| 1. |
- Govindarajan, Nithin, et al.
(author)
-
An operator-theoretic viewpoint to non-smooth dynamical systems: Koopman analysis of a hybrid pendulum
- 2016
-
In: 2016 IEEE 55th Conference on Decision and Control, CDC 2016. - : Institute of Electrical and Electronics Engineers (IEEE). - 9781509018376 ; , s. 6477-6484
-
Conference paper (peer-reviewed)abstract
- We apply an operator-theoretic viewpoint to a class of non-smooth dynamical systems that are exposed to event-triggered state resets. The considered benchmark problem is that of a pendulum which receives a downward kick at certain fixed angles. The pendulum is modeled as a hybrid automaton and is analyzed from both a geometric perspective and the formalism of Koopman operator theory. A connection is drawn between these two interpretations of a dynamical system by establishing a link between the spectral properties of the Koopman operator and the geometric properties in the state-space.
|
|
| 2. |
- Tegling, Emma, 1988-
(author)
-
Fundamental Limitations of Distributed Feedback Control in Large-Scale Networks
- 2018
-
Doctoral thesis (other academic/artistic)abstract
- Networked systems accomplish global behaviors through local feedback interactions. The purpose of a distributed control design is to select interaction rules and control protocols that achieve desired global control objectives. In this thesis, we address the question of fundamental limitations to such control designs, in terms of the global performance that is achievable in large-scale networks. We consider networked dynamical systems with single- and double- integrator dynamics controlled with linear consensus-like protocols. Such systems can be used to model, for example, vehicular formation dynamics and synchronization in electric power networks. We assume that the systems are subject to distributed disturbances and study performance in terms of H2 norm metrics that capture the notion of network coherence. In the context of power networks, we also show how such metrics can be used to quantify resistive losses caused by non-equilibrium, or transient, power flows due to a lack of synchrony. Distributed static feedback control based on localized, relative state measurements is subject to known limitations that, for example, cause coherence metrics to scale unfavorably with network size in lattices of low spatial dimensions. This causes an inevitable lack of rigidity in one-dimensional formations, such as strings of vehicles. We show here that the same limitations in general apply also to dynamic feedback controllers that are locally of first order. The proof relies partly on a fundamental limitation of localized relative feedback in networks of integrators of order three or higher, which we show to cause instability if the network grows beyond a certain finite size. This result holds unless the controller can access measurements of its local state with respect to an absolute reference frame, in which case dynamic feedback in the form of distributed derivative or integral control can fundamentally improve performance. This case applies, for example, to frequency control in power networks. However, if the absolute state measurements are subject to noise, the advantage of the distributed integral controller in terms of its performance scaling is lost. We show that scalable integral control of networks in principle requires centralization or all-to-all communication. For electric power networks, we show that performance in terms of transient power losses scales with the number of generator nodes in a network. However, in sharp contrast to the previous results, an increased connectivity does not in general improve performance. We discuss possible implications of these results in terms of the design of future power grids with increasingly distributed electricity generation.
|
|
| 3. |
- Tegling, Emma, 1988-, et al.
(author)
-
On Fundamental Limitations of Dynamic Feedback Control in Regular Large-Scale Networks
- 2019
-
In: IEEE Transactions on Automatic Control. - : IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. - 0018-9286 .- 1558-2523. ; 64:12, s. 4936-4951
-
Journal article (peer-reviewed)abstract
- In this paper, we study fundamental performance limitations of distributed feedback control in large-scale networked dynamical systems. Specifically, we address the question of whether dynamic feedback controllers perform better than static (memoryless) ones when subject to locality constraints. We consider distributed linear consensus and vehicular formation control problems modeled over toric lattice networks. For the resulting spatially invariant systems, we study the large-scale asymptotics (in network size) of global performance metrics that quantify the level of network coherence. With static feedback from relative state measurements, such metrics are known to scale unfavorably in lattices of low spatial dimensions, preventing, for example, a one-dimensional string of vehicles to move like a rigid object. We show that the same limitations in general apply also to dynamic feedback control that is locally of first order. This means that the addition of one local state to the controller gives a similar asymptotic performance to the memoryless case. This holds unless the controller can access noiseless measurements of its local state with respect to an absolute reference frame, in which case the addition of controller memory may fundamentally improve performance. In simulations of platoons with 20-200 vehicles, we show that the performance limitations we derive manifest as unwanted accordionlike motions. Similar behaviors are to be expected in any network that is embeddable in a low-dimensional toric lattice, and the same fundamental limitations would apply. To derive our results, we present a general technical framework for the analysis of stability and performance of spatially invariant systems in the limit of large networks.
