Showing papers on "Closed-loop pole published in 2010"

Design of a Robust State Feedback Controller for a STATCOM Using a Zero Set Concept

Abstract: A static synchronous compensator (STATCOM) is one of the fundamental flexible ac transmission system devices that can be used for voltage regulation and dynamic voltage control. In this paper, a new approach to the problem of the STATCOM state feedback design is presented. The proposed solution technique is based on a zero set concept. It allows one to calculate a complete set of the admissible feedback gains that place closed-loop poles into a prespecified region in the complex plane under parametric uncertainties in the plant model. These uncertainties represent load pattern variations and topological changes due to line tripping. Computational examples show that by using the design technique based on the zero set concept, it is possible to derive the state feedback controllers with better robustness properties than those achieved using the approaches utilizing linear matrix inequalities.

Particle Swam Optimization for Stabilizing Controller of a Self-erecting Linear Inverted Pendulum

Abstract: This paper presents an advanced application of particle swarm optimization, PSO to find state feedback controller gains for stabilizing controller in a linear inverted pendulum. This plant is used as an application example of the proposed method. In conventional method of state feedback control design such as pole placement and linear quadratic regulator method, controller designers often face troublesome exercise of tuning several parameters. Particularly, one has to face trial-and- error approach to select suitable Q and R matrices to design a state feedback control using linear quadratic regulator method. To overcome this problem, an intelligent approach employing PSO- based constrained optimization is proposed. The objective of the optimization is to minimize error function, while closed loop poles region is incorporated as an optimization constraint whose parameter is selected based on the desired control performance. In this study, Clerc's PSO is adopted together with dynamic objective constraint handling where efficient optimization run is shown in the simulation results.

Transfer function identification from phase response data

Abstract: This paper introduces an improved procedure for the identification of a transfer function from phase angle data with prescribed frequency variation. It is shown how a transfer function can be identified from phase response data samples, by fitting a normalized function with constant magnitude using the vector fitting algorithm. The presented approach is numerically robust and leads to more accurate results than conventional approaches.

Robust transfer function identification via an enhanced magnitude vector fitting algorithm

Abstract: The study introduces an enhanced version of the magnitude vector fitting (magVF) algorithm, a robust procedure for the identification of a transfer function from magnitude frequency domain data. The approach is based on the rational approximation of the magnitude square function with enforcement of symmetric poles and zeros, followed by the elimination of poles and zeros located in the right half-plane. The obtained transfer function is stable and of minimum-phase shift type. Robustness and accuracy of the basic magVF algorithm are enhanced by enforcing that the magnitude square rational function is non-negative definite and by introducing a new method to remove purely imaginary conjugate poles from the approximation. Practical application of the proposed approach is demonstrated for measured transformer responses and transmission line propagation functions.

Partial pole placement with minimum norm controller

Abstract: The problem of placing an arbitrary subset (m) of the (n) closed loop eigenvalues of a nth order continuous time single input linear time invariant(LTI) system, using full state feedback, is considered. The required locations of the remaining (n − m) closed loop eigenvalues are not precisely specified. However, they are required to be placed anywhere inside a pre-defined region in the complex plane. The resulting non-uniqueness is utilized to minimize the controller effort through optimization of the feedback gain vector norm. Using a variant of the boundary crossing theorem, the region constraint on the unspecified (n−m) poles is translated into a quadratic constraint on the characteristic polynomial coefficients. The resulting quadratically constrained quadratic program can be approximated by a quadratic program with linear constraints. The proposed theory is demonstrated for power oscillation damping controller design, where the eigenvalues corresponding to poorly damped electro-mechanical modes are critical for performance and hence are specified precisely by the designer, whereas the remaining eigenvalues are non-critical and need not be specified precisely. Acceptable closed loop pole placement is achieved for this example along with a 51% reduction in controller norm.

LMI-region pole placement control scheme for an electrostatically actuated micro Cantilever Beam

Abstract: In the present article the modeling and control design aspects of a narrow micro Cantilever Beam (μCB) with fringing and squeezed thin film damping effects are presented. The suspended clamped-free μCB can move via the application of an external electrically induced force. The nonlinear model of the μCB is linearized at multiple operating points with respect to the beam's displacement. An LMI-region based pole placement controller is designed for the set of the resulting multiple operating models. Particular attention has been paid in order to examine the effects of the system's pressure variations. In addition, variations of the LMI-region where the closed loop poles lie, are investigated in order to check changes in critical characteristics of the closed loop system such like velocity, transient effects etc. Numerous test cases have been applied on the μCB's model and simulation results prove the efficacy of the suggested modeling and control techniques.

