Application of Lyapunov matrix inequality based unsymmetrical saturated control to a multi-vectored propeller airship

The problem of the design of a controller for a multi-vectored propeller airship is addressed. The controller includes anti-windup that takes into account unsymmetrical actuator constraints. First, a linear transformation is applied to transform the unsymmetrical constraints into symmetric constraints with an amplitude-bounded exogenous disturbance. Then, a stability condition based on a quadratic Lyapunov function for the saturated closed-loop system is proposed. The condition considers both amplitude-bounded and energy-bounded exogenous disturbances. Thus, the controller design problem is transformed into a convex optimization problem expressed in a bilinear matrix inequality form. Two controller design methods were applied: one-step controller and traditional anti-windup controller. The one-step method obtains the controller and the anti-windup compensator in one step while the anti-windup controller method separates this process into the linear controller design and the compensator design. Simulation results showed that both controllers enlarge the stability zone of the saturation system and have good tracking performance. It is shown that the anti-windup controller design method not only has a larger region of stability, but the demanded actuator output exceeds the constraints less and has a smaller anti-windup coefficient matrix compared to the one-step method

Application of Lyapunov matrix inequality based unsymmetrical saturated control to a multi-vectored propeller airship

The problem of the design of a controller for a multi-vectored propeller airship is addressed. The controller includes anti-windup that takes into account unsymmetrical actuator constraints. First, a linear transformation is applied to transform the unsymmetrical constraints into symmetric constraints with an amplitude-bounded exogenous disturbance. Then, a stability condition based on a quadratic Lyapunov function for the saturated closed-loop system is proposed. The condition considers both amplitude-bounded and energy-bounded exogenous disturbances. Thus, the controller design problem is transformed into a convex optimization problem expressed in a bilinear matrix inequality form. Two controller design methods were applied: one-step controller and traditional anti-windup controller. The one-step method obtains the controller and the anti-windup compensator in one step while the anti-windup controller method separates this process into the linear controller design and the compensator design. Simulation results showed that both controllers enlarge the stability zone of the saturation system and have good tracking performance. It is shown that the anti-windup controller design method not only has a larger region of stability, but the demanded actuator output exceeds the constraints less and has a smaller anti-windup coefficient matrix compared to the one-step method

Digital repetitive control under varying frequency conditions

Premi extraordinari doctorat curs 2011-2012, àmbit d’Enginyeria IndustrialThe tracking/rejection of periodic signals constitutes a wide field of research in the control theory and applications area and Repetitive Control has proven to be an efficient way to face this topic; however, in some applications the period of the signal to be tracked/rejected changes in time or is uncertain, which causes and important performance degradation in the standard repetitive controller. This thesis presents some contributions to the open topic of repetitive control working under varying frequency conditions. These contributions can be organized as follows: One approach that overcomes the problem of working under time varying frequency conditions is the adaptation of the controller sampling period, nevertheless, the system framework changes from Linear Time Invariant to Linear Time-Varying and the closed-loop stability can be compromised. This work presents two different methodologies aimed at analysing the system stability under these conditions. The first one uses a Linear Matrix Inequality (LMI) gridding approach which provides necessary conditions to accomplish a sufficient condition for the closed-loop Bounded Input Bounded Output stability of the system. The second one applies robust control techniques in order to analyse the stability and yields sufficient stability conditions. Both methodologies yield a frequency variation interval for which the system stability can be assured. Although several approaches exist for the stability analysis of general time-varying sampling period controllers few of them allow an integrated controller design which assures closed-loop stability under such conditions. In this thesis two design methodologies are presented, which assure stability of the repetitive control system working under varying sampling period for a given frequency variation interval: a mu-synthesis technique and a pre-compensation strategy. On a second branch, High Order Repetitive Control (HORC) is mainly used to improve the repetitive control performance robustness under disturbance/reference signals with varying or uncertain frequency. Unlike standard repetitive control, the HORC involves a weighted sum of several signal periods. With a proper selection of the associated weights, this high order function offers a characteristic frequency response in which the high gain peaks located at harmonic frequencies are extended to a wider region around the harmonics. Furthermore, the use of an odd-harmonic internal model will make the system more appropriate for applications where signals have only odd-harmonic components, as in power electronics systems. Thus an Odd-harmonic High Order Repetitive Controller suitable for applications involving odd-harmonic type signals with varying/uncertain frequency is presented. The open loop stability of internal models used in HORC and the one presented here is analysed. Additionally, as a consequence of this analysis, an Anti-Windup (AW) scheme for repetitive control is proposed. This AW proposal is based on the idea of having a small steady state tracking error and fast recovery once the system goes out of saturation. The experimental validation of these proposals has been performed in two different applications: the Roto-magnet plant and the active power filter application. The Roto-magnet plant is an experimental didactic plant used as a tool for analysing and understanding the nature of the periodic disturbances, as well as to study the different control techniques used to tackle this problem. This plant has been adopted as experimental test bench for rotational machines. On the other hand, shunt active power filters have been widely used as a way to overcome power quality problems caused by nonlinear and reactive loads. These power electronics devices are designed with the goal of obtaining a power factor close to 1 and achieving current harmonics and reactive power compensation.Award-winningPostprint (published version

