Passivity-based Control Design Research Articles

Energy-balancing passivity-based control is equivalent to dissipation and output invariance

Passivity-based controllers (PBCs) achieve stabilization of nonlinear systems, rendering the closed-loop passive with a desired energy (storage) function. A natural question is, under which conditions is it possible to make this function equal to the difference between the plant and controller energies—when the controller is said to be energy-balancing. In this paper we prove that a necessary and sufficient condition for energy-balancing is that the open and the closed-loop systems have the same dissipation functions and passive outputs. A second contribution of our work is the identification of a new passive output for Port–Hamiltonian systems, which is invariant to the action of PBCs that modify only the energy function–so-called basic interconnection and damping assignment PBCs–proving that they are energy-balancing. To establish these results a new algebraic framework for analysis and design of PBCs, centered around the principles of output and dissipation invariance, is developed. Using this framework several PBC schemes reported in the literature are compared. Also, we present a systematic procedure to generate new passive outputs, this result is of interest on its own, since it allows to extend the applicability of PBC to systems that are non-minimum phase and/or have relative degree larger than one.

Frequency-domain passivity-based current controller design

Current controller design for three-phase voltage–source converters, by which a passive input admittance is ideally obtained, is considered. Two design alternatives, with and without voltage feedforward, respectively, are shown to give similar performance. It is demonstrated how additional parts can be added to the controller while preserving the passivity property. This is applied particularly to resonant parts. The design method is finally applied to converters with an LCL input filter, where it is shown in many cases to compare favourably with a scheme where an inner loop is added for improved damping of the LCL resonance.

Interconnection and Damping Assignment Passivity—Based Control of the Pendubot

In this paper, we apply the interconnection and damping assignment passivity—based control design technique to the underactuated mechanical system called pendubot . The proposed control system drives a class of pendubot systems to the upward configuration, starting from a neighborhood of this configuration. Simulation results show the performance of the proposed control system.

선형 시스템 수동화를 위한 병렬 앞먹임 보상기 설계방법 연구

A passivity-based dynamic output feedback controller design is considered for a finite collection of non-square linear systems. Design of a single controller for a set of plants i.e. simultaneous stabilization is an important issue in the area of robust control design. We first determine a squaring gain matrix and an additional dynamics that is connected to the systems in a feedforward way, then a static passivating control law is designed. Consequently, the actual feedback controller will be the static control law combined with the feedforward dynamics. A necessary and sufficient condition for the existence of the parallel feedforward compensator is given by the static output feedback formulation. In contrast to the previous result [1], a technical condition for constructing the parallel feedforward compensator is removed by proposing a new type of the parallel compensator.

Asymptotic stabilization of non-holonomic port-controlled hamiltonian systems

A novel method for asymptotic stabilization of a class of non-holonomic systems is presented. The method is based on the port-controlled Hamiltonian description of electro-mechanical systems. The general system is augmented with so-called kinematic inputs, thus representing a special class of mobile robots. The asymptotic stabilityguarantees are obtained by applying a passivity based control design, based on energy shaping and damping injection. The method has been successfully applied to a particular four wheel steered, four wheel driven robot.

Modelling, Identification, and Passivity-Based Robust Control of Piezo-actuated Flexible Beam

This paper presents modelling, system identification, simulation, and experimental results for passivity-based robust control of piezo-actuated flexible beam. The flexible beam configuration considered is a cantilever aluminum beam with a piezoelectric transducer used as the actuator and tip-accelerometer as the sensor. The actuator and sensor are non-collocated. The Lagrangian formulation is used to obtain mathematical model of the flexible link dynamics with piezo actuator. For control design purposes, a finite dimensional approximate model is derived using assumed modes approach. It is shown that the approximate model compares very well with the experimentally identified model. Since the system is inherently not passive, passification techniques are used to render the system robustly passive which enables the use of passivity-based feedback control design. The controller design is validated both in simulation as well as in experiments. The simulation and experimental results demonstrate the effectiveness of controller in suppressing the tip vibrations of the link. The controller design is shown to be robust to both parametric uncertainties and unmodeled dynamics.

Physical Damping in IDA-PBC Controlled Underactuated Mechanical Systems

Energy shaping and passivity-based control designs have proven to be effective in solving control problems for tinderactttated mechanical systems. In recent works, interconnection and damping assignment passivity-based control (IDA-PEC) has been successfully applied to open-loop conservative models, that is, with no physical damping (e.g. friction) present. In a number of cases, in particular when IDA-PBC control only involves potential energy shaping, the actual presence of physical damping will not compromise the achieved closed-loop stability. However, when IDA-PBC control also includes the shaping of the kinetic energy, closed-loop stability or even passivity for the model without physical damping may be lost if physical damping is present. This raises two fundamental questions. First, in which cases is the IDA-PBC controlled system designed on the basis of the undamped model still stable and passive when physical damping is present? Second, if this is not the case, when is it possible to redesign the IDA-PBC control law for the undamped systems such that stability and passivity are regained? This paper provides necessary and sufficient conditions for the existence of such a control redesign for a particular choice of the closed-loop energy function. Furthermore, if these conditions are satisfied then two methods for redesign arc presented, which can be chosen depending on the problem structure and the parameter uncertainties. Finally, even in the cases where the addition of physical damping does not hamper the stability properties of the IDA-PBC design based on the undamped model, we show that the aforementioned redesign is still useful in order to reduce the mathematical complexity in exponential and asymptotic stability analysis.

