http://courses.ece.ubc.ca/574/Hjalmarsson_Automatica_March05.pdf

From experiment design to closed-loop control

Identification and control—closed-loop issues

This paper aims at introducing the reader to the various issues that arise in the development of a coherent methodology for the development of robust control design on the basis of models identified from data. When a reduced complexity model is identified with the purpose of designing a robust controller, the model is just a vehicle for the computation of a controller. The design of the identification and of the controller must be seen as two parts of a joint design problem. The central message of this paper is to show that the global control performance criterion must determine the identification criterion. This leads to non standard identification criteria, which can be minimized by appropriate experimental set-ups.

Towards a Joint Design of Identification and Control

Worst-case control-relevant identification

After several years of effort, constrained model predictive control (MPC), the de facto standard algorithm for advanced control in process industries, has finally succumbed to rigorous analysis. Yet successful practical implementations of MPC were already in place almost two decades before a rigorous stability proof for constrained MPC was published. What then, is the importance of recent theoretical results for practical MPC applications? In this publication we present a pedagogical overview of some of the most important recent developments in MPC theory and discuss their implications for the future of MPC theory and practice.

Model predictive controllers: A critical synthesis of theory and industrial needs

A criterion for system identification is developed that is consistent with the intended use of the fitted model for modern robust control synthesis. Specifically, a joint optimization problem is posed which simultaneously solves the plant model estimate and control design, so as to optimize robust performance over the set of plants consistent with a specified experimental data set. >

A criterion for joint optimization of identification and robust control

The lifting of Lozano (1989) is generalized and shown to be one in a large class of liftings which enjoy the same zero annihilation properties (i.e., placement of transmission zeros to the origin). The new class of liftings allows for longer horizons and leads to plant-inverse controllers for nonminimum-phase systems having significantly reduced control gains and peak torque requirements. >

Extended horizon liftings for stable inversion of nonminimum-phase systems

In this paper, an algorithm is introduced to find a minimum phase transfer function of specified order whose magnitude "tightly" overbounds a specified real-valued nonparametric function of frequency. This method has direct application to transforming nonparametric uncertainty bounds (available from system identification experiments and/or plant modeling) into parametric representations required for modern robust control design software (i.e., a minimum-phase transfer function multiplied by a norm-bounded perturbation). >

A globally optimal minimax solution for spectral overbounding and factorization

It is shown that the m -measurement feedback (mM) policy for nonlinear stochastic control, performs as well or better than the open-loop optimal policy and hence becomes one of only a few suboptimal policies presently known to be quasi-adaptive in the sense of Witsenhausen.

Proof of quasi-adaptivity for the m-measurement feedback class of stochastic control policies

Averaging methods are applied to analyzing and optimizing the transient response associated with the direct adaptive control of an oscillatory second-order minimum-phase system. In order to implement the optimal adaptive design, it is necessary to have knowledge of certain parameters well beyond what needs to be known for adaptive stability, and this may or may not be feasible, depending on the application. However, even if the optimal design cannot by implemented exactly, partial knowledge of the system dominant mode may suffice to improve performance in practical implementations. >

D.S. Bayard

Papers

A criterion for joint optimization of identification and robust control

Extended horizon liftings for stable inversion of nonminimum-phase systems

A globally optimal minimax solution for spectral overbounding and factorization

Proof of quasi-adaptivity for the m-measurement feedback class of stochastic control policies

Transient analysis of an adaptive system for optimization of design parameters