Controller Design Example Research Articles

TP Model Transformation as a Way to LMI-Based Controller Design

The main objective of this paper is to propose a numerical controller design methodology. This methodology has two steps. In the first step, tensor product (TP) model transformation is applied, which is capable of transforming a dynamic system model, given over a bounded domain, into TP model form, including polytopic or Takagi-Sugeno model forms. Then, in the second step, Lyapunov's controller design theorems are utilized in the form of linear matrix inequalities (LMIs). The main novelty of this paper is the development of the TP model transformation of the first step. It does not merely transform to TP model form, but it automatically prepares the transformed model to all the specific conditions required by the LMI design. The LMI design can, hence, be immediately executed on the result of the TP model transformation. The secondary objective of this paper is to discuss that representing a dynamic model in TP model form needs to consider the tradeoff between the modeling accuracy and computational complexity. Having a controller with low computational cost is highly desired in many cases of real implementations. The proposed TP model transformation is developed and specialized for finding a complexity minimized model according to a given modeling accuracy. Detailed control design examples are given.

LMI를 기반으로 한 퍼지 피드백 선형화 제어 시스템의 L2 강인 안정성 해석

This paper presents the robust stability analysis and design methodology of the fuzzy feedback linearization control systems. Uncertainty and disturbances with known bounds are assumed to be included Un the Takagi-Sugeno (TS) fuzzy models representing the nonlinear plants. robust stability of the closed system is analyzed by casting the systems into the diagonal norm bounded linear differential inclusions (DNLDI) formulation. Based on the linear matrix inequality (LMI) optimization programming, a numerical method for finding the maximum stable ranges of the fuzzy feedback linearization control gains is also proposed. To verify the effectiveness of the proposed scheme, the robust stability analysis and control design examples are given.

Genetic Algorithm Based Controller Design

Controller design approach is described, which is based on genetic algorithms. The approach uses an optimisation procedure, where the cost function to be minimised consists of the closed-loop system simulation and a performance index evaluation. The designed system may be complex and practically without any limitations on its type, structure and size. The proposed approach is demonstrated on a robust controller design example

Adaptive parameter estimator based on T–S fuzzy models and its applications to indirect adaptive fuzzy control design

In this paper, a new on-line parameter estimation methodology for the general continuous time Takagi–Sugeno (T–S) fuzzy model whose parameters are poorly known or uncertain is presented. An estimator with an appropriate adaptive law for updating the parameters is designed and analyzed based on the Lyapunov theory. The adaptive law is designed so that the estimation model follows the parameterized plant model. By the proposed estimator, the parameters of the T–S fuzzy model can be estimated by observing the behavior of the system and it can be a basis for indirect adaptive fuzzy control. In order to show the applicability of the proposed estimator, indirect adaptive fuzzy control design examples with the proposed estimator are presented.

The periodic optimality of LQ controllers satisfying strong stabilization

An LQ strong stabilization problem is proposed. To determine when a controller with periodic gains is locally superior to a linear time invariant compensator for this problem, a Π test is presented. For systems with strictly proper transfer functions, it is proven that the frequency range where stable periodic controllers based on weak variations about the LTI case can give better performance than stable LTI compensators is finite. In the development, a means to evaluate the second partials of functions with respect to matrix-valued parameters is introduced. For those systems where periodic control is warranted, techniques for designing optimal periodic strongly stabilizing controllers are presented. Two examples detailing the application of the Π test are provided, as well as an optimal periodic controller design example.

Aeronautical and Space Vehicle Control in Dynamic Sliding Manifolds

Multiple loop multiple time scale sliding mode control technique based on dynamic sliding manifold is developed and applied to aeronautical and space vehicle control. Minimum and nonminimum phase output tracking problems for aeronautical and space vehicles are addressed in dynamic sliding manifold. Numerical examples of the flight controller design for controlling minimum and nonminimum phase maneuvers of F-16 jet fighter are presented. An example of an attitude controller design for the X-33 technology demonstration reusable launch vehicle using sliding mode control based on dynamic sliding manifold is also considered. Numerical simulations illustrate effectiveness of the dynamic sliding manifold technique.

Aeronautical and space vehicle control in dynamic sliding manifolds

Multiple loop multiple time scale sliding mode control technique based on dynamic sliding manifold is developed and applied to aeronautical and space vehicle control. Minimum and non-minimum phase output tracking problems for aeronautical and space vehicles are addressed in dynamic sliding manifold. Numerical examples of the flight controller design for controlling minimum and non-minimum phase manoeuvres of an F-16 jet fighter are presented. An example of an attitude controller design for the X-33 technology demonstration reusable launch vehicle using sliding mode control based on dynamic sliding manifold is also considered. Numerical simulations illustrate the effectiveness of the dynamic sliding manifold technique.

