SISO QFT Design With Non-Parametric Uncertainties

Performance robustness has been an important issue in control and it has been increasingly recognised as an area of significance in many design applications. This issue has particular importance among the engineering community because it offers a solution to control system design problems for plant and processes that cannot be described by a single linear time-invariant model. The aim of this paper is to describe one of the methods available for robust control system design called Quantitative Feedback Theory (QFT) and discuss its application to engineering problems. QFT is a powerful design technique based on multi degree-of-freedom use of feedback. The basic building block of a multi-degree-of-freedom system is a two-degree-of-freedom system in which two controllers are present, one inside the feedback loop, used to reduce closed-loop uncertainty, and the other prior to the loop, used to shape the input in order to achieve the required output. To show the power of the method, the application to an aero engine described by a non-linear model, linearised at five operating conditions, is discussed. A comparison of the QFT method is also made with the H-infinity method. It is shown that the H-infinity formulation of the QFT problem can produce a more conservative solution than the QFT method.

This paper presents the design of a robust proportional integral and derivative (PID) controller for a first-order lag with pure delay (FOLPD) model using particle swarm optimization (PSO)-enabled automated quantitative feedback theory (QFT). The plant model considered here can be approximated as a first-order system with a non-minimum phase (NMP) zero. Synthesis of controller for the FOLPD model via manual graphical technique involved in the QFT method is always a challenging and cumbersome task, because an NMP system stabilizes by a small gain. In this paper, a proposal is being presented to automate the loop-shaping phase in the QFT design method to synthesize a robust controller that can undertake the exact amount of plant uncertainty even in the presence of larger uncertainties than those assumed initially and can ensure a proper trade-off between robust stability and tracking performance specifications over the entire range of design frequencies. In this paper,s the PSO technique has been employed to tune the controller automatically,which can significantly reduce the computational effort compared with manual graphical techniques. It has also been demonstrated that this methodology not only automates loop shaping but also improves design quality and, most usefully, improves performance with optimally tuned PID controller in quantitative manner.

A review is presented of the basis of the Horowitz quantitative feedback theory (QFT). It is shown that the basic assumptions of (QFT) have mathematical justification. However, necessary and sufficient conditions for the solvability of the QFT problem are presently not known. By reposing the QFT problem as an M-matrix design problem, it is possible to develop the desired existence conditions as well as simplify the design of the controllers which solve the QFT problem. Some preliminary results are presented and form the basis of ongoing work into the automation of the QFT design process.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

: The purpose of this report is to determine the applicability of the Quantitative Feedback Theory (QFT) approach to designing the control laws for a modern military flight control system. This report documents a portion of the QFT research program, specifically, the implementation of a QFT design on a manned simulation of the NF-16D Variable Stability Inflight Simulator Test Aircraft (VISTA F-16). The control law design addresses the subsonic flight envelope of the VISTA F-16 including changes in aircraft configuration. The design was accomplished as a SISO longitudinal loop and a MIMO lateral loop, and incorporates pilot handling qualities within the specifications. Imbedding handling qualities in the system through prudent choice of control variable ensured that the performance specifications were met. Flexibility in the prefilter design allowed the closed loop response to be shaped for proper feel. The handling qualities were evaluated in a high fidelity, manned simulation of the system. The QFT design provided level 1 handling qualities per the specifications in the pitch channel. It did not provide level 1 handling qualities in the lateral channel, but the design requires minor modification to meet level 1.

Magnetic bearings can not only solve the bearing wear and life problems but also reduce the loss and noise of bearings. However, the strong non-linear and uncertainty of parameter of the magnetic bearings make the traditional PID controller difficult to ensure its long-term and stable operation. Based on the theory of quantitative feedback theory (QFT) and H∞ control theory, this paper presents a design method of magnetic bearing controller for high speed motors. QFT is able to implement design requirements to robust stability and robust performance of the system with large scope uncertainties, but it requires loop-shaping on the Nichols chart and tedious graphical process. Based on QFT, the adoption of H∞ control theory can reduce the drawing process which greatly simplifies the design process. The simulation and experimental results show that the proposed QFT-H∞ controller makes the control system of magnetic bearings have a strong anti-jamming performance for uncertainty of parameters and loading disturbances to ensure the long-term stable operation of the magnetic bearings.

Landing is a challenging flight phase for automatic control of fixed-wing aircraft. For unmanned air vehicles in particular, it is imperative that model uncertainty be considered in the control synthesis. These vehicles tend to have limited sensors and instrumentation yet must achieve sufficient performance in the presence of modeling uncertainties and exogenous inputs such as turbulence. Quantitative feedback theory has been reported in the literature for design of automatic landing control laws, but none of these controllers has been flight-tested. In this paper, quantitative feedback theory is employed to synthesize robust discrete-time controllers for automatic landing of an unmanned air vehicle. A low-cost flight vehicle with standard aileron, rudder, elevator, and throttle controls is used. Dynamic simulation is conducted using uncertain aircraft models and sensor noise profiles derived from flight hardware. Controllers are initially synthesized in deterministic simulations. Control validation is performed using a Monte Carlo analysis of stochastic simulations. Sources of uncertainty considered are sensor noise, model uncertainty, and static winds. Landing-phase simulations presented in this paper indicate a routinely high probability of a successful landing in relatively calm wind conditions. The flight-testing process is discussed, and time histories from two automatic landings are presented. Dynamic responses in flight test are found to be similar to the simulation, but a significant amount of control redesign is still required to achieve adequate experimental performance. The methodology is judged to be a promising candidate for an automatic landing controller for unmanned air vehicles.