Design of state-feedback controllers for linear parameter varying systems subject to time-varying input saturation

All real-world systems are affected by the saturation phenomenon due to inherent physical limitations of actuators. These limitations should be taken into account in the controller’s design to prevent a possibly severe deterioration of the system’s performance, and may even lead to instability of the closed-loop system. Contrarily to most of the control strategies, which assume that the saturation limits are constant in time, this paper considers the problem of designing a state-feedback controller for a system affected by time-varying saturation limits with the objective to improve the performance. In order to tie variations of the saturation function to changes in the performance of the closed-loop system, the shifting paradigm is used, that is, some parameters scheduled by the time-varying saturations are introduced to schedule the performance criterion, which is considered to be the instantaneous guaranteed decay rate. The design conditions are obtained within the framework of linear parameter varying (LPV) systems using quadratic Lyapunov functions with constant Lyapunov matrices and they consist in a linear matrix inequality (LMI)-based feasibility problem, which can be solved efficiently using available solvers. Simulation results obtained using an illustrative example demonstrate the validity and the main characteristics of the proposed approach.Peer ReviewedPostprint (published version

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

Continuous-time anti-windup generalized predictive control of non-minimum phase processes with input constraints

This paper deals with a design problem of a continuous-time anti-windup generalized predictive control system using coprime factorization approach for non-minimum phase processes with input constraints. Based on the proposed design scheme, a condition for stability of the closed-loop system with input constraints and a straightforward method to improve the output response of the system with input constraints are given. Simulation results are presented to support the theoretical analysis.</p

Nonlinear constrained and saturated control of power electronics and electromechanical systems

Power electronic converters are extensively adopted for the solution of timely issues, such as power quality improvement in industrial plants, energy management in hybrid electrical systems, and control of electrical generators for renewables. Beside nonlinearity, this systems are typically characterized by hard constraints on the control inputs, and sometimes the state variables. In this respect, control laws able to handle input saturation are crucial to formally characterize the systems stability and performance properties. From a practical viewpoint, a proper saturation management allows to extend the systems transient and steady-state operating ranges, improving their reliability and availability. The main topic of this thesis concern saturated control methodologies, based on modern approaches, applied to power electronics and electromechanical systems. The pursued objective is to provide formal results under any saturation scenario, overcoming the drawbacks of the classic solution commonly applied to cope with saturation of power converters, and enhancing performance. For this purpose two main approaches are exploited and extended to deal with power electronic applications: modern anti-windup strategies, providing formal results and systematic design rules for the anti-windup compensator, devoted to handle control saturation, and “one step” saturated feedback design techniques, relying on a suitable characterization of the saturation nonlinearity and less conservative extensions of standard absolute stability theory results. The first part of the thesis is devoted to present and develop a novel general anti-windup scheme, which is then specifically applied to a class of power converters adopted for power quality enhancement in industrial plants. In the second part a polytopic differential inclusion representation of saturation nonlinearity is presented and extended to deal with a class of multiple input power converters, used to manage hybrid electrical energy sources. The third part regards adaptive observers design for robust estimation of the parameters required for high performance control of power systems

Advanced Anti-Windup Techniques for the Limitation of the Effects of the Actuator Saturation

In this thesis an industrial issue is analysed. The issue consist on the undesirable effect of actuator sturation. Two approaches are given to solve the issue: an accurate inertia identification algorithm based on the DFT coefficient; and advanced anti-windup compensators. The principle of the modern anti-windup (DLAW and MRAW, LMI-based design approach), and a systematic design design procedure for the observer-based anti-windup are given. Simulation and test results are also given.ope

An almost Anti-Windup scheme for plants with magnitude, rate and curvature saturation

peer reviewedWe address the anti-windup augmentation problem for plants with saturations on the magnitude, rate and curvature of the control input. To this aim, given an unconstrained closed-loop, we generate a slightly modified strictly proper controller for which the derivatives of the control signal are available and we solve the anti-windup problem for this modified control scheme (namely, an almost anti-windup for the original closed-loop). Based on this “almost” approach, we revisit an existing Model Recovery anti-windup solution for rate and magnitude saturated plants and then we extend the results to the case of rate, magnitude and curvature saturation, by providing a Model Recovery solution to this additional problem. An example illustrates the peculiarities and the effectiveness of the proposed solutions