Dr Julio Braslavsky

It is well known that feedback may be used in a control design to obtain desirable properties that are not achievable with open-loop control. Among these are the ability to stabilize an unstable system and "73648_C010" - #2 to reduce the effects of plant disturbances and modeling errors upon the system output. On the other hand, use of feedback control can also have undesirable consequences: feedback may destabilize a system, introducemeasurement noise, amplify the effects of disturbances andmodeling errors, and generate large control signals. A satisfactory control design will, if possible, achieve the potential benefits of feedback without incurring excessive costs.

In this paper we study frequency stabilisation in inverter-based microgrid systems with primary droop controller and three types of secondary control strategies. Particularising the microgrid to the case of two inverter buses, we propose structured models for which frequency regulation, ultimate bounds and an estimate of the region of attraction associated with the ultimate bound set are obtained in closed-form analytical expressions.

The additive increase multiplicative decrease (AIMD) algorithm, that is commonly used for congestion avoidance in communication networks, has recently been suggested in other fields such as load management in electric power networks. As for congestion avoidance, in such systems a large number of agents are required to share a given resource. In recent work by Shorten, Wirth and Leith on congestion control in networking a stochastic model has been developed to analyse AIMD algorithms. However, the analysis assumes a continuous implementation of the algorithm and a constant available resource. These assumptions are no longer useful if the AIMD algorithm is applied in fields such as load management in electric power networks, where a discrete implementation is often required, and the available resource shared may be inherently variable. In this paper we develop a disturbed AIMD model based on the model introduced by Shorten et al. that includes discrete time implementation and time varying resource availability. Further, we use that model to bound the influence of these disturbances, caused by either a discrete implementation or small variations in the available resource.

In this paper we study frequency stabilisation in inverter-based microgrid systems with primary droop controller and decentralised secondary control strategy. For the microgrid with any configuration of inverter buses, we establish conditions for trajectory ultimate boundedness and derive an explicit description of an estimate of the region of attraction to the ultimate bound set.

Recent approaches for direct load control (DLC) of populations of air conditioners (ACs) to provide demand-side services in the electricity grid rely on mathematical models of the aggregate demand dynamics of these populations. These models can be parametrised by the physical characteristics of the ACs in the population, for example their thermal power. The knowledge of how their physical parameters are distributed in the population of real devices is instrumental in the analysis and implementation of controllers based on such models. For large populations, it is typically assumed that these parameters are stochastically distributed according to some probability distribution, e.g., log-normal, which has been effective in simulations. However, the identification of such distribution for a specific population remains an open problem for real-world deployments of DLC. This paper formulates a Bayesian framework for the state and parameter estimation of a previously developed input/output model for the aggregate demand response of heterogeneous populations of ACs. This framework enables us to assign a prior distribution to the parameters of the model, which is then updated using measurements of power demand data for the population to reach a posterior distribution that is more informative about the true value of these parameters. The framework uses sequential Monte Carlo methods, which are well-suited to existing high-performance computer hardware, and aims to provide a way to fill a gap between simulation and real implementation by validating posterior parameter distributions using real measurements. Simulation results indicate that our approach can successfully capture the values defining the distributions of physical parameters in a population simulated by 10,000 ACs with a standard hybrid dynamic model for each device.

The increasing penetration of renewable sources in electricity grids has motivated interest in controlling loads to compensate for variability of these generation sources. Air conditioners (ACs) are one type of loads that can be effectively controlled by broadcasting temperature setpoint offsets and using measurements of aggregate power demand for feedback, as shown in recent works. While such control approach can arbitrarily shape demand, it does so at the expense of end-use comfort, which may be a deterrent to participation in such programmes. This paper explores the use of an alternative to setpoint offsets to shape aggregate demand of ACs without violating end-use comfort levels. The proposed control consists in manipulating the width of the ACs' temperature regulation bands by raising the low temperature limit (or lowering the high temperature limit) to change aggregate demand while keeping AC temperatures within the specified ranges. We develop a deterministic mathematical model for the AC aggregate demand response to changes in the new proposed control input, and numerically validate it against a simulated population of ACs. The resulting model is amenable to systematic analysis and design for direct load control with guaranteed comfort margins. We illustrate this point by deriving a theoretical upper bound on the maximum energy that may be released from a given population of ACs controlled using the proposed control input.

Load control of populations of thermostatically-controlled loads (TCLs) is considered a promising approach to match generation and consumption in electricity grids from the demand side. However, when these loads become synchronised they present a decaying oscillatory aggregate demand, which results in undesired power peaks. In this paper we describe the nature of these oscillations and develop a list of factors that determine its shape. We perform a sensitivity analysis which allows us to identify important relations between the physical parameters of the TCLs and their aggregate dynamics. Beyond describing fundamental behaviour, these relations can help develop and validate analytical expressions that facilitate control design, enabling the use of TCLs for demand response. © 2013 Australasian Committee for Power Engineering (ACPE).