Self-repairing control for UAVs via quantitative feedback theory and quantum control techniques

Loop shaping is the principle step for synthesising the quantitative feedback theory (QFT) based robust controllers. The controller assures performance robustness in the presence of plant uncertainties. This paper explores a template and bounds free approach for the automated synthesis of low order fixed structure QFT controller for a highly uncertain pneumatic servo actuator system. In this work, the loop-shaping problem has been posed as a multi-objective optimisation problem and solved using the multi-objective variant of the genetic algorithm. At the end of the design process, a set of Pareto optimal solutions (POS) are obtained, to aid the decision maker in choosing an ideal solution from the POS, use of level diagrams has been explored. The simulation of the results and time and frequency domain analysis has been carried out using MATLAB and the results obtained clearly unveil that the designed QFT controller offers robust behaviour over a range of plant's parametric uncertainty.

Implementing the QFT Method in the MATLAB Environment

Quantitative feedback theory (QFT) is an engineering design method with strong practical value in the field of robust control and it is aimed at the objects with parameters changes. This paper introduces the basic principles and the design process of QFT, and for parameter uncertainty of the robot joint control, this paper designs the feedback-controller and the pre-filter of the system based on QFT. MATLAB simulation results show that the method is with good robust performance and dynamic performance in the robot joint control, and meets the performance indicators.

Natural vibration analysis of plates represents an important issue in engineering applications. In this paper, a new and simplify method for vibration analysis of circular and rectangular plates is presented. The design of an effective robust controller, which consistently attenuates transverse vibration of the plate caused by an external disturbance force, is given. The dynamics of the plate is modeled as a distributed parameter system. We have studied the control vibration of the plate using quantitative feedback theory method by determining the transfer functions between various factors of control system. In this method we have developed the general distributed parameter system method for uncertainty problem for simply supported rectangular plate and clamped circular plate. The quantitative feedback method is one of the robust control methods which is capable to solve problems despite structural and non-structural uncertainty. Quantitative Feedback Theory introduces the new technique to design one-point feedback controllers for distributed parameter systems. The results demonstrate that the control law provided a significant reduction in the plate vibration. The numerical simulation of the designed controller demonstrates that the QFT controller can consistently attenuate the vibration compared to a passive system.

We describe a novel flight control design in which dynamic inversion is used to linearize the aircraft dynamics, and then quantitative feedback theory (QFT) is used to yield robust performance in the presence of model uncertainties. The approach is applied to the unstable, nonlinear, short-period dynamics of an F-16 aircraft. A second-order, dynamic inversion linearizes the alpha dynamics before applying QFT. Comparisons are made between three dynamic inversion designs and a baseline linear control design obtained by direct application of nonlinear QFT. The baseline controller demonstrates considerable robustness, successfully following large-alpha commands at flight speeds ranging from 53 to 150 m/sec while subjected to +/- 20 percent variations in pitch moment derivatives. Including dynamic inversion in the control law permits significantly lower loop gain, leading to reduced control usage at all flight speeds; however this control scheme is less robust to perturbations of the pitch moment terms. (Author)

In this work, the design of a quantitative PID controller is proposed for Ball and Beam system. This controller is designed to robustly compensate for the nonlinear and uncertain behavior of the ball and beam system. The PID controller parameters are obtained using the Black Hole Optimization (BHO) method subject to Quantitative Feedback Theory (QFT) consteaints. The QFT is used to design a simple and robust controller with a more desirable performance. The simulation results show that the proposed quantitative PID controller can effectively compensate the ball and beam system with robust behavior and desirable time response specifications. Index Terms— Robust control, Quantitative Feedback Theory (QFT), PID, Ball and Beam System, Black Hole Optimization.

This paper presents quantitative feedback theory (QFT) based control and tracking of ball and beam system. QFT is a frequency domain approach using Nichols chart. This technique achieves desired robust design over a specified range of plant uncertainty. QFT is used for the design of robust controllers for the plant with uncertainties in the parameters, input/output disturbances and noises. Ball and beam system with parametric uncertainty is defined in state space form using QFT control toolbox and templates are generated. Then, based upon the performance and tracking specifications, bounds are determined. After determining the bounds, controller and prefilter are designed which fulfill the necessary control and tracking requirements. Additionally, a first order sliding mode controller (SMC) is intended for the comparison purpose.

The current interest in robust control has called into question the applicability of the quantitative feedback theory (QFT) robust design method introduced by Horowitz. A number of issues have been raised regarding inherent restrictions of both the design method and the uncertain plant set. Using a multivariable root-locus technique extended to uncertain systems, this paper shows that the QFT assumptions are indeed not restrictive and are in fact equivalent to other well-known conditions for robust stabilizability. Because QFT is one of the very few methods to specifically address the quantitative robust performance issue, these results should lead to better methods of developing new QFT-design software, as well as improved robust control methods to satisfy a priori quantitative performance bounds.