|
|
| 4. |
- Tegling, Emma, 1988-
(author)
-
On performance limitations of large-scale networks with distributed feedback control
- 2016
-
Licentiate thesis (other academic/artistic)abstract
- We address the question of performance of large-scale networks with distributed feedback control. We consider networked dynamical systems with single and double integrator dynamics, subject to distributed disturbances. We focus on two types of problems. First, we consider problems modeled over regular lattice structures. Here, we treat consensus and vehicular formation problems and evaluate performance in terms of measures of “global order”, which capture the notion of network coherence. Second, we consider electric power networks, which we treat as dynamical systems modeled over general graphs. Here, we evaluate performance in terms of the resistive power losses that are incurred in maintaining network synchrony. These losses are associated with transient power flows that are a consequence of “local disorder” caused by lack of synchrony. In both cases, we characterize fundamental limitations to performance as networks become large. Previous studies have shown that such limitations hold for coherence in networks with regular lattice structures. These imply that connections in 3 spatial dimensions are necessary to achieve full coherence, when the controller uses static feedback from relative measurements in a local neighborhood. We show that these limitations remain valid also with dynamic feedback, where each controller has an internal memory state. However, if the controller can access certain absolute state information, dynamic feedback can improve performance compared to static feedback, allowing also 1-dimensional formations to be fully coherent. For electric power networks, we show that the transient power losses grow unboundedly with network size. However, in contrast to previous results, performance does not improve with increased network connectivity. We also show that a certain type of distributed dynamic feedback controller can improve performance by reducing losses, but that their scaling with network size remains an important limitation.
|
|
| 5. |
- Tegling, Emma, 1988-, et al.
(author)
-
On the Coherence of Large-Scale Networks With Distributed PI and PD Control
- 2017
-
In: IEEE Control Systems Letters. - : Institute of Electrical and Electronics Engineers (IEEE). - 2475-1456. ; 1:1, s. 170-175
-
Journal article (peer-reviewed)abstract
- We consider distributed control of double-integrator networks, where agents are subject to stochastic disturbances. We study performance of such networks in terms of coherence, defined through an H2 norm metric that represents the variance of nodal state fluctuations. Specifically, we address known performance limitations of the standard consensus protocol, which cause this variance to scale unboundedly with network size for a large class of networks. We propose distributed proportional integral and proportional derivative controllers that relax these limitations and achieve bounded variance, in cases where agents can access an absolute measurement of one of their states. This case applies to, for example, frequency control of power networks and vehicular formation control with limited sensing. We discuss optimal tuning of the controllers with respect to network coherence and demonstrate our results in simulations.
|
|
| 6. |
- Tegling, Emma, 1988-, et al.
(author)
-
Performance metrics for droop-controlled microgrids with variable voltage dynamics
- 2015
-
In: Decision and Control (CDC), 2015 IEEE 54th Annual Conference on. - : IEEE. - 9781479978847 ; , s. 7502-7509
-
Conference paper (peer-reviewed)abstract
- This paper investigates the performance of a microgrid with droop-controlled inverters in terms of the total power losses incurred in maintaining synchrony under persistent small disturbances. The inverters are modeled with variable frequencies and voltages under droop control. For small fluctuations from a steady state, these transient power losses can be quantified by an input-output H2 norm of a linear system subject to distributed disturbances. We evaluate this H2 norm under the assumption of a dominantly inductive network with identical inverters. The results indicate that while phase synchronization, in accordance with previous findings, produces losses that scale with a network's size but only weakly depend on its connectivity, the losses associated with the voltage control will be larger in a highly connected network than in a loosely connected one. The typically higher rate of convergence in a highly interconnected network thus comes at a cost of higher losses associated with the power flows used to reach the steady state.
|
|
