Multi-input Multi-output Quantitative Feedback Theory Research Articles

A discussion on robust multi-variable I/O fractional transfer function of types DC or FBLFD in motion control

Motion control and robust path tracking design are the objective of this paper. The Multi-Input Multi-Output Quantitative Feedback Theory (MIMO-QFT) method is considered. This methodology permits to divide the MIMO system into sub-Multi-Input-Single-Output (MISO) equivalent structures. After obtaining the sub-structures, the objective is the design of the controller and prefilter in order to achieve some specifications. A multi-variable robust path tracking design is already studied based on fractional approaches. These developed approaches are based on two fractional prefilters of types Davidson Cole (DC) and Frequency Band Limited Fractional Differentiator (FBLFD). A new methodology that combines I/O (Input Output) fractional transfer function of types DC and FBLFD with a fractional PID controller tuning is studied in this paper. This approach is based on considering the I/O transfer function matrix as a fractional prefilter of types DC or FBLFD. Using this approach a reduced settling time of the I/O transfer function can be obtained. The multivariable fractional PID controller is tuned based on a multi-objective optimisation using genetic algorithm. The obtained method is tested with a SCARA robot model to demonstrate the efficacy and robustness of our approach.

Automated synthesis of multivariable QFT controller using interval constraint satisfaction technique

Robust controller synthesis of Multi-Input–Multi-Output (MIMO) systems is of great practical interest and their automation is a key concern in control system design. The synthesis problem consists of obtaining a controller that ensures stability and meets a given set of performance specifications, in spite of the disturbance and model uncertainties. In addition to perform the above tasks, a MIMO controller also has to perform the difficult task of minimizing the interaction between the various control loops.Unlike existing manual or convex optimization based Quantitative Feedback Theory (QFT) design approaches, the proposed method gives a controller which meets all performance requirements in QFT, without going through the conservative and sequential design stages for each of the multivariable sub-systems. In this paper, a new, simple, and reliable automated MIMO QFT controllers design methodology is proposed. A fixed structure MIMO QFT controller has been synthesized by solving QFT quadratic inequalities of robust stability and tracking specifications. The quadratic inequalities (constraints) are posed as Interval Constraint Satisfaction Problem (ICSP). The constraints are solved by constraint solver — RealPaver. The main feature of this method is that the algorithm finds all the solutions to within the user-specified accuracy. The designed MIMO QFT controllers are tested on the experimental setup designed by Educational Control Product (ECP) Magnetic Levitation Setup ECP 730. From the experimental results presented, it is observed that, the designed controller satisfies the desired performance specifications. It is also observed that, the interactions between the loops are within the specified limits. The robustness of the designed controllers are verified by putting extra weights on the magnets.

QFT Based Robust Control of a Single-Link Flexible Manipulator

This article presents the application of multi-input multi-output (MIMO) quantitative feedback theory (QFT) to the control of a single-link flexible manipulator. The manipulator employs an actuation scheme comprised of a DC motor that provides spatially discrete actuation and a surface bonded piezoelectric ceramic that provides spatially distributed actuation. The efficacy of the sequential MIMO QFT methodology for articulating flexible structure control is investigated using the flexible manipulator testbed, with the control system designed to achieve rapid, rest-to-rest positioning of the manipulator tip in the presence of significant parametric and non-parametric structured uncertainty. Numerical simulations and experiments are employed to validate the synthesised control system and the combined discrete-distributed actuation scheme. Conservatisms in the MIMO QFT methodology are identified and partly alleviated using recent theoretical and design improvements.

Non‐sequential MIMO QFT control of the X‐29 aircraft using a generalized formulation

AbstractThis paper presents a generalized formulation for multi‐input multi‐output (MIMO) quantitative feedback theory (QFT) based controller design and analysis, and its application to the control of the X‐29 aircraft. The formulation is based on a more general control structure, where input and output transfer function matrices are included to provide additional degrees of freedom in the decentralized MIMO QFT feedback structure, that facilitates the exploitation of directions in MIMO QFT designs. The formulation captures existing design approaches for fully populated MIMO QFT controller design and provides for a directional design logic involving the plant and controller alignment and the directional properties of their multivariable poles and zeros. Horowitz's Singular‐G design methodology is placed in the context of the generalized formulation and the Singular‐G design for the X‐29 is analysed and redesigned using non‐sequential MIMO QFT and the formulation, demonstrating its utility. The results highlight a fundamental trade‐off between multivariable controller directions for stability and performance in classically formulated design methodologies, elucidate the properties of Singular‐G designed controllers for the X‐29 and validate recent contributions to the theory for non‐sequential MIMO QFT. Copyright © 2006 John Wiley & Sons, Ltd.

An improved non‐sequential multi‐input multi‐output quantitative feedback theory design methodology

AbstractThis paper presents an improved non‐sequential multi‐input multi‐output (MIMO) Quantitative Feedback Theory (QFT) design methodology for uncertain systems. A non‐sequential MIMO QFT stability theorem is derived that serves as the basis for an improvement of the design methodology, whereby it can be successfully applied to non‐minimum phase systems, albeit with a degree of conservatism partially inherent in independent and decentralized design methodologies. The results reduce the conservatism in a non‐sequential MIMO QFT design and provide insight into the plant cases for which the methodology can be successfully applied. Copyright © 2006 John Wiley & Sons, Ltd.

Robust Stability of Sequential Multi-input Multi-output Quantitative Feedback Theory Designs

This paper re-examines the stability of multi-input multi-output (MIMO) control systems designed using sequential MIMO quantitative feedback theory (QFT). In order to establish the results, recursive design equations for the SISO equivalent plants employed in a sequential MIMO QFT design are established. The equations apply to sequential MIMO QFT designs in both the direct plant domain, which employs the elements of plant in the design, and the inverse plant domain, which employs the elements of the plant inverse in the design. Stability theorems that employ necessary and sufficient conditions for robust closed-loop internal stability are developed for sequential MIMO QFT designs in both domains. The theorems and design equations facilitate less conservative designs and improved design transparency.

Multivariable quantitative feedback design for tracking error specifications

The use of tracking error specifications in quantitative feedback theory (QFT) design is discussed for multi-input, multi-output (MIMO) systems. These specifications bound the closed loop transfer function within a disk around some nominal (model) performance while preserving the QFT approach that allows treatment of highly structured (and unstructured) uncertainty. Because the specifications capture phase information, the level of over-design in certain MIMO QFT designs is reduced. The method presented allows independent, two-degree-of-freedom design.

Analytic Loop Shaping Methods in Quantitative Feedback Theory

Quantitative Feedback Theory (QFT), a robust control design method introduced by Horowitz, has been shown to be useful in many cases of multi-input, multi-output (MIMO) parametrically uncertain systems. Prominent is the capability for direct design to closed-loop frequency response specifications. In this paper, the theory and development of optimization-based algorithms for design of minimum-gain controllers is presented, including an illustrative example. Since MIMO QFT design is reduced to a series of equivalent single-input, single-output (SISO) designs, the emphasis is on the SISO case.