Quantitative feedback theory based control of ball and beam system with parametric uncertainty

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.

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.

Sliding mode control, one of the tools available to design robust controllers, is introduced in the outer loop of a double-loop feedback control of the Ball and Plate (B&P) system. Fuzzy Logic is used to attenuate the chattering introduced by Sliding mode control. Genetic algorithm is implemented to determine the parameters of the fuzzy system in an optimal manner. Linear algebraic method is used to design an inner loop angle controller by solving a set of Diophantine equations. The mathematical model of the B&P system, obtained from Euler-Lagrange Equations of Motion, of the proposed controller is evaluated through simulation studies. Simulation results show that the ball could be stabilized anywhere on the plate in 3.5 seconds and it could also track a circular trajectory of 0.4 m radius at 0.8 rad/s in 10 seconds without significant chattering.

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.

For track-following control in an optical disk drive, a compensator should be designed to satisfy disturbance attenuation property, overall system stability, and so on. In order to ease the compensator design procedure by reducing trial and error, a disturbance observer is added on to a conventional single loop track-following control system, which may cause control input saturation due to excessive loop gain. Because the track-following control system is conditionally stable, control input saturation leads to actual reduction of loop gain whereby the system becomes unstable. To preserve the overall stability during transient response, where control input saturation possibly occurs, the circle criterion based on the pull-in condition is utilized to check the stability under control input saturation. The constraints from the circle criterion and robust stability condition are converted into frequency domain bounds, which are represented on a Nichols chart. Then a design method using quantitative feedback theory (QFT) is applied to satisfy the constraints shown on the Nichols chart. To show the feasibility, some experiments are conducted, and the results are presented.

QFT emphasizes that the major reason for using feedback in control is plant parameter and disturbance uncertainties. The parameter uncertainty is quantitatively expressed by a set P=(P) of possible plants and the quantitative formulation of system performance by a set of acceptable command-response functions A and of disturbance response functions Ad. This paper is devoted to the latter. The design problem is to find a compensator G(s) which guarantees that the actual disturbance transfer function Td is in Ad for all P in P.

The load frequency control (LFC) problem has been one of the major subjects in electric power system design and operation. LFC is becoming much more significant today in accordance with increasing size, changing structure and complexity in interconnected power systems. Practice LFC systems use simple proportional-integral (PI) controllers, but parameters of PI controllers are usually tuned based on the trial-and-error approaches and they are incapable to obtain good dynamic performance under a wide range of operating conditions. For this problem, in this paper quantitative feedback theory (QFT) method is used for LFC problem. A multi-area electric power system with a wide range of parametric uncertainties is given to illustrate proposed method. To show effectiveness of proposed method, a classical PI type controller optimized by genetic algorithms (GA) is designed to compare with QFT controller. The simulation results visibly show the validity of QFT method in comparison with traditional method. Key words: Multi-area electric power system, electric power system load frequency control, robust control, quantitative feedback theory method.

An online delay estimation algorithm is adopted for the adaptive Smith predictor in the networked control systems (NCS) design under the significant delay time. However, the Smith predictor is sensitive to parameter uncertainties within the system model and time delay. The quantitative feedback theory (QFT) controller is suitable to cope with parameter uncertainties of the Smith predictor in this paper; moreover, a template expressed in phase and gain for the QFT design has been constructed by considering the bounded variations with the time delay and the external loading. Therefore, the adaptive Smith predictor control scheme with QFT controller provides better tolerance to parameter uncertainties. Both simulation and experimental results on AC servo motor with both the hybrid controller area network (CAN) bus and the Ethernet network have proven the feasibility and improved performance of the proposed NCS.

A graphical method is introduced that solves the robust infinite horizon H/sub /spl infin// multiple-objective control problem for single measurement, single control input systems. The solution is obtained by describing boundaries on the Nichols chart. Each boundary defines the set of all admissible gain and phase values for the loop transmission at a given frequency. These boundaries are obtained by using the well-known parameterization of all the solutions for a single objective H/sub /spl infin// control problem. The new method links between the theories of H/sub /spl infin// and quantitative feedback theory (QFT). It can be used to design robust H/sub /spl infin// controllers with almost no overdesign, and it provides a convenient solution of H/sub /spl infin// multiple-objective problems that are difficult to solve by the standard four-block setting. It also extends the methods of SISO QFT to deal with a vector of disturbances. The latter may affect the controlled plant through any input coupling matrix and not necessarily through the controller input, or the measurement output.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This paper presents a comprehensive comparative study for the tracking control of a class of underactuated nonlinear uncertain systems. A given nonlinear model of the underactuated system is, at first stage, transformed into an input output form and the driving applied control input of the transformed system is then designed via four sliding mode control strategies, i.e., conventional first order sliding mode control, second order sliding mode, fast terminal sliding mode, and integral sliding mode. At second stage, a ball and beam system is considered and the aforementioned four control design strategies are experimentally implemented. A comprehensive comparative study of the simulation and experimental results is then conducted which take into account the tracking performance, i.e., settling time, overshoots, robustness enhancement, chattering reduction, sliding mode convergences, and control efforts.

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.

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>

This paper focuses on maintaining the liquid level in tank two in the coupled tank control system with the help of the sliding mode control (SMC). SMC is the potent controller for coupled tank liquid level system under tracking conditions. Sliding mode controller (SMC) is nonlinear control it applies a discontinuous control signal. The main advantages of sliding mode are low sensitivity to plant parameter variations and disturbances. To maintain desired liquid levels in a nonlinear coupled tank is a great challenging task so this problem better handled by SMC. To control this liquid level process a SMC strategy is used we have first order SMC and second order SMC. Regulating this system in less time with proper control signal is not possible in first order SMC due to chattering is obtained which yields unwanted control signal. To fill tank-2 in less time with smooth control signal is possible in higher order SMC. Next, second order SMC is applied and stability is reached fast and no chattering phenomenon. These can be shown in the simulation results with the help of MATLAB. This application report describes how to develop SMC for liquid level control in coupled tank system.

: 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.

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.