Output Regulation of Stochastic Sampled-Data Systems with Post-processing Internal Model

This paper deals with the output regulation problem (ORP) of a linear time-invariant (LTI) system in the presence of sporadically sampled measurement streams with the inter-sampling intervals following a stochastic process. Under such sporadically available measurement streams, a regulator consisting of a hybrid observer, continuous-time post-processing internal model, and stabilizer are proposed, which resets with the arrival of new measurements. The resulting system exhibits a deterministic behavior except for the jumps that occur at random sampling times and therefore the overall closed-loop system can be categorized as a piecewise deterministic Markov process (PDMP). In existing works on ORPs with aperiodic sampling, the requirement of boundedness on inter-sampling intervals precludes extending the solution to the random sampling intervals with possibly unbounded support. Using the Lyapunov-like theorem for the stability analysis of stochastic systems, we offer sufficient conditions to ensure that the overall closed-loop system is mean exponentially stable (MES) and the objectives of the ORP are achieved under stochastic sampling of measurement streams. The resulting LMI conditions lead to a numerically tractable design of the hybrid regulator. Finally, with the help of an illustrative example, the effectiveness of the theoretical results are verified

Emulation-based semiglobal output regulation of minimum phase nonlinear systems with sampled measurements

International audienceWe investigate the semiglobal output regulation of minimum-phase single-input single-output nonlinear systems with sampled measurements. We proceed by emulation. We start by considering a continuous-time regulator, which solves the problem in the absence of sampling. Then, we consider sampled measurements and we model the overall system as a hybrid system. We show that the original continuous-case properties are preserved when the measurements are sampled provided that the maximum allowable transmission interval satisfies a given explicit bound

Efficient Control Approaches for Guaranteed Frequency Performance in Power Systems

Due to high penetration of renewable energy, converter-interfaced sources are increasing in power systems and degrading the grid frequency response. Synthetic inertia emulation and guaranteed primary frequency response is a challenging task. Still, there is high potential for application of highly controllable converter-interfaced devices to help performance. Renewable energy sources and demand side smart devices also need to be equipped with innovative frequency control approaches that contribute to frequency regulation operations. First, the wind turbine generator is chosen to represent an example of a converter- interfaced source. An augmented system frequency response model is derived, including the system frequency response model and a reduced-order model of the wind turbine generator representing the supportive active power due to supplementary inputs. An output feedback observer-based control is designed to provide guaranteed frequency performance. System performance is analyzed for different short circuit ratio scenarios where a lower bound to guarantee the performance is obtained. Second, the load side control for frequency regulation with its challenges is introduced. 5G technology and its potential application in smart grids are analyzed. The effect of communication delays and packet losses on inertia emulation are investigated to show the need of using improved communication infrastructure. Third, a robust delay compensation for primary frequency control using fast demand response is proposed. Possible system structured uncertainties and communication delays are considered to limit frequency variations using the proposed control approach. An uncertain governor dead-band model is introduced to capture frequency response characteristics. Guaranteed inertial response is achieved and compared with a PI-based Smith predictor controller to show the effectiveness of the proposed method. Fourth, set theoretic methods for safety verification to provide guaranteed frequency response are introduced. The Barrier certificate approach using a linear programming relaxation by Handelman’s representation is proposed with its application to power systems. Finally, the Handelman’s based barrier certificate approach for adequate frequency performance is studied. The computational algorithm is provided for the proposed method and validated using power system benchmark case studies with a discussion on a safety supervisory control (SSC)

L-2 State Estimation With Guaranteed Convergence Speed in the Presence of Sporadic Measurements

This paper deals with the problem of estimating the state of a nonlinear time-invariant system in the presence of sporadically available measurements and external perturbations. An observer with a continuous intersample injection term is proposed. Such an intersample injection is provided by a linear dynamical system, whose state is reset to the measured output estimation error whenever a new measurement is available. The resulting system is augmented with a timer triggering the arrival of a new measurement and analyzed in a hybrid system framework. The design of the observer is performed to achieve exponential convergence with a given decay rate of the estimation error. Robustness with respect to external perturbations and L2-external stability from plant perturbations to a given performance output are considered. Computationally efficient algorithms based on the solution to linear matrix inequalities are proposed to design the observer. Finally, the effectiveness of the proposed methodology is shown in an example