This paper addresses the stabilisation of switching discrete-time linear systems with control inputs under arbitrary switching, based on the existence of a common quadratic Lyapunov function (CQLF). While stabilising feedback gains may be directly designed by solving linear matrix inequalities (LMIs), LMI-based designs in general do not provide information about closed-loop system structure. The authors have begun a line of work dealing with control design based on the Lie-algebraic solvability property. In contrast to LMI-based design, although at the expense of generality, control design based on such Lie-algebraic property seeks to assign closed-loop structure approximating that required to satisfy Lie algebraic conditions that guarantee existence of a CQLF. The present paper expands on earlier work by deriving conditions under which the closed-loop system can be caused to satisfy the Lie-algebraic solvability property generically, i.e. for almost every set of system parameters, furthermore admitting straightforward and efficient numerical implementation. © 2011 ENGINEERS AUSTRALIA & AUSTRALIAN OPTICAL.

We present a direct torque and flux control (DTFC) design for an electric induction motor using a sliding-mode control technique. A distinctive feature of our approach is that, by appropriately parameterizing and implementing the sliding-mode controller, we explicitely take into account the discontinuous nature of the actuator in the design process. As a result, we obtain an improved implementation of DTFC, which significantly reduces the levels of steady-state ripple with respect to those typically obtained with conventional implementations of DTFC.

We present two redesigns to robustify backstepping control laws against dynamic uncertainties at the input of the plant. In the first redesign we construct a passivating control law from a CLF obtained by backstepping. In the second redesign we simplify the passivation redesign which becomes cumbersome for high order systems. We also review the two main versions of backstepping: cancelation and LGV-backstepping, and compare their stability margins.

We examine some recent methods for System Identification, that also deliver non-parametric error bounds, suited for a robust controller design. In particular, we look at Stochastic Embedding, Set Membership Identification and Model Error Modelling. We briefly review the main ideas together with existing computational solutions and present a comparative example.

Dynamic operating envelopes (DOEs) have been introduced in recent years as a means to manage the operation of distributed energy resources (DERs) within the network operational constraints. DOEs can be used by network operators to communicate DER dispatchable capacity to aggregators or customers without further consideration of network constraints and are thus viewed as a key enabler for demand-side participation in future electricity markets and for ensuring the integrity of distribution networks. While a number of approaches have been developed to calculate DOEs, uncertainties in system data are typically ignored, which can lead to unreliable results and introduce security risks in network operations. This article presents a deterministic procedure to calculate robust DOEs (RDOEs) explicitly hedged against uncertainty and variability in customers' loads and generations. The approach is based on a geometric construction strictly included within the feasible region of a linear unbalanced three-phase optimal power flow problem that specifies the network operational constraints. The article analyses and rigorously shows that the proposed approach also delivers proportional fairness in capacity allocations, and demonstrates how the RDOEs can be enlarged by i) exploiting the knowledge of customer operational statuses and ii) by optimising customers' controllable reactive powers. The efficiency and compliance of the proposed approach are characterised and discussed for three numerical case studies of varying complexity: a 2-bus conceptual distribution network, a 33-bus real-world Australian representative low-voltage distribution network, and a 132-bus low-voltage distribution network synthetically constructed by extending the 33-bus network model.

Dynamic stability across a range of operating conditions and disturbances is an essential requirement in the control of wind turbines. To analyse and design for closed-loop stability, existing methods typically rely on the numerical evaluation of a small-signal model of the system around each operating condition. This approach, however, is an inefficient way to capture and shape dynamic behaviour over the wide ranges of operating conditions and parameter values arising in practical implementations. This work presents an analytic stability analysis for presents an analytic stability analysis for (PMSG) wind turbines. The proposed methodology, based on a Lyapunov function constructed from an analytic expression of the system Jacobian, enables the identification of regions of operation and parameter values for the wind turbine system within which its stability can be guaranteed. A feedback linearisation control strategy is adopted to deal with the nonlinear relationship between the generator speed and the DC-link voltage in the turbine back-to-back converter. The closed-loop response performance of the design based on the proposed methodology is compared to that of a conventional PI control design via simulation tests conducted on a 2 MW turbine model and a 5 MW (PMSG) reference turbine model on the FAST physics-based simulation tool developed by NREL.

