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Assessment of prospective controllers : data-based approaches tailor-made for current knowledge

  • Author(s): Cheong, Seunggyun;
  • Cheong, Seunggyun
  • et al.

This dissertation is focused on assessment of prospective controllers in the sense of their closed-loop stability and performance. We consider a variety of circumstances depending on knowledge of a given plant and propose corresponding strategies for the assessment. The assessment is performed based on the data from experiments and the strategies assess not only the controller in the loop where the experiments are taken but also the other prospective controllers out of the loop. The first circumstance is challenging such that there is no available knowledge of a plant and a disturbance signal except we can observe the input and the output signals of the plant. Among many prospective controllers, one controller makes a closed-loop system with the plant and the input and the output signals of the plant are observed. Then, the controller in the loop is assessed by a data-based cost function for the closed-loop stability and performance. The other prospective controllers can be assessed by data-based cost functions with computed fictitious reference signals in corresponding fictitious closed-loop systems. The experiment is performed with a switching control scheme, in which we compare online the cost functions of the controllers and switch the one with the smallest cost into the loop. The stability and performance of this switching control system is shown to be guaranteed when at least one of the controllers is feasible. In the second circumstance, the available knowledge of the plant is that the plant is known to be a SISO LTI discrete-time system and the disturbance signal is an i.i.d. random process with zero mean, unknown bounded variance, and finite fourth moment. We consider only one controller and determine its ability to yield closed-loop stability by performing an experiment on the closed-loop system with the plant and the controller. The collection of least squares AR estimators of various orders is shown to have the capacity to detect the instability of the closed-loop system. The order of the system is not necessary information but, instead, an upper bound of the number of unstable poles with the maximal magnitude outside the unit circle is assumed to be known. In the third circumstance, which is the best situation in this dissertation, we know that the plant is a MIMO LTI discrete-time system stabilized by a MIMO LTI controller in a closed-loop and we also know a bound on the impulse response of the closed-loop system and a bound on a disturbance signal which is additive to the output of the plant. With this knowledge, the closed-loop stability and performance of another prospective controller is assessed without constructing this closed-loop. This is performed through nonparametric identification of the frequency response functions of the plant or other transfer functions, based on a limited amount of signal data collected from experiments on the internally stable closed -loop system excited by designed reference signals and corrupted by disturbances. An error analysis is provided and conditions for the reliable assessments of the closed- loop stability and performance are characterized. Based on the strategy developed for the third circumstance, we search for a MIMO LTI discrete-time controller better than the currently stabilizing controller in the sense of a certain performance measure. This searching procedure is formulated in the form of an optimization problem. FRF estimates for coprime factors of the plant are obtained with known error bounds from the experimental data collected from the closed-loop system with the currently stabilizing controller and the optimization problem is built in terms of these FRF estimates. In order to reduce the numerical difficulty of the optimization problem, we employ a controller parametrization and propose an algorithm that may not produce the optimal controller but has fast computation ability

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