A review of convex approaches for control, observation and safety of linear parameter varying and Takagi-Sugeno systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).Peer ReviewedPostprint (published version

Non-linear discrete-time observer design by sliding mode

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University, 09/02/2007.Research into observer design for non-linear discrete-time systems has produced many design methods. There is no general design method however and that provides the motivation to search for a new simple and realizable design method. In this thesis, an observer for non-linear discrete-time systems is designed using the sliding mode technique. The equation of the observer error is split into two parts; the first part being a linearized model of the system and the second part an uncertain vector. The sliding mode technique is introduced to eliminate the uncertainty caused by the uncertain vector in the observer error equation. By choosing the sliding surface and the boundary layer, the observer error is attracted to the sliding surface and stays within the sliding manifold. Therefore, the observer error converges to zero. The proposed technique is applied to two cases of observers for nonlinear discrete-time systems. The second case is chosen to be a particular practical system, namely the non-linear discrete-time ball and beam system. The simulations show that the sliding mode technique guarantees the convergence of the observer error for both systems

Advanced Control Strategies for Mobile Hydraulic Applications

Mobile hydraulic machines are affected by numerous undesired dynamics, mainly discontinuous motion and vibrations. Over the years, many methods have been developed to limit the extent of those undesired dynamics and improve controllability and safety of operation of the machine. However, in most of the cases, today\u27s methods do not significantly differ from those developed in a time when electronic controllers were slower and less reliable than they are today. This dissertation addresses this aspect and presents a unique control method designed to be applicable to all mobile hydraulic machines controlled by proportional directional valves. In particular, the proposed control method is targeted to hydraulic machines such as those used in the field including construction (wheel loaders, excavators, and backhoes, etc.), load handling (cranes, reach-stackers, and aerial lift, etc.), agriculture (harvesters, etc.), forestry, and aerospace. For these applications the proposed control method is designed to achieve the following goals: A. Improvement of the machine dynamics by reducing mechanical vibrations of mechanical arms, load, as well as operator seat; B. Reduction of the energy dissipation introduced by current vibration damping methods; C. Reduction of system slowdowns introduced by current vibration damping methods. Goal A is generally intended for all machines; goal B refers to those applications in which the damping is introduced by means of energy losses on the main hydraulic transmission line; goal C is related to those applications in which the vibration attenuation is introduced by slowing down the main transmission line dynamics. Two case studies are discussed in this work: 1. Hydraulic crane: the focus is on the vibrations of the mechanical arms and load (goals A and B). 2. Wheel loader: the focus is on the vibrations of the driver\u27s seat and bucket (goals A and C). The controller structure is basically unvaried for different machines. However, what differs in each application are the controller parameters, whose adaptation and tuning method represent the main innovations of this work. The proposed controller structure is organized so that the control parameters are adapted with respect to the instantaneous operating point which is identified by means of feedback sensors. The Gain Scheduling technique is used to implement the controller whose set of parameters are function of the specific identified operating point. The optimal set of control parameters for each operating point is determined through the non-model-based controller tuning. The technique determines the optimal set of controller parameters through the optimization of the experimental machine dynamics. The optimization is based on an innovative application of the Extremum Seeking algorithm. The optimal controller parameters are then indexed into the Gain Scheduler. The proposed method does not require the modification of the standard valve controlled machine layout since it only needs for the addition of feedback sensors. The feedback signals are used by the control unit to modify the electric currents to the proportional directional valves and cancel the undesired dynamics of the machine by controlling the actuator motion. In order for the proposed method to be effective, the proportional valve bandwidth must be significantly higher than the frequency of the undesired dynamics. This condition, which is typically true for heavy machineries, is further investigated in the research. The research mostly focuses on the use of pressure feedback. In fact, although the use of position, velocity, or acceleration sensors on the vibrating bodies of the machine would provide a more straightforward measurement of the vibration, they are extremely rare on mobile hydraulic machines where mechanical and environmental stress harm their integrity. A comparison between pressure feedback and acceleration feedback alternatives of the proposed method is investigated with the aim to outline the conditions making one alternative preferable over the other one (for those applications were both alternatives are technically viable in terms of sensors and wiring reliability). A mid-sized hydraulic crane (case study 1) was instrumented at Maha Fluid Power Research Center to study the effectiveness of the proposed control method, its stability and its experimental validation. Up to 30% vibration damping and 40% energy savings were observed for a specific cycle over the standard vibration damping method for this application. The proposed control method was also applied to a wheel loader (case study 2), and up to 70% vibrations attenuation on the bucket and 30% on the driver\u27s cab were found in simulations. These results also served to demonstrate the applicability of the control method to different hydraulic machines. Improved system response and a straightforward controller parameters tuning methodology are the features which give to the proposed method the potential to become a widespread technology for fluid power machines. The proposed method also has potential for improving several current vibration damping methods in terms of energy efficiency as well as simplification of both the hydraulic system layout and tuning process

