Negative Imaginary Controller Research Articles

Robust stabilization of LTI negative imaginary systems using the nearest negative imaginary controller

AbstractThis paper considers the problem of robust stabilization of linear time‐invariant systems with respect to unmodelled dynamics and structure uncertainties. To that end, a methodology to find the nearest negative imaginary system for a given non‐negative imaginary system is presented first. Then, this result is employed to construct a near optimal linear quadratic Gaussian controller achieving desired performance measures. The problem is formulated using port‐Hamiltonian method and the required conditions are defined in terms of linear matrix inequalities. The technique is presented using the fast gradient method to solve the problem systematically. The designed controller satisfies a negative imaginary property and guarantees a robust feedback loop. The effectiveness of the approach is demonstrated by a simulation on a numerical example.

A grid-forming control method based on negative imaginary theory for distributed energy resource

Due to the increases of renewable energy penetration and share of power electronic devices in the power system, Grid-forming (GFM) control methods have become one of the most important technology for the power systems with a high proportion of new energy resources. To improve the control performance of the VSC (Voltage Source Converter), a novel GFM control method based on negative imaginary theory is proposed in this paper. Firstly, the typical structure of distributed energy system is analyzed. Then, the negative imaginary characteristic of VSC’s mathematical model is proved and a negative imaginary controller (NIC) is designed. Finally, the effectiveness and feasibility of the proposed control method are verified by simulation results through MATLAB/Simulink.

Negative imaginary feedback control of satellite orbit dynamical model

This article presents observer-based negative imaginary positive feedback control of satellite orbit dynamical model. In this article, satellite orbital model is transformed into a strongly strict negative imaginary system using observer-based transformation scheme, and then, negative imaginary control theory is applied to achieve stability and robustness in orbit control system in the presence of multiplicative uncertainty. The solutions of orbit control problem are investigated with two thrusters input as well as one thruster input. According to the numerical simulation findings reported in this study, the investigated control approach guarantees the robust stabilization of the satellite orbital system.

Static output feedback negative imaginary controller design with H 2 performance

In this paper, the problem of designing static output feedback (SOF) negative imaginary controller has been studied. Because the constraints brought by negative imaginary (NI) property and performance are a set of bilinear matrix inequalities (BMIs), designing an SOF NI controller with performance is a non-trivial problem. To overcome the difficulty of solving BMIs, a linearisation-based method is proposed. First, a necessary and sufficient condition is established, where the constraints of NI property and performance are reformulated as similar forms. Second, inspired by the semidefinite programming, the derived condition is converted to the difference between two convex functions. Then a linearised iterative algorithm with initialisation process is provided to compute the desired SOF NI controller. Finally, two numerical examples are presented to illustrate the proposed results.

Position and attitude tracking control using CCW and SNI system theory with applications to multi-agent systems

This paper considers position and attitude tracking control. Counterclockwise (CCW) input–output maps from force and torque to position and attitude are established for rigid-body position and attitude motion. Using the properties of counterclockwise systems and negative imaginary (NI) systems, a stabilizing strictly negative imaginary (SNI) controller is shown to drive the tracking errors in position and attitude to zero. In addition, a method to synthesize the strictly negative imaginary controller in a H∞-optimal sense is presented. The control laws are then extended to the formation control problem in multi-agent systems. Numerical results are included.

Velocity-Free Attitude Control of Quadrotors: A Nonlinear Negative Imaginary Approach.

In this paper, we propose a new approach to the attitude control of quadrotors, by which angular velocity measurements or a model-based observer reconstructing the angular velocity are not needed. The proposed approach is based on recent stability results obtained for nonlinear negative imaginary systems. In specific, through an inner-outer loop method, we establish the nonlinear negative imaginary property of the quadrotor rotational subsystem. Then, a strictly negative imaginary controller is synthesized using the nonlinear negative imaginary results. This guarantees the robust asymptotic stability of the attitude of the quadrotor in the face of modeling uncertainties and external disturbances. First simulation results underline the effectiveness of the proposed attitude control approach are presented.

Retrofitting of bridge superstructures using negative imaginary control theory

This study evaluates the use of Negative Imaginary (NI) theory to model and control forces in external prestressing cables used in retrofitting bridge superstructures. The study analytically and experimentally applied the concept to assess the system robustness and its overall performance. A small-scale prototype was built to represent an aged bridge superstructure member. The NI control system was proven to behave robustly and successfully performed as desired. The system was also compared to two other schemes on the prototype from the structural performance perspective. These schemes are the ‘No-prestressing’ and ‘Passive prestressing’ schemes. The actively controlled system was able to limit the superstructure deflections and stresses under the applied vehicular live load compared to the other two schemes.

