Unity-feedback System Research Articles

Implementation Methods of Controllers Designed by $H_\infty$ Loop Shaping

When the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> loop-shaping controller is implemented as a unity feedback system, its step responses are sometimes unsuitable for tracking control, typically, displaying large overshoots. In this paper, the implementation method is studied for tracking control with small overshoots. Three implementation methods that are described by a unity feedback system, a previous simple two-degrees-of-freedom(2DoF) system, and a new simple 2DoF system proposed in this paper are examined. For the closed-loop transfer function of each system, the unstable zeros are analyzed and an upper bound of the peak gains is presented. These results show that the two simple 2DoF systems have adequate properties for tracking control with small overshoots. The new 2DoF system has good features that the system is minimum phase if the plant is minimum phase, and that the resonance peak gain is one. Their tracking performances are compared in several numerical examples.

Consensus in Multi-Agent Systems: A Transfer Function-Based Controller Design Approach

In this brief, the problem of output consensus in a multi-agent system is considered, where a distributed dynamic output feedback control architecture is proposed. The control architecture consists of two components, one is local controllers for the agents, and another is a gain for the network. The transfer function of local controller is designed based on the number of positive real axis (in the complex plane) zeros of the agent transfer function, and then network gain is selected by sketching the root-locus of a unity feedback system. It is shown that the output consensus can be achieved with an integral type controller for a class of agents, irrespective of their order. Moreover, with the proposed control architecture, there is no need of communication between the local controllers. The effectiveness of the developed approach is demonstrated through numerical examples.

Well-Posedness, Internal Stability and Input-Output Stability in Networked Multi-Agent Systems

In this article, we consider a feedback interconnection, which consists of a networked multi-agent system with its distributed controller and two sets of external input signals. Assuming that the agents are identical, and the dynamics of each agent and its local controller are represented by transfer functions, the well-posedness condition, internal stability and input-output stability of the feedback interconnection are investigated. A controller is designed by solving a Diophantine equation, and a gain for the network is selected using root-locus of a unity feedback system to achieve input-output stability. The developed results are demonstrated with a numerical example.

Stability margin of undirected homogeneous relative sensing networks: A geometric perspective

In this paper, we study the stability margin (SM) of undirected homogeneous relative sensing networks (UH-RSNs) from a geometric point of view. SM is an important robustness measure indicating the amount of simultaneous gain and phase perturbations in the feedback channels before the instability occurs. A UH-RSN is characterized by the identical local dynamics (a single-input-single-output (SISO) open-loop transfer function T l o c ( s ) ) of individual agent and the graph Laplacian L G representing how the agents are connected. It is shown in this paper that UH-RSNs having multiple inputs and outputs in general may be represented as a unity feedback system including the SISO T l o c ( s ) and one of the real eigenvalues of L G . This representation then helps to identify a class of cooperative T l o c ( s ) for which (1) SM becomes maximized or equal to 1 when the network’s connectivity (the second smallest eigenvalue of L G ) is greater than or equal to the curvature of the Nyquist plot of T l o c ( s ) at the origin; and (2) two bounds on SM are obtained for the SM estimation based on the geometric shape of Nyquist plot. Also, the representation of unity feedback system implies that UH-RSNs with non-cooperative T l o c ( s ) become unstable when the agents are joined with high connectivity. Numerical examples are provided to demonstrate these findings.

Robust fuzzy stabilisation of interval plants

ABSTRACTThe paper deals with the problem of stabilisation of interval systems. To this end, by using Takagi–Sugeno fuzzy mechanism, a Mamdani-type PID-like fuzzy controller is modified and extended to develop a new PID-like Takagi–Sugeno fuzzy stabilising controller for the plant described by an interval system. Indeed, a PID-like Takagi–Sugeno fuzzy controller and an interval plant are considered in the forward path of a unity feedback system, and parameters in Takagi–Sugeno fuzzy controller are determined so that the stability of the closed-loop system is assured. The closed-loop system has a multilinear uncertainty structure. Therefore, based on the Zero Exclusion Condition for multilinear uncertain systems, a new theorem presenting sufficient conditions for the Takagi–Sugeno fuzzy controller to be robust stability guaranteed is also derived. An example is given to illustrate the application and the effectiveness of the proposed controller.

