output controllers (MROCs) use a fast rate to sample the plant measurement outputs and a slow rate to update the plant control inputs. These controllers can replace observer-based controllers to solve a number of control problems, like the arbitrary pole-placement problem. MROCs present advantages, such as controller dynamics that are low-order and can be specified. However, these controllers tend to show high sensitivity to measurement noise. Two algorithms to compute an MROC with order equal to the number of control inputs and low noise sensitivity to place the closed-loop poles in a specified region are given. In addition, these algorithms allow us to specify the MROC dynamics. One of the algorithms comprises two steps. First, a state-feedback gain is computed to achieve the specified pole-placement. Second, an MROC is computed to implement this state-feedback gain and to minimize the noise sensitivity. The other algorithm utilizes an iterative procedure to improve the noise sensitivity of a given MROC that achieves the specified pole-placement. In addition to the algorithms, other contributions are a δ-operator parameterization for MROCs and a technique for the implementation of a given MROC through a single-rate periodic system. The simultaneous stabilization problem consists in the computation of a single controller to stabilize all plants in a given set. This problem is open for linear time-invariant controllers while it can be solved with linear periodic controllers. A method to compute a linear periodic controller that optimizes the worst-case closed-loop performance over all plants in a given set is described. The method comprises two steps. First, a simultaneous stabilizing linear periodic controller is obtained using already known algorithms. Second, the worst-case performance of this controller is improved through an iterative algorithm. This two-step method is extended to guarantee that the solution controller is stable or decentralized.
Degree
Ph.D.
Advisors
Rotea, Purdue University.
Subject Area
Aerospace materials
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