Fixed-structure Control of LTI Systems with Polytopic-type Uncertainty

This thesis focuses on the development of robust control solutions for linear time-invariant interconnected systems affected by polytopic-type uncertainty. The main issues involved in the control of such systems, e.g. sensor and actuator placement, control configuration selection, and robust fixed-structure control design are included. The problem of fixed-structure control is intrinsically nonconvex and hence computationally intractable. Nevertheless, the problem has attracted considerable attention due to the great importance of fixed-structure controllers in practice. In this thesis, necessary and sufficient conditions for fixed-structure H_inf control of polytopic systems with a single uncertain parameter in terms of a finite number of bilinear matrix inequalities (BMIs) are developed. Increasing the number of uncertain parameters leads to sufficient BMI conditions, where the number of decision variables grows polynomially. Convex approximations of robust fixed-order and fixed-structure controller design which rely on the concept of strictly positive realness (SPRness) of transfer functions in state space setting are presented. Such approximations are based on the use of slack matrices whose duty is to decouple the product of unknown matrices. Several algorithms for determination and update of the slack matrices are given. It is shown that the problem of sensor and actuator placement in the polytopic interconnected systems can be formulated as an optimization problem by minimizing cardinality of some pattern matrices, while satisfying a guaranteed level of H_inf performance. The control configuration design is achieved by solving a convex optimization problem whose solution delivers a trade-off curve that starts with a centralized controller and ends with a decentralized or a distributed controller. The proposed approaches are applied to inverter-interfaced microgrids which consist of distributed generation (DG) units. To this end, two important control problems associated with the microgrids are considered: (i) Current control of grid-connected voltage-source converters with L/LCL filters and (ii) Voltage control of islanded microgrids. The proposed control strategies are able to independently regulate the direct and quadrature (dq) components of the converter currents and voltages at the point of common couplings (PCC) in a fully decoupled manner and provide satisfactory dynamic responses. The important problem of plug-and-play (PnP) capability of DGs in the microgrids is also studied. It is shown that an inverter-interfaced microgrid consisting of multi DGs under PnP functionality can be cast as a system with polytopic-type uncertainty. By virtue of this novel description and use of the results from theory of robust control, the stability of the microgrid system under PnP operation of DGs is preserved. Extensive case studies, based on time-domain simulations in MATLAB/SimPowerSystems Toolbox, are carried out to evaluate the performance of the proposed controllers under various test scenarios, e.g., load change, voltage and current tracking. Real-time hardware-in-the-loop case studies, using RT-LAB real-time platform of OPAL-RT Technologies, are also conducted to validate the performance of the designed controllers and demonstrate their insensitivity to hardware implementation issues, e.g., noise and PWM non-idealities. The simulation and experimental results demonstrate satisfactory performance of the designed controllers.

A Data-Driven Frequency-Domain Approach for Robust Controller Design via Convex Optimization

Achille Nicoletti

The objective of this dissertation is to develop data-driven frequency-domain methods for designing robust controllers through the use of convex optimization algorithms. Many of today's industrial processes are becoming more complex, and modeling accurate physical models for these plants using first principles may be impossible. With the increased developments in the computing world, large amounts of measured data can be easily collected and stored for processing purposes. Data can also be collected and used in an on-line fashion. Thus it would be very sensible to make full use of this data for controller design, performance evaluation, and stability analysis. The design methods imposed in this work ensure that the dynamics of a system are captured in an experiment and avoids the problem of unmodeled dynamics associated with parametric models. The devised methods consider robust designs for both linear-time-invariant (LTI) single-input-single-output (SISO) systems and certain classes of nonlinear systems. In this dissertation, a data-driven approach using the frequency response function of a system is proposed for designing robust controllers with H∞ performance. Necessary and sufficient conditions are derived for obtaining H∞ performance while guaranteeing the closed-loop stability of a system. A convex optimization algorithm is implemented to obtain the controller parameters which ensure system robustness; the controller is robust with respect to the frequency-dependent uncertainties of the frequency response function. For a certain class of nonlinearities, the proposed method can be used to obtain a best-linear-approximation with an associated frequency dependent uncertainty to guarantee the stability and performance for the underlying linear system that is subject to nonlinear distortions. The concepts behind these design methods are then used to devise necessary and sufficient conditions for ensuring the closed-loop stability of systems with sector-bounded nonlinearities. The conditions are simple convex feasibility constraints which can be used to stabilize systems with multi-model uncertainty. Additionally, a method is proposed for obtaining H∞ performance for an approximate model (i.e., describing function) of a sector-bounded nonlinearity. This work also proposes several data-driven methods for designing robust fixed-structure controllers with H∞ performance. One method considers the solution to a non-convex problem, while another method convexifies the problem and implements an iterative algorithm to obtain the local solution (which can also consider H2 performance). The effectiveness of the proposed method(s) is illustrated by considering several case studies that require robust controllers for achieving the desired performance. The main applicative work in this dissertation is with respect to a power converter control system at the European Organization for Nuclear Research (CERN) (which is used to control the current in a magnet to produce the desired field in controlling particle trajectories in accelerators). The proposed design methods are implemented in order to satisfy the challenging performance specifications set by the application while guaranteeing the system stability and robustness using data-driven design strategies.

EPFL2018

Contracts for Real-Time, Safety Critical Systems

Chandrakana Nandi

Verifying real-time systems goes beyond the verification of functional properties: it also requires the checking of real-time properties. This makes traditional contract-frameworks partially inept for checking real-time programs. This is a major problem because the failure of real-time and safety critical systems can have serious consequences. This thesis presents a solution to this problem by incorporating Design by Contract (annotating programs with function pre and post conditions) to such systems. The main contribution of this thesis is the development of a contract framework for cyclic real-time control applications written in C++. The contract framework allows the users to specify both functional and temporal properties for the applications. A novel approach of empirical cumulative distribution function (cdf ) based statistical inference is used for dynamically estimating temporal constraints and incorporating them in future contracts. The thesis also illustrates the use of Real-time Logic (RTL) for formal specification of the temporal properties. For evaluating our methodology, we have integrated it to a component-based framework called FASA (Future Automation System Architecture) developed at ABB Corporate Research for writing hard real time control applications. Experiments show that this contract framework can be smoothly integrated to existing control applications thereby increasing their reliability while having a acceptable overhead (less than 10%) on the performance.

2014

A Two-Time-Scale Control Scheme for Fast Systems

Dominique Bonvin, Davide Buccieri, Sébastien Gros, Philippe Müllhaupt

Model predictive control (MPC) is a very effective approach to control nonlinear systems, especially when the systems are high dimensional and/or constrained. MPC formulates the problem of input trajectory generation as an optimization problem. However, due to model mismatch and disturbances, frequent re-calculation of the trajectories is typically called for. This paper proposes a two-time-scale control scheme that uses less frequent repeated trajectory generation in a slow loop and time-varying linear feedback in a faster loop. Since the fast loop reduces considerably the effect of uncertainty, trajectory generation can be done much less frequently. The problem of trajectory generation can be treated using either optimization-based MPC or flatness-based system inversion. As proposed, the method cannot handle hard constraints. Both MPC and the two-time-scale control scheme are tested via the simulation of a flying robotic structure. It is seen that the MPC scheme is too slow to be considered for real-time implementation on a fast system. In contrast, the two-time-scale control scheme is fast, effective, and robust.

2007

A Data-Driven Frequency-Domain Approach for Robust Controller Design via Convex Optimization

Achille Nicoletti

EPFL2018