This paper deals with the problem of control of partially known nonlinear systems, which have an open-loop stable equilibrium, but we would like to add a PI controller to regulate its behavior around another operating point. Our main contribution is the identification of a class of systems for which a globally stable PI can be designed knowing only the systems input matrix and measuring only the actuated coordinates. The construction of the PI is done invoking passivity theory. The difficulties encountered in the design of adaptive PI controllers with the existing theoretical tools are also discussed. As an illustration of the theory, we consider port--Hamiltonian systems and a class of thermal processes.
In this paper, we propose a novel four-stage distributed controller for a DC microgrid that achieves power sharing and average voltage regulation for the voltages at actuated and unactuated buses. The controller is presented for a DC microgrid comprising multiple distributed generating units (DGUs) with time-varying actuation states; dynamic RLC lines; nonlinear constant impedance, current and power (ZIP) loads and a time-varying network topology. The controller comprising a nonlinear gain, PI controllers, and two dynamic distributed averaging stages is designed for asymptotic stability. This …
In this paper we present new (stochastic) passivity properties for Direct Current (DC) power networks, where the unknown and unpredictable load demand is modelled by a stochastic process. More precisely, the considered power network consists of distributed generation units supplying ZIP loads, i.e., nonlinear loads comprised of impedance (Z), current (I) and power (P) components. Differently from the majority of the results in the literature, where each of these components is assumed to be constant, we consider time-varying loads whose dynamics are described by a class of stochastic differenti…
Rapid developments in power distribution systems and renewable energy have widened the applications of dc--dc buck--boost converters in dc voltage regulation. Applications include vehicular power systems, renewable energy sources that generate power at a low voltage, and dc microgrids. It is noted that the cascade--connection of converters in these applications may cause instability due to the fact that converters acting as loads have a constant power load (CPL) behavior. In this paper, the output voltage regulation problem of a buck--boost converter feeding a CPL is addressed. The constructio…
In this work, we propose a new passivity-based sliding mode control method for mechanical port-Hamiltonian systems. Passivity-based sliding mode control (PBSMC) is unification of sliding mode control and passivity-based control. It achieves sliding mode control and Lyapunov stability simultaneously by employing an energy based Lyapunov function. The proposed method gives a family of stabilizing controllers which smoothly interpolates passivity-based control and sliding mode control with free parameters. The freedom is useful to adjust the trade-off between robustness against external disturban…
This paper presents a new passivity property for distributed piezoelectric devices with integrable port-variables. We present two new control methodologies by exploiting the integrability property of the port-variables. The derived controllers have a Proportional-Integral (PI) like structure. Finally, we present the simulation results and in-depth analysis on the tuning gains explaining their transient and steady-state behaviors.
This paper presents a method for developing single and multi-port frequency dependent network equivalent (FDNE) based on a passivity enforced online recursive least squares identification algorithm, which identifies the input admittance matrix in z-domain. Furthermore, with the proposed architecture, a real-time hybrid model of the reduced power system is developed that integrate transient stability analysis and FDNE. Main advantages of the proposed architecture are, it identifies the FDNE even with unknown network parameters in the frequency range of interest, and yet can be implemented direc…
In this paper we propose a PI passivity-based controller, applicable to a large class of switched power converters, that ensures global state regulation to a desired equilibrium point. A solution to this problem was reported in \cite{HERetal} but it requires full state-feedback, which makes it practically unfeasible. To overcome this limitation we construct a state observer that is implementable with measurements that are available in practical applications. The observer reconstructs the state in finite-time, ensuring global convergence of the PI. The excitation requirement for the observer is…
Flow and storage volume regulation is essential for the adequate transport and management of energy resources in district heating systems. In this letter, we propose a novel and suitably tailored -- decentralized -- adaptive control scheme addressing this problem whilst offering closed-loop stability guarantees. We focus on a system configuration comprising multiple heat producers, consumers and storage tanks exchanging energy through a common distribution network, which are features of modern and prospective district heating installations. {\color{black}The proposed controller is based on pas…
Series Elastic Actuation (SEA) is a widely-used approach for interaction control, as it enables high fidelity and robust force control, improving the safety of physical human-robot interaction (pHRI). Safety is an imperative design criterion for pHRI that limits the interaction performance since there exists a fundamental trade-off between stability robustness and rendering performance. The safety of interaction necessitates the closed-loop stability of a pHRI system when coupled to a wide range of unknown operators and environments. In this study, we provide the necessary and sufficient condi…