Robust broadband control of acoustic noise in ducts: a passivity-based approach

Control of acoustic systems is a challenging problem for several reasons. Some primary reasons include computational complexity resulting from very high-order models, nonminimum phase behavior introduced by finite dimensional approximations and transportation delays, uncertainties introduced by non-uniform boundary conditions, and acoustic interaction with the dynamics of the enclosure structure. Until recently, most active noise control techniques focused on feedforward cancellation. It is only in the last few years that attempts have been made to use feedback for active noise control. Work by Hu and co-workers is remarkable for its thoroughness in setting up the system model, the theoretical analysis, and providing experimental demonstrations. 1-3 The work by Bernstein and co-workers also provides a solid analysis and application of feedback control. 4 Other examples of feedback control approaches are direct-rate feedback 5 and pole placement. 6 Much work continues towards the design and analysis of feedback control methods for achieving broadband reduction which is also robust to uncertainties. Acoustic ducts have certain dynamic characteristics that make it difficult to design an active feedback controller. Firstly, the model has no natural roll-off at high frequencies and it is modally very rich. Also, the frequency response is characterized by resonant peaks which dominate the dynamics. In the presence of these characteristics, any uncertainty in the system model has a significant affect on closed-loop stability. Much of the design of feedback controllers for acoustic systems is based on models identified using experimental frequency response. Acoustic ducts in the form of heating, ventilation, air-conditioning, and exhaust ducts form a significant category of systems which need active noise control. An ability to derive analytical models for this class of systems will be most helpful in developing controllers for active noise control. A simple method using symbolic computation is presented in Ref. 7 to derive models for virtually any configuration of an acoustic duct. The analytically derived model for an acoustic duct is linear, time-invariant, and infinite-dimensional. For most control designs, however, a finite-dimensional approximation is needed. In this paper, a finite-dimensional approximation model is obtained using an assumed modes approach. A detailed discussion of the modelling and identification of acoustic ducts can be found in Ref. 7. The control design methodology used in this paper is based on passivity theory. An experimental validation of the passivity-based robust control design methodology based on the ideas given in Refs. 8-12 is presented. It is shown that controllers designed using passivity theory can achieve broadband reduction of noise. It is also shown that the controller design is not only robust to unmodelled dynamics (higher order modes) and modelling errors, but also to parametric variations. The experimental verification demonstrates the efficacy of the controller. To facilitate understanding of passivity-based control design as presented in later sections of this paper a brief review of passivity-based control is given next.

An energy-shaping approach to the design of excitation control of synchronous generators

In this paper we discuss the estimation of the domain of attraction of equilibria in power systems and propose a new passivity-based controller design methodology for excitation control of synchronous generators. The methodology goes beyond the widely popular damping injection ( L g V) schemes, to actually shape the total energy function via modification of the energy transfer between the mechanical and electrical components of the system. Applying the procedure it is shown that a, properly tuned, linear state feedback enlarges both the estimates and the actual domain of attraction, thus increasing critical clearing time for faults. This is illustrated in two case studies, including a benchmark comparison with the classical control scheme.

Passivity-Based Robust Control with Application to Benchmark Active Controls Technology Wing

A passivity-based robust control design methodology is presented. A brief review of the stability results is given for passive linear and nonlinear systems followed by four different passie cation methods for rendering nonpassive systems passive. The robust control methodology via robust passie cation is demonstrated by application to the Benchmark Active Controls Technology subsonic wing. The controller design is shown to provide robust stability and satisfactory performance.

From Adaptive PBC to PI Nested Control for STATCOM

Abstract This paper presents an application of the dissipativity-based approach for the dynamic control of reactive power compensators based on PWM Voltage Sourced Inverter (VSI), such as STATCOM's (Static Synchronous Compensators). To achieve ac current and dc voltage regulation, we propose a control law obtained following the passivity-based controller (PBC) design procedure known as nested-loop PBC . Moreover, adaptive laws are introduced to consider the uncertainties in some parameters and to avoid steady-state errors. We show that the nonlinear control law thus obtained can be interpreted as a nested connection of two proportional-integral algorithms. The inner PI control loop is devoted to the control of the current amplitude, and the outer PI loop regulates the output voltage in the capacitor of the STATCOM system. Simulation results are included to demonstrate the performance of the proposed controller.

Physical insights on passivity-based TORA control designs

Jankovic et al. (ibid., vol.4, p.292-7, 1996) developed a series of cascadeand passivity-based control designs for the control of a translational oscillation rotational actuation (TORA) benchmark example. Two of the passivity-based control designs have strong mechanical underpinnings. In this brief letter, valuable physical insight into the passivity-based control is demonstrated using a basic theory of vibration analysis.

TORA example: cascade- and passivity-based control designs

We consider the problem of feedback stabilization of translational oscillations by a rotational actuator (TORA) system. The main obstacle to controller design is nonlinear coupling from the rotational to the translational motion through a sinusoidal term. We present several controller designs based on the cascade and passivity paradigms.