Sourav Patra

Stability Analysis of Interconnected Systems With “Mixed” Negative-Imaginary and Small-Gain Properties

In this letter, an analytical framework is proposed to examine stability of two stable, linear time invariant systems interconnected in positive feedback where the systems have “mixed” properties of negative-imaginary and small-gain. Using the notion of dissipativity, the interconnection of systems is guaranteed to be finite-gain stable under the condition that the dc loop gain is contractive. This work builds on Griggs, and exploits a new set of frequency dependent triplets that was introduced in above reference to “mix” two unconditional stability statements, i.e., small-gain and passivity. Unlike the above reference the present work explores the important question of how a conditional stability statement as needed when two negative-imaginary systems are connected in a feedback loop can be “mixed” with an unconditional stability statement as needed when two contractive systems are connected in a feedback loop. The usefulness of the proposed analytical framework is demonstrated via a numerical example.

Towards Controller Synthesis for Systems with Negative Imaginary Frequency Response

This technical note provides a reformulation of closed-loop systems that have negative imaginary frequency response into closed-loop systems that have bounded gain, so that theory and results from H∞ control can be borrowed to enable controller synthesis for the former class of systems. Systems with negative imaginary frequency response (negative-imaginary systems for short) arise for example in structures with collocated position sensors and force actuators, and finding a systematic controller synthesis treatment for such systems has important applications in, for example, lightly damped large space structure problems. The key result in this technical note assists by reformulating such systems into a bounded-real framework. This technical note also addresses a controller synthesis problem in an H∞ optimal control framework for a generalized plant with an invariant zero at the origin in its (1,2) element which is due to the reformulation of the closed-loop system from a negative-imaginary system to a bounded-real framework. An example demonstrates the feasibility of the reformulation given herein.

Reconfigurable Direct Allocation for Multiple Actuator Failures

Flight control systems are often equipped with reconfigurable control allocation schemes to redistribute control commands in the event of actuator failures. In this brief, a reconfiguration scheme is proposed and is based on the direct allocation method. An iterative algorithm is developed and uses the same lookup tables prepared offline for normal operations, thereby saving a considerable amount of computation time and process memory. To elucidate the effectiveness of the method, the proposed allocation algorithm is applied to a satellite launch vehicle model. Simulation results show satisfactory performance of the method in the presence of multiple actuator failures.

Design of Robust Load Frequency Controller: H ∞ Loop Shaping Approach

Abstract In this article, a robust load frequency controller is designed by adopting H ∞ loop shaping design procedure given in [1]. Using a selected pre-compensator, the singular values of the nominal system are modified to satisfy the requirements for closed-loop performance specifications along with the sufficient robust stability margin of the system. The design of stabilizing controller for the perturbed plant is performed in the framework of normalized coprime factors of the shaped plant. This method does not require an iterative procedure for robust stability margin and thus improves the computational efficiency. The real μ-analysis is adopted to ensure the robust stability of the system. The effectiveness of the method has been demonstrated through the simulation studies of a two-area interconnected power system.

Smooth weight optimization in ℋ∞ loop-shaping design

Abstract Smooth variation in the magnitude response of weights facilitates ℋ ∞ loop-shaping design, as it prevents the cancellation of important modes of the system, for example, lightly damped poles/zeros of flexible structures, when the shaped plant is formed based on closed-loop design specifications. For accurate fitting of transfer functions to magnitude data, smooth weights also allow low-order transfer functions to be used when such smooth variations in their magnitude responses are computed point-wise in frequency. In this paper, smoothness constraints for weights, expressed as gradient constraints on a log scale in dB/decade, which is intuitive from a design perspective, are imposed in a weight optimization framework for ℋ ∞ loop-shaping control. This work builds on [A. Lanzon, Weight optimization in ℋ ∞ loop-shaping, Automatica 41 (1) (2005) 1201–1208], where additional constraints are formulated in linear matrix inequality (LMI) form to cast a complete weight optimization framework. The resulting algorithm thus maximizes the robust stability margin and simultaneously synthesizes smooth weights along with a stabilizing controller. A numerical example is given to elucidate the efficacy of the smoothness constraints in ℋ ∞ loop-shaping control.