LPV control of a 6-DOF vehicle

A linear parameter varying (LPV) controller design example for the position and attitude control of a spacecraft is presented. The six degree-of freedom (DOF) model including the aerodynamics is described. Simulations with the nonlinear 6-DOF model show the usefulness of the design procedure. The practical problem of "fast dynamics" in the controller is solved by an ad hoc method based on the use of a single quadratic Lyapunov function with pole clustering constraints for each frozen linear time invariant (LTI) system in the parameter variation set. The results show that the method facilitates simulation and allows for addressing implementation aspects such as the sampling rate.

Three Practical Examples of Magnetic Bearing Control Design Using a Modern Tool

The use of magnetic bearing in industrial applications has increased due to their unique properties. Nowadays efficiency and predictability in handling rotors on magnetic bearings is asked with the same standard as conventional rotors on oil or roller bearings. First of all one must be aware of the special technical properties of magnetic bearing designs. The dynamic behavior of the rotor combined with requirements of the application define the desired bearing characteristic. With modern tools covering the mechanical aspects as well as the electronic controllers and their digital implementation on a DSP, these properties can be designed. However, despite the use of such efficient tools engineering practice is needed. Therefore this paper summarizes the major steps in the control design process of industrial applications. Three rotors supported on magnetic bearing with their specific dynamic behavior are presented: a very small high speed spindle (120,000 rpm); a small industrial turbo molecular pump rotor (36,000 rpm); and a large multistage centrifugal compressor (600 to 6300 rmp). The results of the analyses and their experimental verification are given.

Robust Flight Control Design With Eigenstructure Assignment

Although the H∞ control method is a powerful tool to design robust controller, it is difficult to attain the performances in time domain. A new design method of H∞ state feedback controller is proposed which guarantees the robust stability and assigns eigenstructure in the desired regions. Conditions of robust stability and closed loop eigenstructure assignment are solved in LMI form with one nonlinear constraint. This method is validated with numerical example of flight control design.

固有構造の存在範囲を指定したロバスト飛行制御系の設計

Although the H∞ control method is powerful tool to design robust controller, it is difficult to attain the performances in time domain. A new design method of H∞ state feedback controller is proposed which guarantees the robust stability and assigns eigenstructure in the desired regions. The time responses can be shaped with assigning appropriate eigenstructure. Conditions of robust stability and closed-loop eigenstructure assignments are solved in LMI form with one nonlinear constraint. This method is validated with numerical example of flight control design.

Multiple Blended Controller Design for Bilinear Systems

In this paper a possible approach for designing multiple blended controller for bilinear systems is presented. Velocity-based linearisation framework for analysis of non-linear systems is used to assist control design. Due to this analysis tool the design of relatively simple controller is possible. The design procedure enables use of knowledge from linear systems control design and achieving desired performance not just in equilibrium points where system can be linearised but in whole operating region. The approach is illustrated by an example of combustion process control design.

Mapping of Frequency Response Performance Specifications Into Parameter Space

A procedure is presented that enables frequency response performance specifications (e.g. magnitude, phase, sensitivity, H∞, etc.) to be mapped directly into parameter space. This procedure significantly enhances the versatility of parameter space techniques by facilitating the design and analysis for systems with both structured and unstructured uncertainty. For analysis, the procedure can be used to immediately show at which operating conditions the system provides the desired performance. For control design, the simplicity and transparency attributed to parameter space techniques are retained, while ensuring that the additional frequency domain specifications are also satisfied. This new procedure is demonstrated by designing a flutter suppression controller for NASA Langley’s Benchmark Active Controls Technology (BACT) wing flutter model. The control design example incorporates both eigenvalue specifications and frequency response magnitude specifications.

