Passivity Degradation In Discrete Control Implementations: An Approximate Bisimulation Approach

In this paper, we present some preliminary results for compositional analysis of heterogeneous systems containing both discrete state models and continuous systems using consistent notions of dissipativity and passivity. We study the following problem: given a physical plant model and a continuous feedback controller designed using traditional control techniques, how is the closed-loop passivity affected when the continuous controller is replaced by a discrete (i.e., symbolic) implementation within this framework? Specifically, we give quantitative results on performance degradation when the discrete control implementation is approximately bisimilar to the continuous controller, and based on them, we provide conditions that guarantee the boundedness property of the closed-loop system.Comment: This is an extended version of our IEEE CDC 2015 paper to appear in Japa

Networked control systems in the presence of scheduling protocols and communication delays

This paper develops the time-delay approach to Networked Control Systems (NCSs) in the presence of variable transmission delays, sampling intervals and communication constraints. The system sensor nodes are supposed to be distributed over a network. Due to communication constraints only one node output is transmitted through the communication channel at once. The scheduling of sensor information towards the controller is ruled by a weighted Try-Once-Discard (TOD) or by Round-Robin (RR) protocols. Differently from the existing results on NCSs in the presence of scheduling protocols (in the frameworks of hybrid and discrete-time systems), we allow the communication delays to be greater than the sampling intervals. A novel hybrid system model for the closed-loop system is presented that contains {\it time-varying delays in the continuous dynamics and in the reset conditions}. A new Lyapunov-Krasovskii method, which is based on discontinuous in time Lyapunov functionals is introduced for the stability analysis of the delayed hybrid systems. Polytopic type uncertainties in the system model can be easily included in the analysis. The efficiency of the time-delay approach is illustrated on the examples of uncertain cart-pendulum and of batch reactor

On Some Relations between Accretive, Positive, and Pseudocontractive Operators and Passivity Results in Hilbert Spaces and Nonlinear Dynamic Systems

This paper investigates some parallel relations between the operators (I-G) and G in Hilbert spaces in such a way that the pseudocontractivity, asymptotic pseudocontractivity, and asymptotic pseudocontractivity in the intermediate sense of one of them are equivalent to the accretivity, asymptotic accretivity, and asymptotic accretivity in the intermediate sense of the other operator. If the operators are self-adjoint then the obtained accretivity-type properties are also passivity-type properties. Such properties are very relevant in stability theory since they refer to global stability properties of passive feed-forward, in general, nonlinear, and time-varying controlled systems controlled via feedback by elements in a very general class of passive, in general, nonlinear, and time-varying controllers. These results allow the direct generalization of passivity results in controlled dynamic systems to wide classes of tandems of controlled systems and their controllers, described by G-operators, and their parallel interpretations as pseudocontractive properties of their counterpart (I-G)-operators. Some of the obtained results are also directly related to input-passivity, output-passivity, and hyperstability properties in controlled dynamic systems. Some illustrative examples are also given in the framework of dynamic systems described by extended square-integrable input and output signals.The author is very grateful to the Spanish Government and European Fund of Regional Development FEDER for Grant DPI2015-64766-R and to UPV/EHU for Grant PGC 17/33

New Results on Positive Realness in the Presence of Delayed Dynamics

Positive realness is a very important tool for the achievement of hyperstability and passivity of dynamic systems. This paper is devoted to extend some positive realness results of transfer functions in the presence of point-delayed delayed dynamics. Sufficiency-type conditions which guarantee the positive realness of delayed transfer functions under point delays are given. The value of the direct input-output interconnection gain is seen to be crucial in the performed analysis. The relevance of the results rely in the importance of the hyperstability property of closed-loop systems under non-linear and time-varying controller devices. In fact if the feed-forward controlled plant has a strictly positive real transfer function then the closed-loo system is asymptotically hyperstable , that is, globally asymptotically Lyapunov´s stable for any non-linear time-varying controller which belongs to a hyperstable class defined as that which satisfies a Popov´s type inequality

Phase synchronization of autonomous AC grid system with passivity-based control

This paper discusses a ring‐coupled buck‐type inverter system to harness energy from direct current (DC) sources of electricity. The DC‐DC buck converter circuit is modified with an H‐bridge to convert the DC input voltage to a usable alternating current (AC) output voltage. Passivity‐based control (PBC) with port‐controlled Hamiltonian modelling (PCHM) is a method where the system is controlled by considering not only the energy properties of the system but also the inherent physical structure. PBC is applied to achieve stabilization of the AC output voltage to a desired amplitude and frequency. Unsynchronized output voltages in terms of phase angle or frequency can cause detrimental effects on the system. Phase‐locked loop (PLL) is employed in the ring structure to maintain synchronization of the AC output voltage of all inverter units in the ring‐coupled system

Finite-time extended state observer and fractional-order sliding mode controller for impulsive hybrid port-Hamiltonian systems with input delay and actuators saturation: Application to ball-juggler robots

This paper addresses the robust control problem of mechanical systems with hybrid dynamics in port-Hamiltonian form. It is assumed that only the position states are measurable, and time-delay and saturation constraint affect the control signal. An extended state observer is designed after a coordinate transformation. The effect of the time delay in the control signal is neutralized by applying Pade ́ approximant and augmenting the system states. An assistant system with faster convergence is developed to handle actuators saturation. Fractional-order sliding mode controller acts as a centralized controller and compensates for the undesired effects of unknown external disturbance and parameter uncertainties using the observer estimation results. Stability analysis shows that the closed-loop system states, such as the observer tracking error, and the position/velocity tracking errors, are finite-time stable. Simulation studies on a two ball-playing juggler robot with three degrees of freedom validate the theoretical results’ effectiveness