Designing simple indoor navigation system for UAVs

The wide range of applications and configurations of UAVs raises the need for different types of navigation methodologies compared to the conventional INS/GPS system. For instance, the limitation in cost, size and weight of indoor UAVs makes conventional navigation system unsuitable for these vehicles. In addition, the INS/GPS navigation system is impractical for indoor applications because the GPS signal is not reliable in closed territories. This paper proposes a new, cost-effective and simple indoor navigation system using three laser beams fixed to the body of the UAV and shooting to the ground. Then, a camera and computer vision algorithm are used to capture the laser dots on the ground and determine their coordinates. The position of laser dots is used to obtain full information about the position and orientation of the UAV. The proposed navigation system can be classified as a vision based navigation system, yet, it does not depend highly on the quality of the video shots taken from the vision camera and does not require a heavy image processing algorithm. An illustrative simulation study is conducted to demonstrate the validity of the proposed navigation system.

A linear matrix inequality approach to parametric H∞ loop shaping control

Abstract The parametric H ∞ loop shaping technique explores more design flexibility by introducing a free parameter that ensures robust stabilization with regard to normalized coprime factor uncertainty of the shaped plant. This paper addresses a design framework for parametric H ∞ loop shaping control using linear matrix inequality (LMI) approach that provides a new set of solvability condition along with the larger feasibility region of solution space over the work of Gu et al. (1999) [6] . An equivalence between the Riccati equation based state-space approach and the proposed LMI framework is established and subsequently, an observer-based structure for parametric H ∞ loop shaping controller has been realized. A numerical example is considered to demonstrate the effectiveness of the proposed method and the results therein are compared with the work of Gu et al. (1999) [6] .

Analysis of robust performance for uncertain negative-imaginary systems using structured singular value

Negative-Imaginary systems are important in engineering practise as this class of systems quite often appears in practical problems, for example, lightly damped flexible structures with collocated position sensors and force actuators. In this paper, the problem of assessing the robust ℋ∞ performance of uncertain negative-imaginary systems is investigated. It is shown that a structure singular value condition for a transformed input/output map equivalently gives a quantitative performance (measured via an ℋ∞-norm) test for systems with strictly negative-imaginary uncertainty.

On LTI output strictly negative-imaginary systems☆

Abstract This paper deals with the notion of output strictly negative-imaginary systems. A definition is given for the class of output strictly negative-imaginary systems and a lemma is proposed to test the necessary and sufficient conditions required to satisfy output strictly negative-imaginary system properties. A set theoretic relationship is established between the existing class of strictly negative-imaginary systems and the newly defined output strictly negative-imaginary systems class. A stability analysis result for interconnected systems with positive feedback is presented while one of the systems is negative-imaginary and the other one is output strictly negative-imaginary, contrary to the existing results where at least one of the systems in the interconnection belongs to the strictly negative-imaginary class. Several numerical examples have been studied to demonstrate the proposed results.

A closed-loop data based test for robust performance improvement in iterative identification and control redesigns

In robust iterative identification and control redesign techniques, a stabilizing controller connected in a closed loop is normally replaced by an alternative attractive stabilizing controller to improve robustness and performance of the closed-loop system. In this paper, novel test methods are proposed to check whether a new stabilizing controller improves performance or not when the existing controller is replaced by this new controller in the closed loop. The proposed tests are based on closed-loop data and no plant model, and can be used for both the SISO and MIMO linear time-invariant systems. For the proposed tests, the plant dynamics is assumed to be unknown whereas the existing and new controller transfer function matrices are known to the designer. These assumptions are common in iterative identification and control redesign techniques. The performance improvement test methods proposed in this paper build on the experimental set-up proposed in Dehghani, Lecchini, Lanzon, and Anderson (2009) which was used to only check whether controllers ensure internal stability of a feedback interconnection or not. In this paper, new test methods are proposed to ascertain robust performance improvement that cannot be obtained from test results of Dehghani et al. (2009). A numerical example is illustrated to show effectiveness of the proposed test methods.