Verification of advanced controllers for safety-critical systems

In order to design and deploy a feedback controller in a real application, one must determine suitable specifications that the design must meet ("validate"), and then ensure that the chosen specifications have been met ("verify"). In this thesis, we investigate a verification paradigm based on formal methods, such as the Satisfiability Modulo Theories (SMT) and quantifier elimination (Weispfenning’s virtual term substitution and quantifier elimination by cylindrical algebraic decomposition) algorithms. Any control design requirement (such as satisfactory performance, robustness to uncertainties, stability, etc.) that can be expressed in a first order logic formula can be (in principle) verified by using one of these methods. Consequently, in principle, this allows us to consider problems like general non-convex optimisation, exact computation of structured singular value, and synthesis of non-convex feasible parameter sets. In practice, the generality of algorithms like quantifier elimination by cylindrical algebraic decomposition come with a downside of high running time when applied to more complex systems with more parameters. This, in some cases, limits the complexity of the system that we could consider. Therefore, we focused our attention on control problems such as obtaining an explicit MPC law for a linear time invariant system with a quadratic objective and polytopic constraints, or computation of the structured singular value for a system under parametric (and not norm-bounded) uncertainty. Such problems can be expressed as quantifier elimination problems with a particular quantification structure that allows us to take advantage of a specialised quantifier elimination algorithm - the quantifier elimination by Weispfenning’s virtual term substitution procedure that has much lower worst-case running time on these types of problems than quantifier elimination by cylindrical algebraic decomposition algorithm. Despite these constraints, we were able to apply a quantifier-elimination-based verification framework to clearance of a flight control law developed for a real world industrial system from the aerospace field not only at particular combination of parameters but throughout the whole flight envelope. In conclusion, while in principle formal methods are applicable to a large body of problems arising in control theory, more widespread practical application depends on further research in efficiency and running time improvement in the implementation of these algorithms.Full EC Project Title: Reconfiguration of control in flight for integral global upset recovery (RECONFIGURE) EC Project #: 314544 RG # & UFS Project Code: RG66745, NMZN/04

Robust Performance Analysis for Gust Loads Computation

In the design process of modern aircraft, a comprehensive analysis of worst case structural gust loads is imperative. Because this analysis requires to consider millions of cases, the examination is extremely time consuming. To solve this problem, a new approach based on robust performance analysis is introduced: the worst case energy-to-peak gain is used to efficiently determine worst case loads of nominal, uncertain, and linear parameter varying gust loads models

Recent Advances in Robust Control

Robust control has been a topic of active research in the last three decades culminating in H_2/H_\infty and \mu design methods followed by research on parametric robustness, initially motivated by Kharitonov's theorem, the extension to non-linear time delay systems, and other more recent methods. The two volumes of Recent Advances in Robust Control give a selective overview of recent theoretical developments and present selected application examples. The volumes comprise 39 contributions covering various theoretical aspects as well as different application areas. The first volume covers selected problems in the theory of robust control and its application to robotic and electromechanical systems. The second volume is dedicated to special topics in robust control and problem specific solutions. Recent Advances in Robust Control will be a valuable reference for those interested in the recent theoretical advances and for researchers working in the broad field of robotics and mechatronics

Cascaded Control for Improved Building HVAC Performance

As of 2011 buildings consumed 41% of all primary energy in the U.S. and can represent more than 70% of peak demand on the electrical grid. Usage by this sector has grown almost 50% since the 1980s and projections foresee an additional growth of 17% by 2035 due to increases in population, new home construction, and commercial development. Three-quarters of building energy is derived from fossil fuels making it a large contributor of the country’s CO2 and NOx output both of which greatly affect the environment and local air quality. Up to half of energy used by the building sector is related to Heating, Ventilation, and Air-Condition systems. Focusing on improving building HVAC control therefore has a large aggregate effect on US energy usage with economic and environmental benefits for end users. This dissertation develops cascaded loop architectures as a solution to common HVAC control issues. These systems display strong load-dependent nonlinearities and coupling behaviors that can lead to actuator hunting (sustained input oscillations) from standard PI controllers that waste energy and cost money. Cascaded loops offer a simple way to eliminate hunting and decouple complex HVAC systems with minimal a priori knowledge of system dynamics. As cascaded loops are easily implementable in building automation systems they can be readily and widely adopted in the field. An examination of the current state of PI control in HVAC and discussion of coordinated, optimal control strategies being developed for reduced energy usage are discussed in Chapter 1. The following two chapters outline the structure and benefits of the cascaded architecture and demonstrate the same using a series of simulation case studies. Implementation approaches and parameterizations of the architecture are explored in Chapter 4 with a derivation showing that the addition of an additional feedback path (i.e., inner loop control) provides more design freedom and ultimately allows for improved control. Finally, Chapter 5 details results from initial cascaded loop implementation at three campus buildings. Results showed improved control performance and an elimination of identified hunting behavior