Design of controllers for MG3 compressor models with general characteristics using graph backstepping

We discuss the design of controllers for compressors with general characteristics, including the right-skewed ones. The controllers can be represented graphically by plotting their throttle surfaces. The graphical representation of controllers enhances understanding of controller action and allows to compare various controllers. We discuss the issue of the right skewness of a compressor characteristic. We show how to design controllers using a graph backstepping procedure involving the construction of the throttle surface. We show that for a quite general compressor characteristic, every potential axisymmetric equilibrium on the decreasing part of the compressor characteristic, the peak of the characterisitic, and every rotating stall equilibrium close to the peak can be globally or semi-globally stabilized by an appropriate choice of the throttle surface and the controller gains. We obtain lower bounds on the gains of the controller in terms of the divided differences related to compressor characteristic. These bounds can be expressed using some bounds on the first and second derivatives of the characteristic in the region of operation. In this way we establish a direct relationship between the shape of the compressor characteristic and the required controller gains. We discuss controllers that stabilize a range of the desired equilibria and guarantee a soft bifurcation of the equilibria as a set-point parameter varies. We give an example of controller design for a right-skew compressor. We provide simple general guidelines for choosing the throttle surface.

Vibrational Control of an Underactuated Mechanical System: Control Design through Averaging Analysis

An open loop vibrational control for an underactuated mechanical system with amplitude and frequency modulation is investigated. Because there is no direct control input to an unactuated joint, the dynamic coupling between actuated and unactuated joints is utilized for controlling unactuated joints. The actuated joints are first of all positioned to their desired locations. Then, periodic oscillatory inputs are applied to the actuated joints to move the remaining unactuated joints to their target positions. The amplitudes and frequencies of the vibrations introduced are determined through averaging analysis. A systematic way of obtaining an averaged system for the underactuated system via a coordinate transformation is developed. In the event of actuator failure, a manipulator in zero gravity space can be controlled in this way. A control design example of the planar 2R manipulator with a free joint with no brake is illustrated. Simulation and experimental results are provided.

Multidisciplinary optimization with evolutionary computing for control design

Abstract Multidisciplinary optimization (MDO) is concerned with complex systems exhibiting challenges in terms of organization and scale. Complex multivariable control design can benefit from advances in MDO architectures. An example of model-based PI control design of a gas turbine engine is presented Three MDO architectures including collaborative optimization are applied to this example. The optimization is earned out through a multiobjective genetic algorithm framework. Implementation and results provided suggest viability of such techniques for complex control design problems and potential improvements over existing techniques.

Construction Method of Linear Suboptimal Controllers from Input-Output Data

In this paper, we consider a suboptimal control problem based on the input-output data through the LFT representation. First we describe the suboptimal control problem in a general setting via the LFT. Then we solve the problem via numerical optimization, where the relation between the design parameters and the cost function plays a key role. For this equation, we discuss how to solve the optimization problem. Finally, we give numerical examples of controller design to demonstrate its effectiveness.

Vibrational control of underactuated mechanical systems control design through averaging analysis

An open loop vibrational control for an underactuated mechanical system with amplitude and frequency modulation is investigated. Since there is no direct external input to an unactuated joint, the dynamic coupling between the actuated and unactuated joint is utilized for controlling the unactuated joint. Feedback linearization has been performed to fully incorporate the known nonlinearities of the underactuated system considered. The actuated joints are firstly positioned to their desired locations, and then periodic oscillatory inputs are applied to the actuated joints to move the remaining unactuated joints to their target positions. The amplitudes and frequencies of the vibrations introduced are determined through averaging analysis. A systematic way of obtaining an averaged system for the underactuated system via a coordinate transformation is developed. A manipulator in the zero gravity space can be vibrationally controlled in the event of actuator failure. A control design example of the 2R planar manipulator with a free joint with no brake is provided.

Simulation support for recipe driven process operation

Flexible batch plants are characterised by combination of discrete and continuous dynamics. Several processes taking place inside batch reactors are best described by continuous dynamics. The sequence of steps required to make a product, on the other hand, can be very well described by discrete event dynamics system representation. Such sequences are defined by batch recipes. A design methodology for such recipe driven process operation based on recipe models is proposed. Supervisory control framework is employed to combine procedures defined by recipes with co-ordination and resource-allocation functions. A simulation support for the proposed design approach is discussed and an example of a corresponding simulation tool is presented. An application example of a batch process cell controller design is presented to illustrate the described concepts.

A general canonical form for feedback passivity of nonlinear systems

In this article projection operators are used for obtaining a natural canonical form, for non-linear single-input single-output systems, which clearly exhibits the conservative, the dissipative and the locally destabilizing forces present in the drift vector field of a given system, for which a storage function is known. When the system's natural 'energy management' structure is revealed, a suitable state-dependent input coordinate transformation makes the system passive or strictly output passive. A direct application of the 'energy shaping plus damping injection' controller design method, whch is a well known controller design option for passive systems, may then be attempted. A bioreactor controller design example is presented, for illustrative purposes, which includes computer simulations.