Field-oriented control using sliding mode linearization technique for induction motor

Abstract: In the following paper, we propose a new input-output sliding mode linearization control for induction motor combined with field oriented control (FOC). We develop two loops to control the speed and rotor flux modulus. The first one, inner loop, allows to linearize the system by a choose of closed loop poles to achieve a good linearization. The choice of a particular sliding surface permits to create a link between sliding mode theory and input- output linearization. The second loop, an outer one, allows to modifying the dynamics obtained by the first one using PI controller to guarantee stability and tracking performance of speed and rotor flux modulus. When the rotor flux cannot be measured, a nonlinear sliding mode observer is introduced to estimate the rotor flux. The effectiveness of this new approach has been successfully verified through computer simulations

Guaranteed robust state feedback controller via constrained optimization using Differential Evolution

Abstract: Computational intelligence has been successfully applied into many engineering applications including control engineering problems. In this paper, a robust state feedback control design via constrained optimization based on Differential Evolution (DE) is proposed. The feedback controller is designed based on state space model of the plant with structured uncertainty such that the closed-loop system would have maximum stability radius. A wedge region is assigned as a constraint to locate desired closed loop poles. The proposed method is applied into design of anti-swing control of an automatic gantry crane. The experimental result is shown and comparison with that of LQ (linear quadratic) optimal controller is made. The proposed method effectively locates the closed loop poles within the prescribed wedge region and its robust performance is guaranteed.

Small signal modeling and analysis of control speed for two mass resonant system

Abstract: This paper presents a speed control strategy for the torsional vibration systems. A state feedback control law using an integrator is designed. The pole-placement controller and integral of time multiplied by absolute error (ITAE) is used to assign closed-loop poles of the system characteristic equation. The simulation results are show to verify good performance obtained using the proposed controller.

Simulation study on pressure control using nonlinear input/output linearization method and classical PID approach

Abstract: This paper deals with the comparison of linear PID and a nonlinear control strategy to control pressure in a constant volume using a 4/3 way control valve. For the PID control at least three parameters have to be tuned. Rule sets for PID pressure control are very powerful if they derive directly from parameters which can be found in data sheets of the hydraulic components. Nonlinear control techniques are more complex. Their advantage, however, is that they take the nonlinearities of the plant into account and compensate them. The applied nonlinear approach in this paper is the input/output linearization in combination with full state feedback and state observer. The pole placement problem is approached by analyzing a set of PID control rules which is widely accepted in industry and choosing the pole placement for the nonlinear controller accordingly. In addition, this paper presents another set of PID tuning rules which are derived using ITAE performance criterion. The closed loop poles of these two PID designs have been used to calculate the feedback controller gains of the nonlinear controller. The performance of these two linear PID and nonlinear controller designs is evaluated and compared in simulation based on overshoot, settling time, robustness and complexity.

Robust PI controller design for a laboratory time delay process

Abstract: The paper presents an approach to robust PI controller design for systems with interval parametric uncertainty and time delay. It is supposed that the controlled system is described by a transfer function with parameters lying in certain intervals and with a time delay term. The transfer function of the controlled system is modified by approximation of the time delay term by its Pade expansion. The area of all PI controller parameters k p , k i , that are able to assure the robust stability of the feedback closed loop, is found by the method, which is based on plotting the stability boundary locus in the (k p , k i )-plane. Then the pole-placement method is used to specify those controller parameters from the robust stability area, which assure quality of the control performance prescribed by a choice of closed loop poles or relative damping or natural undamped frequency of the control response. The contribution presents theoretical results confirmed by practical experiments in laboratory conditions. Robust PI controllers are found using designed approach for control of an electronic equipment with varying time delay. Designed robust PI controllers are realized using the PLC SIMATIC S7–300.

Derivation of a transfer function model for a high pressure pipeline

Abstract: In this report a lumped transfer function model for High Pressure Natural Gas Pipelines is derived. Starting with a partial nonlinear differential equation (PDE) model a high order continuous state space (SS) linear model is obtained using a finite difference method. Next, from the SS representation an infinite order transfer function (TF) model is calculated. In the end, this TF is approximated by a compact non-rational function.