Entwurf eines Beobachterbasierten Robusten Nichtlinearen Reglers

Due to observers ability in the estimation of internal system states, observers play an important role in the field of control and monitoring of dynamical systems. In reality, using sensors to measure the desired system states may be costly and/or affects the reliability of technical systems. Besides, some signals are impractical or inaccessible to be measured and using of sensors leads to significant errors such as stochastic noise. The solution of using observers is well-known since 1964. Besides the estimation of system states, some observers are able to estimate unknown inputs affecting the system dynamics such as disturbance forces or torques. These features are helpful for supervision and fault diagnosis tasks by monitoring the sensors and system components or for advanced control purposes by realizing observer-based control for practical systems. Among the state and disturbance observers, Proportional-Integral-Observer (PIO) is highly appreciated because of its simple structure and design procedure. Furthermore, using sufficiently high gain PIO, a robust estimation of system states and unknown inputs can be achieved. Besides taking the advantages of high gain design, the disadvantages of large overshoot and strong influence from measurement noise (as typical drawbacks of high gain utilization) in the control and estimation performance can not be neglected. Recently, some researches have been done to overcome the disadvantages of high gain observers and to adaptively adjust the gain of observer based on the resulting actual performance. Considering the advantages and disadvantages of high gain PIO besides the recent developments, it is evident that there are still open problems and questions to be solved in the area of optimal design of PIO and robust nonlinear control approaches based on PIO. On the other hand, the PI-Observer can be used in combination with linear/nonlinear control approaches (due to its simple structure and capability to estimate the system states and disturbances) to improve the performance and robustness of the closed-loop control results. Therefore, this thesis focuses on development and improvement of high gain Proportional-Integral-Observer as well as utilization of this observer in combination with well-known robust control approaches for possible general application in nonlinear systems. The Modified Advanced PIO (MAPIO) is introduced in this work as the extended version of Advanced PIO (APIO) to tune the gain of PIO according to the current situation. A cost function is defined so that the estimation performance and the related energy can be evaluated. Comparison between advanced observer design approaches has been done in the task of reconstructing the nonlinear characteristics and estimating the external inputs (contact forces) acting to elastic mechanical structures. Simulation results in open-loop and closed-loop cases verified that the performance of MAPIO in the task of unknown input estimation is more robust to different levels of measurement noise in comparison to previous methods e.g. APIO and standard high/low gain PIO. Furthermore, a new gain design approach of Proportional-Integral-Observer is proposed to overcome the disadvantages of high gain PIO and to realize the estimation of fast dynamical behaviors like unknown impact force. The dynamics of this force input is assumed as unknown. The idea of funnel control is taking into consideration to design the PIO gain. The important advantage of the proposed approach compared to previously published PIO gain design is the self-adjustment of observer gains according to the actual estimation situation inside the predefined funnel area. In this thesis it is shown that the proposed funnel PI-Observer algorithm allows adaptive PIO gain calculation, being able to be situatively adjusted even in the presence of measurement noise. Stability proof of funnel PI-Observer is investigated according to the switching observer condition and Lyapunov theory. The effectiveness of the proposed method is evaluated by simulation and experimental results using an elastic beam test rig. Furthermore, a nonlinear MIMO mechanical system is used to verify the effectiveness of the proposed method in the closed-loop context. Additionally, this thesis provides two new PI-Observer-based robust controllers as PIO-based sliding mode control and PIO-based backstepping control to improve the position tracking performance of a hydraulic differential cylinder system in the presence of uncertainties e.g. modeling errors, disturbances, and measurement noise. To use the linear PIO for estimation of system states and unknown inputs, the input-output feedback linearization approach is used to linearize the