A Data-driven Approach to Robust Control of Multivariable Systems by Convex Optimization

The frequency-domain data of a multivariable system in different operating points is used to design a robust controller with respect to the measurement noise and multimodel uncertainty. The controller is fully parametrized in terms of matrix polynomial functions and can be formulated as a centralized, decentralized or distributed controller. All standard performance specifications like $H_2$, $H_\infty$ and loop shaping are considered in a unified framework for continuous- and discrete-time systems. The control problem is formulated as a convex-concave optimization problem and then convexified by linearization of the concave part around an initial controller. The performance criterion converges monotonically to a local optimal solution in an iterative algorithm. The effectiveness of the method is compared with fixed-structure controllers using non-smooth optimization and with full-order optimal controllers via simulation examples. Finally, the experimental data of a gyroscope is used to design a data-driven controller that is successfully applied on the real system

A shifting pole placement approach for the design of performance-varying multivariable PID controllers via BMIs

© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/In this paper, the design of a performance-varying multivariable Proportional-Integral-Derivative (PID) controllers is presented. The main objective is to provide a framework for changing online the closed-loop behavior of the controlled system using the shifting pole placement approach. In order to carry out this target, the PID design problem is transformed into a static output feedback design problem which is analyzed through the linear parameter-varying (LPV) paradigm. An academic example is used to demonstrate the effectiveness of the proposed approach.Peer ReviewedPostprint (author's final draft

Návrh robustného decentralizovaného PID regulátora : prípadová štúdia

Robust stability is an important aspect in control of real world systems, since uncertainties have to be considered in dynamic system model. This paper studies the robust decentralized controller design for case study: quadruple tank process, [3,4]. Several important aspects of system analysis are shown to choose appropriate pairing and assess stabilizability via decentralized control structure; the main contribution is in decentralized discrete-time controller design. Simulation results illustrate the obtained results and their qualities.Robustná stabilita je dôležitou stránkou pri návrhu riadenia reálnych systémov. Tento príspevok sa zaoberá návrhom robustného decentralizovaného regulátora pre prípadovú štúdiu: systém štyroch nádrží, [3,4]. Príspevok ilustruje niektoré dôležité aspekty analýzy systému potrebné na správny výber párovania vstupov a výstupov umožňujúci stabilizáciu systému decentralizovaným riadením; hlavným prínosom je návrh decentralizovaného diskrétneho algoritmu riadenia. Výsledky simulácie ilustrujú vlastnosti získaných regulátorov

Design of Low-Order Controllers using Optimization Techniques

In many applications, especially in the process industry, low-level controllers are the workhorses of the automated production lines. The aim of this study has been to provide simple tuning procedures, either optimization-based methods or tuning rules, for design of low-order controllers. The first part of this thesis deals with PID tuning. Design methods or both SISO and MIMO PID controllers based on convex optimization are presented. The methods consist of solving a nonconvex optimization problem by deriving convex approximations of the original problem and solving these iteratively until convergence. The algorithms are fast because of the convex approximations. The controllers obtained minimize low-frequency sensitivity subject to constraints that ensure robustness to process variations and limitations of control signal effort. The second part of this thesis deals with tuning of feedforward controllers. Tuning rules that minimize the integrated-squared-error arising from measurable step disturbances are derived for a controller that can be interpreted as a filtered and possibly time-delayed PD controller. Using a controller structure that decouples the effects of the feedforward and feedback controllers, the controller is optimal both in open and closed loop settings. To improve the high-frequency noise behavior of the feedforward controller, it is proposed that the optimal controller is augmented with a second-order filter. Several aspects on the tuning of this filter are discussed. For systems with PID controllers, the response to step changes in the reference can be improved by introducing set-point weighting. This can be interpreted as feedforward from the reference signal to the control signal. It is shown how these weights can be found by solving a convex optimization problem. Proportional set-point weight that minimizes the integrated-absolute-error was obtained for a batch of over 130 different processes. From these weights, simple tuning rules were derived and the performance was evaluated on all processes in the batch using five different feedback controller tuning methods. The proposed tuning rules could improve the performance by up to 45% with a modest increase in actuation

Robust Optimal Control Strategies for a Hybrid Fuel Cell Power Management System

International audienceAbstract--In this paper several optimal control strategies are proposed for the power management subsystem of a hybrid fuel cell/supercapacitor power generation system. The control strategies are based on different control configurations involving the power converters associated to the hybrid source. Given certain desired performances, Linear Matrix Inequalities methods are used to solve the controller design problem that is written as an optimization problem with inequalities constraints. The solution to the optimization problem yields a simple PID controller with H∞ desired performance. For the several control strategies proposed, robustness is a primary issue. Time simulations and robustness analysis shows the effectiveness of the proposed strategies when compared with the classic control strategies used for this type of hybrid power generation system