Anti-Windup Design for Internal Model Control

This paper considers linear control design for systems with input magnitude saturation. A general anti-windup scheme which optimizes nonlinear performance, applicable to MIMO systems, is developed. Several examples, including an ill-conditioned plant, show that the scheme provides graceful degradation of performance. The attractive features of this scheme are its simplicity and effectiveness

A Unified Framework for the Study of Anti-Windup Designs

We present a unified framework for the study of linear time-invariant (LTI) systems subject to control input nonlinearities. The framework is based on the following two-step design paradigm: "Design the linear controller ignoring control input nonlinearities and then add anti-windup bumpless transfer (AWBT) compensation to minimize the adverse eflects of any control input nonlinearities on closed loop performance". The resulting AWBT compensation is applicable to multivariable controllers of arbitrary structure and order. All known LTI anti-windup and/or bumpless transfer compensation schemes are shown to be special cases of this framework. It is shown how this framework can handle standard issues such as the analysis of stability and performance with or without uncertainties in the plant model. The actual analysis of stability and performance, and robustness issues are problems in their own right and hence not detailed here. The main result is the unification of existing schemes for AWBT compensation under a general framework

Performance analysis of switching systems

Performance analysis is an important aspect in the design of dynamic (control) systems. Without a proper analysis of the behavior of a system, it is impossible to guarantee that a certain design satisfies the system’s requirements. For linear time-invariant systems, accurate performance analyses are relatively easy to make and as a result also many linear (controller) design methods have appeared in the past. For nonlinear systems, on the other hand, such accurate performance analyses and controller design methods are in general not available. A main reason hereof is that nonlinear systems, as opposed to linear time-invariant systems, can have multiple steady-state solutions. Due to the coexistence of multiple steady-state solutions, it is much harder to define an accurate performance index. Some nonlinear systems, i.e. the so-called convergent nonlinear systems, however, are characterized by a unique steady-state solution. This steady-state solution may depend on the system’s input signals (e.g. reference signals), but is independent of the initial conditions of the system. In the past, the notion of convergent systems has already been proven to be very useful in the performance analysis of nonlinear systems with inputs. In this thesis, new results in the field of performance analysis of nonlinear systems with inputs are presented, based on the notion of convergent systems. One part of the thesis is concerned with the question "how to analyse the performance for a convergent system?" Since the behavior of a convergent system is independent of the initial conditions (after some transient time), simulation can be used to find the unique steady-state solution that corresponds to a certain input signal, but this can be very time-consuming. In this thesis, a computationally more efficient approach is presented to estimate the steady-state performance of harmonically forced Lur’e systems, in terms of nonlinear frequency response functions (nFRFs). This approach is based on the method of harmonic linearization. It provides both a linear approximation of the nFRF and an upper bound on the error between this linear approximation and the true nFRF. It is shown in several examples that the approximation of the nFRF is accurate, and that it provides more detailed information on the considered system than the often used ‘L2 gain’ performance index. An additional observation that is made, is that the method of harmonic linearization can sometimes be ‘misleading’ for Lur’e systems with a saturation-like nonlinearity: for the case that the harmonic balance equation has a unique solution, it is shown that the corresponding nonlinear system can have multiple distinct steady-state solutions. Another part of the thesis is concerned with the question "under what conditions is a system with inputs guaranteed to be convergent?" In particular two types of systems were investigated: switched linear systems and Lur’e systems with a saturation nonlinearity and marginally stable linear part. For the switched linear systems, it is assumed that the dynamics of all the separate linear modes are given. For this setting, it was investigated if it is possible to find a switching rule (which defines when to switch between the available modes) such that the closed-loop system is convergent. Both a state-based, an observer-based, and a time-based switching rule are presented that guarantee a convergent system, assuming some conditions on the linear dynamics are met. The second type of systems that are discussed, are Lur’e systems with a saturation nonlinearity and marginally stable linear part. For this type of systems, the goal was to find sufficient conditions under which the closed-loop system is convergent. Because of the marginally stable linear part, however, a quadratically convergent system cannot be obtained. Instead, sufficient conditions are discussed that guarantee uniform convergency of the system. The obtained theory is shown to be also applicable to a class of anti-windup systems with a marginally stable plant. For this class of systems, the results of the convergency-based performance analysis are compared with the analysis results of existing anti-windup methods. It is shown that the convergency-based performance analysis can in some cases provide more detailed information on the steady-state behavior of the system. The results of uniform convergency for anti-windup systems are shown to be also applicable in the field of production and inventory control of discrete-event manufacturing systems. Since a manufacturing machine has a certain production capacity and cannot produce at a negative rate, it can be seen as an integrator plant (input: production rate, output: amount of finished products) preceded by a saturation function. For this marginally stable plant, a controller was constructed in such a way that the closed-loop system is uniformly convergent. The controller was also implemented in the discrete-event domain and the results from discrete-event simulations were compared with those of continuous-time simulations. Similarly, the controller was also applied for the production and inventory control of a line of four manufacturing machines. For both the single machine and the line of four machines, the resulting controlled discrete-event systems are shown to have the desired tracking properties. Besides these theoretical and numerical results, also experimental results are presented in this thesis. By means of an electromechanical construction, several experimental results were obtained, and used to validate the theoretical results for both the switched linear systems and the anti-windup systems

Robust Region-of-Attraction Estimation

We propose a method to compute invariant subsets of the region-of-attraction for asymptotically stable equilibrium points of polynomial dynamical systems with bounded parametric uncertainty. Parameter-independent Lyapunov functions are used to characterize invariant subsets of the robust region-of-attraction. A branch-and-bound type refinement procedure reduces the conservatism. We demonstrate the method on an example from the literature and uncertain controlled short-period aircraft dynamics

Stability and Performance Analysis of Systems Under Constraints

All real world control systems must deal with actuator and state constraints. Standard conic sector bounded nonlinearity stability theory provides methods for analyzing the stability and performance of systems under constraints, but it is well-known that these conditions can be very conservative. A method is developed to reduce conservatism in the analysis of constraints by representing them as nonlinear real parametric uncertainty

Hysteresis-based design of dynamic reference trajectories to avoid saturation in controlled wind turbines

The main objective of this paper is to design a dynamic reference trajectory based on hysteresis to avoid saturation in controlled wind turbines. Basically, the torque controller and pitch controller set-points are hysteretically manipulated to avoid saturation and drive the system with smooth dynamic changes. Simulation results obtained from a 5MW wind turbine benchmark model show that our proposed strategy has a clear added value with respect to the baseline controller (a well-known and accepted industrial wind turbine controller). Moreover, the proposed strategy has been tested in healthy conditions but also in the presence of a realistic fault where the baseline controller caused saturation to nally conduct to instability.Peer ReviewedPostprint (author's final draft

Process operating mode monitoring : switching online the right controller

This paper presents a structure which deals with process operating mode monitoring and allows the control law reconfiguration by switching online the right controller. After a short review of the advances in switching based control systems during the last decade, we introduce our approach based on the definition of operating modes of a plant. The control reconfiguration strategy is achieved by online selection of an adequate controller, in a case of active accommodation. The main contribution lies in settling up the design steps of the multicontroller structure and its accurate integration in the operating mode detection and accommodation loop. Simulation results show the effectiveness of the operating mode detection and accommodation (OMDA) structure for which the design steps propose a method to study the asymptotic stability, switching performances improvement, and the tuning of the multimodel based detector