nonlinear model of hydraulic differential cylinder system. Thereupon the result of state and unknown input estimation is integrated into the structure of robust control design (here SMC and backstepping control) to eliminate the effects of uncertainties and disturbances. The introduced PIO-based robust controllers guarantee the ultimate boundness of the tracking error in the presence of uncertainties. The closed-loop stability is proved using Lyapunov theory in both cases. The proposed methods are experimentally validated and the results are compared with the standard SMC and industrial standard approach P-Controller in the presence of measurement noise, model uncertainties, and external disturbances. A general comparison of SMC and backstepping control approaches is provided in the last part of this work.Die Regelung und Überwachung dynamischer Systeme kann voraussetzen, dass Informationen über interne Systemzustände bekannt sind. Die Verwendung von Sensoren zur Erfassung aller Systemzustände kann erhöhte Kosten zur Folge haben und die Systemzuverlässigkeit negativ beeinflussen. Weitere Probleme ergeben sich dadurch, dass ggf. nicht jeder Systemzustand sensorisch erfasst werden kann. Der Beobachter erlaubt die Rekonstruktion aller Systemzustände auf Grundlage weniger Messungen. Neben Systemzuständen können externe Eingangsgrößen wie Reibmomente und Störungen geschätzt werden. Als Konsequenz ermöglicht der Beobachter eine gegenüber Störungen robuste Regelung und Fehlerdiagnose technischer Systeme. Der Proportional-Integral-Observer (PIO) kann mittels bestehender Entwurfsverfahren einfach implementiert werden. Durch Anpassen der Rückkopplungsmatrix eignet sich der PIO zur kombinierten Schätzung von Zuständen und unbekannten Eingangsgrößen. In diesem Zusammenhang spielt die Wahl einer betragsmäßig großen Rückkopplungsverstärkungsmatrix, als sogenannter High Gain Ansatz, eine entscheidende Rolle. Weiterhin hängt die Performance des PIO von der unbekannten Charakteristik der zu schätzenden Eingangsgröße ab. Diese Arbeit befasst sich mit der Entwicklung optimierter Entwurfsverfahren für den Proportional-Integral-Observer und der Entwicklung und Anwendung beobachterbasierter Konzepte zur robusten Regelung nichtlinearer Systeme. In dieser Arbeit wird der modifizierte Advanced PIO (MAPIO) als erweiterte Version des Advanced PIO (APIO) eingeführt. Der Schätzfehler von MAPIO wird über ein Gütefunktional abgebildet. Das Gütefunktional wird durch Anpassung der Rückkopplungsverstärkungsmatrix an die Charakteristik der unbekannten Eingangsgröße minimiert. Die Performance der modifizierten Beobachterentwurfsansätze wird anhand eines praktischen Beispiels bewertet. Geschätzt wird eine unbekannte Kontaktkraft mit nichtlinearer Charakteristik, die auf ein mechanisches System wirkt. Anhand eines Simulationsbeispiels im offenen und geschlossenen Regelkreis wird die Performance von MAPIO gegenüber vorherigen Verfahren APIO und PIO verifiziert. Basierend auf der Idee des Funnel Reglers wird ein neuartiges Entwurfskonzept für den Proportional-Integral-Observer vorgestellt. Die Nachteile des PIO-Konzeptes mit hohem Verstärkungsfaktor können überwunden werden und Schätzungen schneller dynamischer Verhaltensweisen lassen sich realisieren. Der Vorteil der neuartigen Funnel PIO Methode ist, dass der Schätzfehler in einem definierten Bereich, der sogenannten Funnel-Area, verbleibt. In dieser Arbeit wird gezeigt, dass der vorgeschlagene Funnel PIO Algorithmus eine adaptive PIO Verstärkungsberechnung ermöglicht, die auch in Gegenwart von Messrauschen situativ eingestellt werden kann. Der Stabilitätsnachweis von Funnel PIO wird mittels der Lyapunov Theorie untersucht. Die Wirksamkeit der vorgeschlagenen Methode wird durch Simulation und experimentelle Ergebnisse validiert. Eine auf einen elastischen Balken wirkende äußere Kraft mit nichtlinearer Charakteristik wird geschätzt. Ein nichtlineares MIMO System wird verwendet, um die Wirksamkeit der vorgeschlagenen Methode im geschlossenen Regelkreis zu verifizieren. In dieser Arbeit werden zwei neue PI-Observer basierte robuste Regelungen (PIO-basierte Sliding Mode und PIO-basierte Backstepping Regelung) vorgestellt. Die Positionsregelung eines hydraulischen Differentialzylinders in Gegenwart von Modellunsicherheiten, Störungen und Messrauschen wird untersucht. Zur Anwendung der PIO-basierten Störgrößenschätzung wird eine Ein-/Ausgangs-Linearisierung des nichtlinearen Modells vorgenommen. Die Stabilität des geschlossenen Regelkreises wird in beiden Fällen mit der Lyapunov Theorie bewiesen. Die vorgeschlagenen Methoden werden experimentell validiert und die Ergebnisse werden mit dem Standard Sliding Mode Regler und einem P-Regler in Gegenwart von Messrauschen, Modellunsicherheiten und externen Störungen verglichen