Pitch Aircraft Control with Type-2 FLC and PD Controller

Aircraft systems are inherently unstable systems. The equations governing the motion of an aircraft are a very complicated set of six non-linear coupled differential equations. The linearized equation around the operating point is simulated in simulink MATLAB software. Also, the linear part of the system of nonlinear equations is simulated in simulink MATLAB software. In this study, combinations of PD controllers with fuzzy controller in a unity feedback system has been employed. This paper gives a comparison between the two types of FLC type-1 and type-2 in order to show the great effect of the new type of FLCs in reducing overshoot of the step response and improving the robustness of the system.

CONTROL VALVE STICKBAND COMPENSATOR

Control valve stiction is a common problem experienced by process control loops and is one of the main causes of loop cycling during a control session. This paper proposes a simple effective stickband compensator which was applied to a plant for reducing stickband and limit cycle amplitude within a unity feedback system. The technique is based on a 'stickband-jacket' applied across the input and the output of the actual control valve. The feedback error signal is used to vary the width of the stickband and limit cycle frequency. The compensator adds a single increment to the controller's degree-of-freedom and can be easily added to any existing control loop.

Robust Controller Design for Feedback Systems with Uncertain Backlash and Plant Uncertainties Subject to Inputs Satisfying Bounding Conditions

This paper develops a method for designing unity feedback systems where an uncertain linear time-invariant (possibly distributed-parameter) plant is in cascade connection with an uncertain backlash and a controller. The design problem considered is to determine a robust controller so as to ensure that, despite plant uncertainties, the error and the controller output stay within prescribed bounds for all time and for all inputs whose magnitude and whose slope satisfy given bounding conditions. In essence, the backlash is replaced with a constant gain and a bounded disturbance, thereby resulting in an auxiliary uncertain linear system. Then, by applying the multi-valued version of the fixed-point theorem and the extended version of the theory of majorants, we derive a practical condition in the form of inequalities that can be solved in practice. Further we show that if such inequalities are satisfied for a chosen nominal system, then the original design problem is solved. The usefulness of the method is illustrated by a design example where the plant has a time-delay.

Identification of resonant systems using periodic multiplicative reference signals

System identification of the forward path of a linear unity feedback system, which is almost unstable, is considered through the application of a periodic multiplicative reference signal. Motivation for this problem comes from the need to identify the linear acoustics of a combustion process on the verge of instability. The tools of cyclostationary signal analysis provide an entré to develop methods for understanding the problem and for determining requisite properties of the reference signal.

A new parameterization of stable polynomials

In this note, we develop a new characterization of stable polynomials. Specifically, given n positive, ordered numbers (frequencies), we develop a procedure for constructing a stable degree n monic polynomial with real coefficients. This construction can be viewed as a mapping from the space of n ordered frequencies to the space of stable degree n monic polynomials. The mapping is one-one and onto, thereby giving a complete parameterization of all stable, degree n monic polynomials. We show how the result can be used to generate parameterizations of stabilizing fixed-order proper controllers for unity feedback systems. We apply these results in the development of stability margin lower bounds for systems with parameter uncertainty.

FUNDAMENTAL LIMITATIONS ON THE STEP RESPONSE OF SISO FEEDBACK SYSTEMS

This paper proposes new fundamental limitations on the step response of the unity-feedback system based on its transfer function. Using the definition of Laplace transform, it is shown that time-domain integral equalities have to be satisfied by the step response of SISO (single-input, single-output) stable system, and shown that the maximum magnitude of its step response has some lower bounds with respect to the achievable settling time of the systems. It is also shown that the closed-loop system with open-loop RHP (right half plane) poles and/or zeros has some limitations in the unity-feedback control scheme. These results can be used to check in advance whether desired design specifications are achievable or not.

New IQC for quasi‐concave nonlinearities

AbstractA new set of integral quadratic constraints (IQC) is derived for a class of ‘rate limiters’, modelled as a series connections of saturation‐like memoryless nonlinearities followed by integrators. The result, when used within the standard IQC framework (in particular, with finite gain/passivity‐based argiments, Lyapunov theory, structured singular values, etc.), is expected to be widely useful in nonlinear system analysis. For example, it enables ‘discrimination’ between ‘saturation‐like’ and ‘deadzone‐like’ nonlinearities and can be used to prove stability of systems with saturation in cases when replacing the saturation block by another memoryless nonlinearity with equivalent slope restrictions makes the whole system unstable. In particular, it is shown that the L2 gain of a unity feedback system with a rate limiter in the forward loop cannot exceed \sqrt{2}.In addition, a new, more flexible version of the general IQC analysis framework is presented, which relaxes the homotopy and boundedness conditions, and is more aligned with the language of the emerging IQC software. Copyright © 2001 John Wiley &amp; Sons, Ltd.

