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

Design of a Fractional Order CRONE and PID Controllers for Nonlinear Systems using Multimodel Approach

This paper deals with the output regulation of nonlinear control systems in order to guarantee desired performances in the presence of plant parameters variations. The proposed control law structures are based on the fractional order PI (FOPI) and the CRONE control schemes. By introducing the multimodel approach in the closed-loop system, the presented design methodology of fractional PID control and the CRONE control guarantees desired transients. Then, the multimodel approach is used to analyze the closed-loop system properties and to get explicit expressions for evaluation of the controller parameters. The tuning of the controller parameters is based on a constrained optimization algorithm. Simulation examples are presented to show the effectiveness of the proposed method

A High Order Sliding Mode Control with PID Sliding Surface: Simulation on a Torpedo

Position and speed control of the torpedo present a real problem for the actuators because of the high level of the system non linearity and because of the external disturbances. The non linear systems control is based on several different approaches, among it the sliding mode control. The sliding mode control has proved its effectiveness through the different studies. The advantage that makes such an important approach is its robustness versus the disturbances and the model uncertainties. However, this approach implies a disadvantage which is the chattering phenomenon caused by the discontinuous part of this control and which can have a harmful effect on the actuators. This paper deals with the basic concepts, mathematics, and design aspects of a control for nonlinear systems that make the chattering effect lower. As solution to this problem we will adopt as a starting point the high order sliding mode approaches then the PID sliding surface. Simulation results show that this control strategy can attain excellent control performance with no chattering problem.Comment: 13 pages, 17 figure

Robust and Gain-Scheduled PID Controller Design for Condensing Boilers by Linear Programming

This paper addresses the water temperature control in condensing domestic boilers. The main challenge of this process under the controller design perspective is the fact that the dynamics of condensing boilers are strongly affected by the demanded water flow rate. Two approaches are presented in this paper. First, a robust PI controller is designed that stabilizes and achieves good performance for closed-loop system for a wide range of the water flow rate. Then, it is shown that if the water flow rate information is used to update the controller gains, a technique known as gain-scheduled control, the performance can be significantly improved. Several models of a boiler in different water flow rate are identified in collaboration with Honeywell, and the effectiveness of the results are illustrated by simulation

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

Fixed-order H-infinity Controller Design for Nonparametric Models by Convex Optimization

A new approach for robust fixed-order H-infinity controller design by convex optimization is proposed. Linear time-invariant single-input single-output systems represented by nonparametric models in the frequency domain are considered. It is shown that the H-infinity robust performance condition can be represented by a set of linear or convex constraints with respect to the parameters of a linearly parameterized controller in the Nyquist diagram. Multimodel and frequency-domain uncertainty can be considered straightforwardly in the proposed approach. The proposed method is compared with the standard H-infinity control problem. Moreover, a solution to an international benchmark problem is given that meets all specifications with the lowest order controller

A Robust Data-Driven Controller Design Methodology With Applications to Particle Accelerator Power Converters

A new data-driven approach using the frequency response function (FRF) of a system is proposed for designing robust-fixed structure digital controllers for particle accelerators' power converters. This design method ensures that the dynamics of a system are captured and avoid the problem of unmodeled dynamics associated with parametric models. The H ∞ robust performance condition can be represented by a set of convex constraints with respect to the parameters of a two degree of freedom RST controller. This controller is robust with respect to the frequency-dependent uncertainties of the FRF. A convex optimization algorithm is implemented to obtain the controller parameters. The effectiveness of the method is illustrated by considering two case studies that require robust controllers for achieving the desired performance

H∞ Controller Design for Spectral MIMO Models by Convex Optimization

A new method for robust fixed-order H∞ controller design by convex optimization for multivariable systems is investigated. Linear Time-Invariant Multi-Input Multi- Output (LTI-MIMO) systems represented by a set of complex values in the frequency domain are considered. It is shown that the Generalized Nyquist Stability criterion can be approximated by a set of convex constraints with respect to the parameters of a multivariable linearly parameterized controller in the Nyquist diagram. The diagonal elements of the controller are tuned to satisfy the desired performances, while simultaneously, the off-diagonal elements are designed to decouple the system. Multimodel uncertainty can be directly considered in the proposed approach by increasing the number of constraints. A simulation example illustrates the effectiveness of the proposed approach. by a simulation example on an unstable system