This paper provides a constructive passivity-based control approach to solve the set-point regulation problem for input-affine continuous nonlinear systems while considering saturation in the inputs. As customarily in passivity-based control, the methodology consists of two steps: energy shaping and damping injection. In terms of applicability, the proposed controllers have two advantages concerning other passivity-based control techniques: (i) the energy shaping is carried out without solving partial differential equations, and (ii) the damping injection is performed without measuring the pas…
In this paper we propose a new passivity-based control technique for DC power networks comprising the so-called ZIP-loads, i.e., nonlinear loads with the parallel combination of unknown constant impedance (Z), current (I) and power (P) components. More precisely, we propose a novel passifying input and a storage function based on the so-called mixed potential function introduced by Brayton and Moser, leading to a novel passivity property with output port-variable equal to the first time derivative of the voltage. Differently from the existing results in the literature, where restrictive (suffi…
Voltage and frequency control in an islanded AC microgrid (ImGs) amount to stabilizing an a priori unknown ImG equilibrium induced by loads and changes in topology. This paper puts forth a unified control framework which, while guaranteeing such stability, allows for modular ImGs interconnecting multiple subsystems, that is, dynamic RLC lines, nonlinear constant impedance, current, power (ZIP) and exponential (EXP) loads, and inverter-based distributed generation units (DGUs) controlled with different types of primary controllers. The underlying idea of the framework is based one equilibrium-i…
The design of an observer-based state feedback (OBSF) controller with guaranteed passivity properties for port-Hamiltonian systems (PHS) is addressed using linear matrix inequalities (LMIs). The observer gain is freely chosen and the LMIs conditions such that the state feedback is equivalent to control by interconnection with an input strictly passive (ISP) and/or an output strictly passive (OSP) and zero state detectable (ZSD) port-Hamiltonian controller are established. It is shown that the proposed controller exponentially stabilizes a class of infinite-dimensional PHS and asymptotically st…
Jan C. Willems Center for Systems and Control（扬·C·维勒姆斯系统与控制中心）；Engineering and Technology Institute Groningen (ENTEG)（格罗宁根工程与技术研究所（ENTEG））；Rijksuniversiteit Groningen（格罗宁根大学）
In this work we exploit the universal approximation property of Neural Networks (NNs) to design interconnection and damping assignment (IDA) passivity-based control (PBC) schemes for fully-actuated mechanical systems in the port-Hamiltonian (pH) framework. To that end, we transform the IDA-PBC method into a supervised learning problem that solves the partial differential matching equations, and fulfills equilibrium assignment and Lyapunov stability conditions. A main consequence of this, is that the output of the learning algorithm has a clear control-theoretic interpretation in terms of passi…
In this paper, we prove the exponential stability property of a class of mechanical systems represented in the port-Hamiltonian framework. To this end, we propose a Lyapunov candidate function different from the Hamiltonian of the system. Moreover, we study how the proposed analysis can be used to determine the exponential stability and the rate of convergence of some (nonlinear)-mechanical systems stabilized by two passivity-based control techniques, namely, PID passivity-based control and interconnection and damping assignment. We implement the former control approach to stabilize a three de…
Robust integral action of port-Hamiltonian systems
The University of Newcastle（纽卡斯尔大学）；University of Naples Federico II（那不勒斯费德里科二世大学）；Queensland University of Technology（昆士兰科技大学）；Laboratoire des Signaux et Systèmes, CNRS-SUPELEC（信号与系统实验室，法国国家科学研究中心-苏佩莱克）
Modeling, control, and stiffness regulation of layer jamming-based continuum robots
Department of Electrical Engineering, Polytechnique Montréal and GERAD（电气工程系，蒙特利尔理工学院及GERAD）；Robotics Institute, Faculty of Engineering and Information Technology, University of Technology Sydney（机器人研究所，工程与信息技术学院，技术学院悉尼大学）
The University of Tokyo（东京大学）；Korean Advanced Institute of Science and Technology (KAIST)（韩国高等科学技术研究院（KAIST））；University of Twente（特文特大学）
We introduce optimal energy shaping as an enhancement of classical passivity-based control methods. A promising feature of passivity theory, alongside stability, has traditionally been claimed to be intuitive performance tuning along the execution of a given task. However, a systematic approach to adjust performance within a passive control framework has yet to be developed, as each method relies on few and problem-specific practical insights. Here, we cast the classic energy-shaping control design process in an optimal control framework; once a task-dependent performance metric is defined, an…
In this work we present a constructive method to design a family of virtual contraction based controllers that solve the standard trajectory tracking problem of flexible-joint robots (FJRs) in the port-Hamiltonian (pH) framework. The proposed design method, called virtual contraction based control (v-CBC), combines the concepts of virtual control systems and contraction analysis. It is shown that under potential energy matching conditions, the closed-loop virtual system is contractive and exponential convergence to a predefined trajectory is guaranteed. Moreover, the closed-loop virtual system…
In this paper, we present a model-based frequency controller for microgrids with nonzero line resistances based on a port-Hamiltonian formulation of the microgrid model and real-time dynamic pricing. The controller is applicable for conventional generation with synchronous machines as well as for power electronics interfaced sources and it is robust against power fluctuations from uncontrollable loads or volatile regenerative sources. The price-based formulation allows additional requirements such as active power sharing to be met. The capability and effectiveness of our procedure is demonstra…
