A methodology is proposed for the design of robust structurally constrained controllers for linear time-delay systems, focusing on decentralised and overlapping fixed-order controllers for Multiple Input Multiple Output (MIMO) systems. The methodology is grounded in a direct optimisation approach and relies on the minimisation of the spectral abscissa and H∞ cost functions, as a function of the controller or design parameters. First, an approach applicable to generic MIMO time-delay systems is presented, which is based on imposing a suitable sparsity pattern with the possibility of fixing elements in the controller parameterisation. Second, we show that if the delay system to be controlled has by itself the structure of a network of coupled identical subsystems, this structure can then be exploited by an improved algorithm for the design of decentralised (or overlapping) fixed-order controllers for the infinite-dimensional system, thereby increasing the computational efficiency and scalability with the number of subsystems. The two approaches, which have been implemented in a publicly available software, support system models in terms of delay differential algebraic equations. They allow to model interconnected systems in a systematic way, and include retarded and neutral systems with delays in state, inputs and outputs. Several numerical examples illustrate the effectiveness of the methodology, as well as its extension towards consensus type problems.
A methodology is proposed to design stabilising and robust fixed-order decentralised controllers for heterogeneous vehicular platoons with Cooperative Adaptive Cruise Control (CACC). We consider Linear Time Invariant (LTI) models with constant time-delays at state, input and output. The closed-loop systems of (identical) local controllers and heterogeneous parameter vehicles are modelled by a system of delay differential algebraic equations. The proposed frequency domain approach uses the non-conservative direct optimisation approach towards stabilisation and robustness optimisation of delay systems. In this paper, the design problem of stabilising (identical) controllers achieving L2 string stability for one vehicle look-ahead platoon is reduced to a simultaneous controller design problem for a parameterised (sub)system, where the allowable values of the parameters correspond to heterogeneity (including time-delays) of the vehicles. By treating the heterogeneity in parameters as perturbations contained in specific intervals or regions, we determine the values for pseudo-spectral abscissa and robust induced-L2 norm. Hence, we ensure that the achieved exponential stability and string stability properties along with the overall computational complexity (of designing the controller) are independent of the number of vehicles. The application of CACC is simulated in MATLAB software.
The structurally constrained controller design problem for linear time invariant neutral and retarded timedelay systems (TDS) is considered in this paper. The closedloop system of the plant and structurally constrained controller is modelled by a system of delay differential algebraic equations (DDAEs). A robust controller design approach using the existing spectrum based stabilisation and the H-infinity norm optimisation of DDAEs has been proposed. A MATLAB based tool has been made available to realise this approach. This tool allows the designer to select the sub-controller inputoutput interactions and fix their orders. The results obtained while stabilising and optimising two TDS using structurally constrained (decentralised and overlapping) controllers have been presented in this paper.
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In this article, the stability analysis problem of networked linear systems with decentralized sampled-data controllers is considered. The networks under consideration are composed of interconnected identical systems. A dissipativity-based approach is utilized to analyze stability, grounded in an interconnection interpretation. A structure exploiting and scalable approach is employed to derive a sufficient stability condition for large-scale linear systems, which is independent of the number of subsystems. In the analysis, the effects of uncertainty on the system models, which include uncertainties that render the coupled systems nonidentical, aperiodic sampling, and a switching network topology, are taken into account. Numerical examples are presented to demonstrate the main result and simulate the sampled-data system.
This article introduces a Hybrid Intervention Scheme Based Optimization (HIBO) algorithm solving an Optimal Reactive Power Management (ORPM) problem in real-time using a Mixed Integer Linear Programming (MILP) solver. The ORPM problem presented here contains a linear objective function containing four objectives separated using a set of static penalty factors for each area. The non-linear optimization problem has been assumed linear by localizing the search for solution, this is done by introducing a penalty on the change from the original state or the base case scenario. Thereby, optimizing the non-linear ORPM in linear steps makes it a fast solver for small changes in power system state. A contingency analysis (for N-1 voltage violations) is included for ensuring the safety and reliability of the power system. The results are used to update the ORPM problem or stop if the system is secure. The optimization variables used to represent transformer taps and shunt device switches are handled as discrete integers and remaining variables as continuous real numbers. The intervention scheme, objectives and constraints used in the HIBO have been derived through surveys conducted at a transmission system control center and are supported using literature. Validation of the HIBO algorithm was performed on the Dutch transmission network model after dividing it into four regional areas. Convergence characteristics of the HIBO algorithm are compared using results. From the results, it is concluded that the HIBO algorithm is a competitive optimization solver, suitable for deployment in the secondary voltage control scheme within system operations domain for transmission system operators.
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