Parametrization of stabilizing controllers with integral action

In the standard linear time-invariant multi-input/multi-output unity-feedback system, a parametrization of stabilizing controllers with integral action is obtained. These controllers guarantee asymptotic tracking of step reference inputs at each output channel with zero steady-state error.

Approximating delay elements by feedback

A procedure for obtaining a proper rational approximant of the transfer function of a delayer is suggested. In particular, the step response of the unity-feedback system with the delayer in the direct path is first approximated by truncating the Fourier series expansion of its periodic component, and then the corresponding direct-path rational transfer function is derived, thus arriving at a stable Blaschke product.

Systematic design via the method of inequalities

Based on the method of inequalities, we propose a systematic design method for SISO unity feedback systems. Using this method, we can take account of the influence of pole-zero cancellations. First, we derive a simple pole-zero placement algorithm which can achieve specified pole-zero cancellations, ensuring the steady state characteristics with the order of the controller fixed. Then we show how to modify the search algorithm by considering the properties of the tuning parameters. To illustrate the effectiveness of our method, we present a design example where the proposed design method is compared with another approach.

Simultaneous stabilizability of P and KP

It is shown that there exists a common controller which simultaneously stabilizes any given nominal plant P and perturbed plant KP for any given positive real constant K in the standard linear, time-invariant, multi-input multi-output unity-feedback system. The class of plants such that P and KP can be simultaneously stabilized for negative K is also determined.

Simultaneous stabilization of linear systems under stable additive or feedback perturbations

In the standard linear, time-invariant, multi-input multi-output unity-feedback system, it is shown that a given plant and one obtained by a known stable additive (or feedback) perturbation of this plant can be simultaneously stabilized by a common controller. The plant is not necessarily stable. No small-gain restrictions are imposed on the stable perturbations. A set of simultaneously stabilizing controllers is explicitly derived for any such pairs of plants. The results extend the standard single connected set of plants description in robust control design methods to two (possibly disjoint) sets of plants. >

Stabilization of linear systems under nonlinear stable diagonal perturbations

Stability of linear, time-invariant, multi-input multi-output unity-feedback systems is considered under nonlinear, time-varying, stable perturbations. Necessary and sufficient conditions are obtained for stability of the perturbed system and specialized for the case of one arbitrary failure whose location is unknown. Controller design methods are developed ensuring stability under an unknown stable failure of at most one arbitrary sensor or actuator.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Stabilizing controller design for linear systems with sensor or actuator failures

In this paper, the stability of the standard linear, time-invariant, multi-input multi-output unity-feedback system is investigated in the presence of either sensor or actuator failures. Any diagonal stable perturbation is included in the failure descriptions. Stabilizing controllers are synthesized for two failure classes: the first class allows at most one failure at a time; the second class requires at least one connection without failure. A parameterization of all stabilizing controllers is achieved with prior knowledge of the failure. A controller design method requiring no knowledge of the failure is also presented; this method is restricted to plants for which certain closed-loop transfer functions can be made diagonal.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

DESIGN OF A NEW CONTROLLER FOR A HYDRAULIC SERVOMECHANISM

This work deals with the investigation of the effect of a more recent, powerful control algorithm, called Pseudo Derivative Feedback, PDF, on the performance of a hydraulic servomechanism. The controlled system behavior is theoretically evaluated by developing a mathematical model for the controlled system and by using a computer simulation program. Also, the experimental measurement of the system dynamic performance is conducted. The developed simulation program is validated by comparing theoretical and experimental results of the system response. The simulation program is used to deduce a transfer function for the studied servomechanism. Once the transfer function of the controlled system is obtained, the control algorithm implementation is performed. To define the advantages of the proposed control algorithm, its output is compared to that of the already existing unity feedback system. Finally, A proposal for the design of the PDF controller is presented.