Optimal control and robust estimation for ocean wave energy converters

This thesis deals with the optimal control of wave energy converters and some associated observer design problems. The first part of the thesis will investigate model predictive control of an ocean wave energy converter to maximize extracted power. A generic heaving converter that can have both linear dampers and active elements as a power take-off system is considered and an efficient optimal control algorithm is developed for use within a receding horizon control framework. The optimal control is also characterized analytically. A direct transcription of the optimal control problem is also considered as a general nonlinear program. A variation of the projected gradient optimization scheme is formulated and shown to be feasible and computationally inexpensive compared to a standard nonlinear program solver. Since the system model is bilinear and the cost function is not convex quadratic, the resulting optimization problem is shown not to be a quadratic program. Results are compared with other methods like optimal latching to demonstrate the improvement in absorbed power under irregular sea condition simulations. In the second part, robust estimation of the radiation forces and states inherent in the optimal control of wave energy converters is considered. Motivated by this, low order H∞ observer design for bilinear systems with input constraints is investigated and numerically tractable methods for design are developed. A bilinear Luenberger type observer is formulated and the resulting synthesis problem reformulated as that for a linear parameter varying system. A bilinear matrix inequality problem is then solved to find nominal and robust quadratically stable observers. The performance of these observers is compared with that of an extended Kalman filter. The robustness of the observers to parameter uncertainty and to variation in the radiation subsystem model order is also investigated. This thesis also explores the numerical integration of bilinear control systems with zero-order hold on the control inputs. Making use of exponential integrators, exact to high accuracy integration is proposed for such systems. New a priori bounds are derived on the computational complexity of integrating bilinear systems with a given error tolerance. Employing our new bounds on computational complexity, we propose a direct exponential integrator to solve bilinear ODEs via the solution of sparse linear systems of equations. Based on this, a novel sparse direct collocation of bilinear systems for optimal control is proposed. These integration schemes are also used within the indirect optimal control method discussed in the first part.Open Acces

Preview-based techniques for vehicle suspension control: a state-of-the-art review

Abstract Automotive suspension systems are key to ride comfort and handling performance enhancement. In the last decades semi-active and active suspension configurations have been the focus of intensive automotive engineering research, and have been implemented by the industry. The recent advances in road profile measurement and estimation systems make road-preview-based suspension control a viable solution for production vehicles. Despite the availability of a significant body of papers on the topic, the literature lacks a comprehensive and up-to-date survey on the variety of proposed techniques for suspension control with road preview, and the comparison of their effectiveness. To cover the gap, this literature review deals with the research conducted over the past decades on the topic of semi-active and active suspension controllers with road preview. The main formulations are reported for each control category, and the respective features are critically analysed, together with the most relevant performance indicators. The paper also discusses the effect of the road preview time on the resulting system performance, and identifies control development trends

Benelux meeting on systems and control, 23rd, March 17-19, 2004, Helvoirt, The Netherlands

Book of abstract

Aeronautical engineering: A continuing bibliography, supplement 122

This bibliography lists 303 reports, articles, and other documents introduced into the NASA scientific and technical information system in April 1980