Adaptive Trajectory Tracking for Quadrotor Systems in Unknown Wind Environments Using Particle Swarm Optimization-Based Strictly Negative Imaginary Controllers

Leveraging the benefits of the multiobjective particle swarm optimization (PSO) technique, we introduce a new concept of adaptive strictly negative imaginary (SNI) controllers. The proposed adaptive control systems are specifically designed to minimize a certain performance index, representing the objective of our control design, which is to obtain a stable, robust, and responsive 3-D tracking of the AR.Drone drone in the face of wind gusts. We compare the performance of our proposed adaptive controllers with respect to the performance of PSO-PID control systems and the traditional Ziegler-Nichols PID controllers, not only in simulated flights but also in real flight tests. We also present a stability analysis of the closed-loop control system using the SNI system theory.

Switching formation strategy with the directed dynamic topology for collision avoidance of a multi‐robot system in uncertain environments

This paper tackles the distributed leader–follower cooperative control problem for networked heterogeneous unmanned aerial vehicle–unmanned ground vehicle (UAV-UGV) systems in unknown environments requiring formation keeping, obstacle avoidance, inter-robot collision avoidance, and reliable robot communications. To adopt various formations, we design a novel negative imaginary (NI) switching formation protocol with a directed dynamic topology. To prevent an inter-mobile robot collision, a new method to formulate the virtual propulsive force between robots is employed. To avoid unexpected obstacles, a new obstacle avoidance technique that allows the UGVs' formation to change its shape and the UGVs' roles is developed. To determine each UGV robot's order in obstacle avoidance formation, a quadrotor UAV, controlled by a strictly negative imaginary controller involving good wind resistance characteristics, tracks the center of formation shape to guarantee the maintaining visibility for multi-robot systems on the ground. The proposed control system's efficacy is investigated through a rigorously comparative study with other control techniques, namely, the performance of artificial potential field and an NI obstacle avoidance strategy using the switching formation control method without switching topology. Finally, we also conduct a stability analysis of the closed-loop control system using the NI-systems theory.

Adaptive Second-Order Strictly Negative Imaginary Controllers Based on the Interval Type-2 Fuzzy Self-Tuning Systems for a Hovering Quadrotor With Uncertainties

We introduce a new adaptive control technique based on the second-order strictly negative imaginary (SNI) controller, coupled with the interval type-2 fuzzy self-tuning mechanism. We demonstrate the performance of our controllers in the three control loops of the AR.Drone quadrotor to achieve stable and balanced hover performance in flights with a variable Center-of-Gravity (CoG). To facilitate an automatic tuning mechanicsm in our SNI controller, we employ the knowledge-based interval Type-2 Takagi-Sugeno fuzzy system, known for its ability to accommodate the footprint-of-uncertainties (FoU). The proposed adaptive control law is implemented to compensate the dynamic variations in the quadrotor's CoG when the mass of the payload is constantly varied. The robustness and the effectiveness of the proposed control technique are highlighted not only using extensive computer simulations, but also through numerous real-time flight tests. Besides, we also conduct the stability analysis based on the SNI theorem.

Lyapunov-based Stability of Feedback Interconnections of Negative Imaginary Systems

Abstract Feedback control systems using sensors and actuators such as piezoelectric sensors and actuators, micro-electro-mechanical systems (MEMS) sensors and opto-mechanical sensors, are allowing new advances in designing such high precision technologies. The negative imaginary control systems framework allows for robust control design for such high precision systems in the face of uncertainties due to unmodelled dynamics. The stability of the feedback interconnection of negative imaginary systems has been well established in the literature. However, the proofs of stability feedback interconnection which are used in some previous papers have a shortcoming due to a matrix inevitability issue. In this paper, we provide a new and correct Lyapunov-based proof of one such result and show that the result is still true.

STABILITY ANALYSIS AND VIBRATION CONTROL OF A CLASS OF NEGATIVE IMAGINARY SYSTEMS

This paper presents stability analysis and vibration control of a class of negative imaginary systems. A flexible manipulator that moves in a horizontal plane is considered and is modelled using the finite element method. The system with two poles at the origin is shown to possess negative imaginary properties. Subsequently, an integral resonant controller (IRC) which is a strictly negative imaginary controller is designed for the position and vibration control of the system. Using the IRC, the closed-loop system is observed to be internally stable and simuation results show that satisfactory hub angle response is achieved. Furthermore, vibration magnitudes at the resonance modes are suppressed by 48 dB.

On lossless negative imaginary systems

The paper is concerned with the notion of lossless negative imaginary systems and their stabilization using strictly negative imaginary controllers through positive feedback. Firstly, the concept of lossless negative imaginary transfer functions is introduced and some properties of such transfer functions are studied. Secondly, a Lossless Negative Imaginary Lemma is given which establishes conditions on matrices appearing in a minimal state-space realization that are necessary and sufficient for a transfer function to be lossless negative imaginary. Thirdly, a necessary and sufficient condition is provided for the stabilization of a lossless negative imaginary system by a strictly negative imaginary controller. Finally, a flexible structure example is presented to illustrate the theory.