Multi model control solution for some classes of hysteretic processes

Abstract: The paper proposes a multiple model structure as control solution for some classes of hysteretic processes. This is developed using the nonlinear geometric characteristic of the process and a classical multiple model control algorithm. The components of the proposed structure are designed based on experimental tests, classic identification and closed loop pole placement methods. The applicability of the different implementations of the structure, suitable for each class of studied hysteretic processes, is demonstrated with a real-time control application implementing RST numerical algorithms. The software and the obtained results are presented and commented in terms of efficiency, advantages and disadvantages.

Robust control arithmetic with limitation of system input energy for attitude system of subminiature unmanned helicopter

Abstract: A new robust control arithmetic is put forward to deal with the uncertain attitude model of small unmanned helicopter (SUH). Firstly, the attitude matrix model of SUH is denoted by the block diagonally radioactive matrix. Secondly, based on the restriction of the closed-loop pole and variance constraints, a new robust control, which has the characteristic of system input energy limited, is put forward. Furthermore, the worst system instance of the robust control is analyzed. Finally, simulation proves that the robust control arithmetic has the good performance at the worst condition. In other words, the robust control arithmetic preferably resolves the attitude control of SUH.

Robust pi controllers for systems with transport delay

Abstract: The paper presents robust controller design for systems with uncertain transport delays. Robust PI controllers are designed using approach, which combines the method based on plotting the stability boundary locus in the ( kp, ki)-plane with the pole-placement method. The approach enables to assure robust stability of the closed loop as well as the quality of the control response prescribed by the choice of the closed loop poles or the relative damping or the natural undamped frequency of the control response.

Experimental implementation of Pole Placement Techniques for Active Vibration Control of Smart Structures

Abstract: s-- Fixed controllers can become even unstable, with large changes in system parameters. This problem can be avoided using robust control and adaptive control design techniques. To obtain robust performance, it is desirable that the closed loop poles of the perturbed structure remain at prespecified locations for a range of system parameters. In the present study, the controllers based on adaptive and robust pole placement method are implemented on smart structures. It was observed that, adaptive pole placement controllers are noise tolerant but require high actuator voltages to maintain stability. However, robust pole placement controllers require comparatively small amplitude of control voltage to maintain stability, but are noise sensitive.

A New Implicit Adaptive Zero Pole-Placement PID Controller

Abstract: For most simple processes, PID control can provide satisfactory closed loop performance. However, in spite of the considerable advantages of conventional PID controllers (such as simplicity of their structures, robustness and ease of implementation), they still have a major drawback in that the controllers may need to be re-tuned, if the systems to be controlled are subjected to significant changes, in order to achieve satisfactory performance. For this reason, during the last two decades much work in linear control theory has been devoted to incorporating the flexibility of self-tuning control and the simplicity of PID structures. A lot of self-tuning methods have been developed and special attention is currently being paid to PID self-tuning controllers and their implementation, [e.g. Yusof R. & et al., (1994); Yusof, R.; (1993) and Tokuda M.; & Yamamoto T.; (2002)]. During the past three decades, a special attention has also been given to the problem of designing pole-placement controllers and self-tuning regulators. Various self-tuning controllers based on classical pole-placement ideas were developed and employed in real applications, [e.g. Sirisena H. & Teng F.,(1986); Zhu Q., & et al., (2002); Zayed A. & Hussain A., (2004); Astrom K.., & Wittenmark B., (1973)]. The popularity of pole-placement techniques may be attributed to the fact that in the regulator case they provide mechanisms to over-come the restriction to minimum-phase plants of the original minimum variance self-tuner of Astrom K., & Wittenmark B., (1973). In the servo case, they provide the ability to directly introduce bandwidth and damping ratio as tuning parameters. In addition, there is some improvement in robustness of pole-placement methods, as they simply modify the system dynamics as opposed to cancelling them as per the early optimal self-tuning controllers. Furthermore, unlike many of the self-tuning based PID control designs [see for example Yusof R. & et al., (1994); Yusof, R.; (1993)], in which the tuning parameters must be selected using a trial and error procedure, the tuning parameters for pole-placement controllers can be automatically set on-line by specifying the desired closed loop poles. Comparatively, only little attention has been given to zeros since they are considered to be less crucial than poles. Most of the previous discussion on zeros are centred around the choice of the sampling time so that the resulting system is invertible. However, it is important to note that zeros may be used to achieve better set point tracking Zayed A. & Hussain A., (2004)., and they may also help reduce the magnitude of the control action Sirisena H. & Teng F.,(1986).. 8