Robust Control Design of Gain-scheduled Controllers for Nonlinear Processes

In the chemical or biochemical industry most processes are modeled by nonlinear equations. It is of a great significance to design high-performance nonlinear controllers for efficient control of these nonlinear processes to achieve closed-loop system's stability and high performance. However, there are many difficulties which hinder the design of such controllers due mainly to the process nonlinearity. In this work, comprehensive design procedures based on robust control have been proposed to efficiently deal with the design of gain-scheduled controllers for nonlinear systems. Since all the design procedures proposed in this work rely strongly on the process model, the first difficulty addressed in this thesis is the identification of a relatively simple model of the nonlinear processes under study. The nonlinearity of the processes makes it often difficult to obtain a first-principles model which can be used for analysis and design of the controller. As a result, relatively simple empirical models, Volterra series model and state-affine model, are chosen in this work to represent the nonlinear process for the design of controllers. The second major difficulty is that although the nonlinear models used in this thesis are easy to identify, the analysis of stability and performance for such models using nonlinear control theory is not straightforward. Instead, it is proposed in this study to investigate the stability and performance using a robust control approach. In this approach, the nonlinear model is approximated by a nominal linear model combined with a mathematical description of model error to be referred to, in this work, as model uncertainty. In the current work it was assumed that the main source of uncertainty with respect to the nominal linear model is due to the system nonlinearity. Then, in this study, robust control theoretical tools have been especially developed and applied for the design of gain-scheduled Proportional-Integral (PI) control and gain-scheduled Model Predictive Control (MPC). Gain-scheduled controllers are chosen because for nonlinear processes operated over a wide range of operation, gain-scheduling has proven to be a successful control design technique (Bequette, 1997) for nonlinear processes. To guarantee the closed-loop system's robust stability and performance with the designed controllers, a systematic approach has been proposed for the design of robust gain-scheduled controllers for nonlinear processes. The design procedure is based on robust stability and performance conditions proposed in this work. For time-varying uncertain parameters, robust stability and performance conditions using fixed Lyapunov functions and parameter-dependent Lyapunov functions, were used. Then, comprehensive procedures for the design and optimization of robust gain-scheduled PI and MPC controllers tuning parameters based on the robust stability and performance tests are then proposed. Since the closed-loop system represented by the combination of a state-affine process model and the gain-scheduled controller is found to have an affine dependence on the uncertain parameters, robust stability and performance conditions can be tested by a finite number of Linear Matrix Inequalities (LMIs). Thus, the final problems are numerically solvable. One of the inherent problems with robust control is that the design is conservative. Two approaches have been proposed in this work to reduce the conservatism. The first one is based on parameter-dependent Lyapunov functions, and it is applied when the rate of change of the time-varying uncertainty parameters is a priori available. The second one is based on the relaxation of an input-saturation factor defined in the thesis to deal with the issue of actuator saturation. Finally, to illustrate the techniques discussed in the thesis, robust gain-scheduled PI and MPC controllers are designed for a continuous stirred tank reactor (CSTR) process. A simple MIMO example with two inputs and two outputs controlled by a multivariable gain-scheduled MPC controller is also discussed to illustrate the applicability of the methods to multivariable situations. All the designed controllers are simulated and the simulations show that the proposed design procedures are efficient in designing and comparing robust gain-scheduled controllers for nonlinear processes

Observer-based robust fault estimation for fault-tolerant control

A control system is fault-tolerant if it possesses the capability of optimizing the system stability and admissible performance subject to bounded faults, complexity and modeling uncertainty. Based on this definition this thesis is concerned with the theoretical developments of the combination of robust fault estimation (FE) and robust active fault tolerant control (AFTC) for systems with both faults and uncertainties.This thesis develops robust strategies for AFTC involving a joint problem of on-line robust FE and robust adaptive control. The disturbances and modeling uncertainty affect the FE and FTC performance. Hence, the proposed robust observer-based fault estimator schemes are combined with several control methods to achieve the desired system performance and robust active fault tolerance. The controller approaches involve concepts of output feedback control, adaptive control, robust observer-based state feedback control. A new robust FE method has been developed initially to take into account the joint effect of both fault and disturbance signals, thereby rejecting the disturbances and enhancing the accuracy of the fault estimation. This is then extended to encompass the robustness with respect to modeling uncertainty.As an extension to the robust FE and FTC scheme a further development is made for direct application to smooth non-linear systems via the use of linear parameter-varying systems (LPV) modeling.The main contributions of the research are thus:- The development of a robust observer-based FE method and integration design for the FE and AFTC systems with the bounded time derivative fault magnitudes, providing the solution based on linear matrix inequality (LMI) methodology. A stability proof for the integrated design of the robust FE within the FTC system.- An improvement is given to the proposed robust observer-based FE method and integrated design for FE and AFTC systems under the existence of different disturbance structures.- New guidance for the choice of learning rate of the robust FE algorithm.- Some improvement compared with the recent literature by considering the FTC problem in a more general way, for example by using LPV modeling