Maxim Kristalny

On Using Wind Speed Preview to Reduce Wind Turbine Tower Oscillations

We investigate the potential of using previewed wind speed measurements for damping wind turbine fore-aft tower oscillations. Using recent results on continuous-time H2 preview control, we develop a numerically efficient framework for the feedforward controller synthesis. One of the major benefits of the proposed framework is that it allows us to account for measurement distortion. This results in a controller that is tailored to the quality of the previewed data. A simple yet meaningful parametric model of the measurement distortion is proposed and used to analyze the effects of distortion characteristics on the achievable performance and on the required length of preview. We demonstrate the importance of accounting for the distortion in the controller synthesis and quantify the potential benefits of using previewed information by means of simulations based on real-world turbine data.

On structured realizability and stabilizability of linear systems

We study the notion of structured realizability for linear systems defined over graphs. A stabilizable and detectable realization is structured if the state-space matrices inherit the sparsity pattern of the adjacency matrix of the associated graph. In this paper, we demonstrate that not every structured transfer matrix has a structured realization and we reveal the practical meaning of this fact. We also uncover a close connection between the structured realizability of a plant and whether the plant can be stabilized by a structured controller. In particular, we show that a structured stabilizing controller can only exist when the plant admits a structured realization. Finally, we give a parameterization of all structured stabilizing controllers and show that they always have structured realizations.

Decentralized feedforward control of wind farms: Prospects and open problems

The problem of load mitigation in wind turbines located in wind farms is addressed. The benefits of letting turbines communicate with and account for their neighbors are explored. First, the idea of exploiting previewed wind speed measurements is examined. The problem is formulated as an H2 model matching optimization. The influence of preview length on the performance is analyzed and simulation results are presented. Then, the possibility of cooperation between turbines is studied within a distributed feedforward control scheme. The problem is formulated as a decentralized model matching optimization and several theoretical challenges associated with it are outlined. An approximate frequency domain solution and preliminary simulation results are presented.

On the decentralized H 2 optimal control of bilateral teleoperation systems with time delays

Decentralized control of bilateral teleoperation systems with time delays is considered within the H2 optimization framework. We demonstrate that the problem is quadratically invariant and can be split into two independent model matching optimizations with partial multiplicative delay. The recent loop shifting techniques for delayed systems control are used then to find a complete analytical solution. Explicit state-space formulae for the optimal controller are derived in terms of standard Riccati equations associated with the centralized delay-free problem. It is shown that the resulting optimal controller admits an elegant and easy to implement structure.

On the

The H2 optimization problem with preview and asymptotic behavior constraints is considered in a general two-sided model matching setting. The solution is obtained in terms of two constrained Sylvester equations, associated with asymptotic behavior, and stabilizing solutions of two algebraic Riccati equations. The Riccati equations do not depend on the preview length, yet are affected by asymptotic behavior constraints and are thus different from the standard H2 Riccati equations arising in problems with no steady-state requirements or in one-sided problems.

H^{2}

In this paper we study performance achievable in delayed bilateral teleoperation control. Our goal is to characterize all teleoperation system behaviors that can be achieved with delayed communication but without any restrictive assumptions on the control law, such as passivity. To this end, a recent non-restrictive stabilizing control architecture for bilateral teleoperation is exploited. The main properties of this architecture are discussed and used to obtain parameterization of all the admittance matrices feasible under the nominal stability constraint. The use of this parameterization for shaping system behavior is demonstrated and the results are compared with those obtained using the classical passivity-based control schemes.

Two-Sided Model Matching Problem With Preview

In this paper we consider a problem of delayed bilateral teleoperation control. We exploit a recent parameterization of all feasible teleoperator admittance matrices to propose a control synthesis procedure based on admittance shaping. This leads to an intuitive performance-oriented controller design that reveals important trade-offs inherent to bilateral teleoperaton. In particular, this allows a trade-off between performance and passivity, that is not accessible while using classical passivity-based methods. The proposed controller design is illustrated with simulations and a simple 1 DOF experimental case study.

On the parameterization of feasible admittance matrices in delayed bilateral teleoperation

Stabilization of delayed bilateral teleoperation systems with two master devices is considered. It is shown that allowing communication between the master devices may greatly facilitate the solution rendering the problem quadratically invariant. A convenient structure possessed by stabilizing controllers is revealed, which can be considered as an alternative to passivity-based structures. It is shown that any stabilizing controller can be implemented to comply with this structure, which, in turn, guarantees delay-independent stability of the overall system. The behavior of stabilizing controllers having the proposed structure is illustrated by simulations.

Admittance shaping in delayed bilateral teleoperation control

This paper considers the fully decentralized H2 model matching optimization for continuous-time LTI systems. The properties of vector operator and Khatri-Rao product are exploited to reduce the problem to a one-sided centralized setting of a higher dimension. The potential of this approach for the derivation of explicit state-space formulae is examined. First, a closed-form, though not minimal state-space solution for the general problem is found. Then, non-reducible statespace formulae are derived for the special case of a two-block problem with one-sided dynamics.

On the stabilization of cooperative bilateral teleoperation systems with time delays

The problem of input-output stabilization in a general two-sided model matching setup is studied. As a first step, the problem is reduced to a pair of uncoupled bilateral Diophantine equations over RH infinity. Then, recent results on bilateral Diophantine equations are exploited to obtain a numerically tractable solution given in terms of explicit state-space formulae. The resulting solvability conditions rely on two uncoupled Sylvester equations accompanied by algebraic constraints. This is in contrast to the corresponding one-sided stabilization, where no Sylvester equations are required. It is shown that imposing a mild simplifying assumption is instrumental in obtaining convenient parameterization of all stabilizing solutions, which is affine in a single RH infinity parameter. This demonstrates that if the aforementioned assumption is imposed, the general two-sided stabilization problem is similar to its one-sided counterpart in the sense that the constraints imposed by a stability requirement can be resolved without increasing problem complexity. (Less)