Robust stabilisation of coprime factor plant description subject to plant perturbations

Abstract: This paper presents a new procedure for the synthesis of linear multivariable system subjected to plant perturbations and external disturbances Coprime factorisation approach is used to model the plant perturbations External disturbances is treated as exogenous system whose unstable modes are assumed to be disjoint from the system zeros A stable desired closed loop transfer matrix is obtained which can be expressed as the product of an open loop transfer matrix and any proper rational transfer matrix Internal model principle is employed to realise the closed loop transfer matrix which simultaneously ensures: (1) stability robustness in the presence of plant perturbations, (2) decoupling, (3) complete and arbitrary closed loop pole placement, (4) internal stability and (5) disturbance rejection The compensation scheme is presented in the frequency domain This is compared with H-infinity control technique and the simulation result shows better robust performance for the frequency domain method

Robust control for linear system based on gradient flow neural network

Abstract: A gradient flow algorithm model developed for the on-line robust pole assignment is proposed for solving Sylvester equations. The algorithm shows to be capable of synthesizing linear feedback control systems via on-line computing feedback gain matrix and desired closed-loop poles. Meanwhile, the close-loop system matrix is least sensitive to perturbation or uncertainty, and uniformly asymptotically stable in largely range. Simulation results are shown that the proposed approach is suitable to problem of robust stabilization for nonlinear system and on-line robust pole assignment.

Research on D robust control of a class of uncertain sampled-data system

Abstract: For a class of linear sampled-data systems with norm-bounded uncertainty, sufficient conditions for the existence of state feedback control laws with the closed-loop poles in a pre-specified disk and optimizational robust H ∞ performance are derived in terms of linear matrix inequalities (LMIs). The problem of designing the controllers with smaller gain parameters is formulated as a convex problem with LMI constrains, which can be solved by the existing LMI software, Then a class of proportional integral state observers with stronger anti-disturbance is proposed when some states of the system are difficult to be observed, An example shows that the proposed methods ensure less change of dynamic and stable steady performance with the disturbance.

Optimal opportunity-awaiting control for stochastic systems with state feedback: A parametric approach

Abstract: The problem of designing optimal opportunity-awaiting control strategy for a class of stochastic systems is considered in this note. The performance specifications, such as sector pole region, average waiting time and average residue time indexes, constitute the desired performance index set, which is the requirement of designing controllers. The desired closed-loop poles are restricted in a proper sector region in the complex plane via state feedback using eigenstructure assignment algorithm. A constraint optimization problem is constructed by parameterizing the desired closed-loop poles and free vectors. The optimal opportunity-awaiting controller can be obtained by solving the optimization problem. An example is used to illustrate the proposed method.

Design of Reference Tracking Controllers for LPNI Systems

Abstract: Motivation: In designing linear feedback systems, tracking quality specifications are typically mapped into admissible domains in the complex plane and then the root locus technique is used to synthesize a controller that places closed loop poles in the desired locations. This methodology motivates the first goal of this chapter: to generalize the notion of admissible domains and the root locus technique to LPNI systems. Accomplishing this goal leads to a quasilinear method for PID controller design. Overview: A technique for mapping the random reference tracking quality indicators, introduced in Chapter 3, into admissible domains on the complex plane is introduced (Section 5.1). Next, the root locus method for systems with saturating actuators is developed (S-root locus, Section 5.2). It turns out that the S-root locus is a subset of the usual root locus typically terminating prior to the open loop zeros. A method for calculating these termination points is provided. In addition, we equip the S-root locus with the so-called truncation points, which define its segments where tracking without amplitude truncation is possible. Admissible Pole Locations for Random Reference Tracking Scenario In linear Control Theory, admissible domains for tracking deterministic references are defined using the classical “quality indicators,” that is, overshoot and settling, rise, and delay times. In this section, we develop a similar approach for tracking random references.