© 2015 IEEE. This paper presents a feedback design approach to minimise state ultimate-bounds (UBs) in linear time-invariant discrete-time systems subject to non-vanishing bounded disturbances. A target closed-loop eigenstructure is first constructed to achieve the lowest possible UBs for one or more state components of the system. Structural conditions on the system matrices are then derived to guarantee that the target eigenstructure can be assigned by state feedback. When the required structural conditions are satisfied, an eigenvector assignment procedure can be applied to simultaneously minimise multiple UBs in systems with multiple inputs. The results are illustrated by a numerical example drawn from a distributed voltage control problem in inverter-based microgrids.

Populations of distributed thermostatically controlled loads (TCLs) can be remotely controlled as a demand-side approach to maintain the generation-consumption balance in the electricity grid. Adjusting load to generation can result in reduced emissions and lower network operating costs than adjusting generation to load (its traditional counterpart). TCLs have been the focus of a number of recent studies proposing model-based feedback load control (LC) strategies, with promising results. However, commonly made assumptions limit the practicality of such strategies in LC scenarios involving small populations of TCLs, or where the requirement of power demand readings of the controlled devices for feedback may be prohibitively expensive. This paper exploits a parametric second-order TCL model previously developed by the authors to design a proportionalintegral- derivative (PID) controller readily implementable in such LC scenarios. The proposed PID controller, based on the broadcast of setpoint offset changes, only requires feedback of aggregate demand readings at the distribution feeder level. LC performance is evaluated on a numerical case study that embeds simulated TCLs in real power and temperature data from a 70-house residential precinct. The case study highlights the potential of the proposed model-based approach in practical LC scenarios.

We address state-feedback stabilization of discrete-time switched systems (DTSSs) that describe a continuous-time linear time-invariant (LTI) system sampled at varying rates. We consider a setting in which the controller, in addition to applying feedback, selects and varies the sampling rate. We refer to this situation as controller-driven sampling. Our feedback control design approach relies on Lie-algebraic stability results that involve the solvability of the Lie algebra generated by the DTSS's subsystem closed-loop evolution matrices. In matrix terms, Lie-algebraic solvability is equivalent to the simultaneous triangularization of the generating matrices by means of a single similarity transformation. The present paper continues previous work based on the fact that even if the corresponding Lie algebra may be not solvable, closedloop stability can still be achieved by "approximate" triangularization. A rst contribution of the present paper is to show that the Lie-algebraic stabilization problem arising for the class of DTSSs considered can be much less restrictive than for DTSSs of arbitrary form. A second contribution is the identification of a potential pitfall in the application of the approximate triangularization strategy to the class of DTSSs considered, and a suggestion to avoid it. © 2011 IFAC.

The expanding integration of control and communication networks in recent years has generated an increasing interest in control problems with feedback over a communication channel. Significant research activity has concentrated on stabilisation in face of channel effects such as quantisation and data-rate limits. in a recent paper, the authors have studied the problem of feedback stabilisation over a communication channel with a constraint on the admissible signal-to-noise ratio (SNR). It has been shown therein that for a delay-free, linear time-invariant feedback loop, a SNR constraint in the feedback channel imposes fundamental limitations in the ability to achieve closed-loop stability. The present paper extends these results by introducing a time-delay in the loop, and shows that the lowest SNR required for closed-loop stability increases by a factor that may grow exponentially with the time-delay and the unstable open loop poles of the system. This result contributes to the quantification of performance trade offs in integrated control and communication environments. Copyright © 2005 IFAC.

We recently considered feedback stabilization over a Signal to Noise Ratio (SNR) constrained channel. The results were examined for the state feedback and minimum phase cases, with links to bit-rate limited control. In this paper, we extend this analysis to Non-Minimum Phase (NMP) plants, and show that for Linear Time Invariant (LTI) control, NMP zeros further constrain the ability to stabilize over an SNR limited channel. This differs from the situation of bit-rate limited stabilization where NMP zeros do not play a role. We show that by considering linear time varying feedback the effect of NMP zeros in SNR limited stabilization may be eliminated.

For strict-feedback nonlinear systems, this paper shows that it is impossible to reduce to zero the optimal cost in the regulation of more states than the number of control inputs in the system, even using unrestricted control effort. By constructing a near optimal cheap control law, we characterise the infirm value of the optimal regulation cost as the optimal value of a reduced-order regulator problem where the states with lower relative degree drive those with higher relative degree. We illustrate our results with two examples of practical interest: the optimal regulation of the rotational motion of a free rigid body, and the optimal control of a magnetic suspension system.

This paper develops exact, computable formulas for the frequency gain and L2-induced norm of the sensitivity operator in a sampled-data control system. With sampled data, we refer to a system that combines both continuous-time and discrete-time signals, which is studied in continuous time. The expressions are obtained using lifting techniques in the frequency domain and have application in performance and stability robustness analysis taking into account full intersample information.