Structured Singular Value Theory Research Articles

Structure singular value theory based robust motion control of live maintenance robot with reconfigurable terminal function for high voltage transmission line

In a complex rigid–flexible coupling environment of overhead high-voltage transmission line, the manipulator robust trajectory tracking motion control of live maintenance robot is the premise of fulfilling the entire maintenance operations. In the process of manipulator’s different function reconfigurable (drainage board bolt tightening and insulator strings replacement), in response to the shortage of excessive pursuit of robust stability for robot manipulator when using H∞ control, as it ignores the influence of structure changes caused by terminal reconfigurable on the system stability to a certain extent, the structured singular value theory–based robot robust μ synthesis control method was proposed in this article. The intrinsic relationship between structured singular value control (μ method) and H∞ control was elaborated, a general control model of the multi-arms and multi-actions robot system was established, the multifunction terminal reconfigurable live maintenance robot with its two kinds of operations was set as a research object, and the corresponding robot μ controller was designed. In the MATLAB development environment, simulation results have shown that on the premise of maintaining the robust stability, compared to the H∞ control method, μ control can obtain better performance robustness for the perturbation of its own structural changes in the process of different operation functions switch. Finally, the validity and engineering practicability of this method is verified by actual 220 kV live operation experiments.

Gain-Scheduling Control With Dynamic Multipliers by Convex Optimization

In this paper we provide a solution to the gain-scheduling synthesis problem (GSP) for structured parametric and dynamic passive uncertainties, which encompasses an approach for norm-bounded uncertainties as considered in classical structured singular value theory. If compared to known approaches, the distinguishing feature is the use of frequency-dependent multipliers to guarantee stability and performance of the controlled system. On the basis of suitable parameterizations of these multipliers, we develop necessary and sufficient conditions for the existence of gain-scheduling controllers and discuss the benefits of this new design methodology.

A New Linear Fractional Transformation Based Approach to Power System Robustness Analysis

Large power systems are highly complex systems that defy predictions with any degree of certainty. In this paper, an analytical framework for the assessment of small signal stability under operating uncertainty is presented.A rigorous analysis framework for the description of uncertainty in operating conditions is suggested. Using structured singular value theory and optimization tools, techniques for robust stability analysis of complex power systems are then derived and a method to quantify the effect of parametric uncertainties on the stability of critical inter-area modes is presented. A computationally-efficient method for modeling parametric uncertainty based on linear fractional transformation (LFT) theory is investigated and tested. With this approach, it becomes possible to estimate the effects of variations in the parameters of major transmission resources on the nominal stability of critical inter-area modes.The use of the analysis methods is demonstrated on two systems: i) a two-machine test system, and ii) a two-area, 11-bus, 4-machine test system.

A μ-analysis approach to power system stability robustness evaluation

A general approach based on structured singular value (SSV) theory is proposed for the analysis of robust stability of large power systems with parameter variations. SSV theory is utilized to find a structured-based parametric uncertainty description of the system that explicitly address and treat the effect of multiple, interrelated uncertain parameters on system dynamic behavior. Techniques to handle parametric uncertainties are given and methods to generate linear fractional transformation based uncertainty descriptions for the model and its associated uncertainty are discussed. Attention is focused on the study of uncertainties in the nominal system representation arising from two different sources, namely variations in the system operating conditions and uncertainties in the structure of the power system. The performance robustness of the proposed method is verified through simulation studies on a 6-area, 377-machine practical system. In particular, the developed technique is used to estimate the combined effect of variations in the level of power transfer across a critical system interconnection, and variations in the interconnecting tie-line reactance on the stability of critical inter-area modes. Several case studies are presented in which both conventional eigenanalysis techniques and SSV-theory are used to determine robust stability margins.

Robust stability analysis of large power systems using the structured singular value theory

This paper examines the application of structured singular value (SSV) theory to analyse robust stability of complex power systems with respect to a set of structured uncertainties. Based on SSV theory and the frequency sweep method, techniques for robust analysis of large-scale power systems are developed. The main interest is focused on determining robust stability for varying operating conditions and uncertainties in the structure of the power system. The applicability of the proposed techniques is verified through simulation studies on a large-scale power system. In particular, results for the system are considered for a wide range of uncertainties of operating conditions. Specifically, the developed technique is used to estimate the effect of variations in the parameters of a major system intertie on the nominal stability of a critical inter-area mode.

Robust l1 estimation using the Popov-Tsypkin multiplier with application to robust fault detection

This paper considers the design of robust l1 estimators based on multiplier theory (which is intimately related to mixed structured singular value theory) and the application of robust l1 estimators to robust fault detection. The key to estimator-based, robust fault detection is to generate residuals which are robust against plant uncertainties and external disturbance inputs, which in turn requires the design of robust estimators. Specifically, the Popov-Tsypkin multiplier is used to develop an upper bound on an l1 cost function over an uncertainty set. The robust l1 estimation problem is formulated as a parameter optimization problem in which the upper bound is minimized subject to a Riccati equation constraint. A continuation algorithm that uses quasi-Newton BFGS (the algorithm of Broyden, Fletcher, Goldfab and Shanno) corrections is developed to solve the minimization problem. The estimation algorithm has two stages. The first stage solves a mixed-norm H2/l1 estimation problem. In particular, it is initialized with a steady-state Kalman filter and, by varying a design parameter from 0 to 1, the Kalman filter is deformed to an l1 estimator. In the second stage the l1 estimator is made robust. The robust l1 estimation framework is then applied to the robust fault detection of dynamic systems. The results are applied to a simplified longitudinal flight control system. It is shown that the robust fault detection procedure based on the robust l1 estimation methodology proposed in this paper can reduce false alarm rates.

Synthesis of fixed‐architecture, robust H2 and H∞ controllers

This paper discusses and compares the synthesis of fixed‐architecture controllers that guarantee either robust H2 or H∞ performance. The synthesis is accomplished by solving a Riccati equation feasibility problem resulting from mixed structured singular value theory with Popov multipliers. Whereas the algorithm for robust H2 performance had been previously implemented, a major contribution described in this paper is the implementation of the much more complex algorithm for robust H∞ performance. Both robust H2 and H∞, controllers are designed for a benchmark problem and a comparison is made between the resulting controllers and control algorithms. It is found that the numerical algorithm for robust H∞ performance is much more computationally intensive than that for robust H2 performance. Both controllers are found to have smaller bandwidth, lower control authority and to be less conservative than controllers obtained using complex structured singular value synthesis.

Robust inferential control for a packed-bed reactor

In this paper, two different inferential control schemes are applied to an experimental fixed bed methanation reactor. The first scheme, proposed initially by Brosilow, is designed based on Kalman filter estimation. The second less traditional design uses an estimator computed from the partial least squares regression method (PLS). The second approach was found to give superior performance when the nonlinear system under study is operated in a wide range of operating points. Due to the nonlinearity of the system it is essential to address the issue of robustness of the proposed schemes. This is formally done in this work using structured singular value theory. For the robustness analysis it is crucial to develop a realistic but not overly conservative uncertainty description. Since the PLS estimator uses a large number of measurements, a robust design based on the uncertainty associated with each one of the measurements, a robust design based on the uncertainty associated with each one of the measurements would be very conservative. To overcome this problem, a lumped uncertainty description is proposed which is identified directly form experiments.