Showing papers on "Closed-loop pole published in 2014"

Evolutionary optimisation and real-time self-tuning active vibration control of a flexible beam system

Abstract: Active vibration control has long been recognised as a solution for flexible beam structure to achieve sufficient vibration suppression. The flexible beam dynamic model is derived according to the Euler Bernoulli beam theory. The resonance frequencies of the beam are investigated analytically and the validity was experimentally verified. This thesis focuses on two main parts: proportional-integralderivative (PID) controller tuning methods based on evolutionary algorithms (EA) and real-time self-tuning control using iterative learning algorithm and poleplacement methods. Optimisation methods for determining the optimal values of proportional-integral-derivative (PID) controller parameters for active vibration control of a flexible beam system are presented. The main objective of tuning the PID controller is to obtain a fast and stable system using EA such as genetic algorithm (GA) and differential evolution (DE) algorithms. The PID controller is tuned offline based on the identified model obtained using experimental input-output data. Experimental results have shown that PID parameters tuned by EA outperformed conventional tuning method in term of better transient response. However, in term of vibration attenuation, the performance between DE, GA and Ziegler-Nichols (ZN) method produced about the same value. For real-time selftuning control, successful design and implementation has been accomplished. Two techniques, self-tuning using iterative learning algorithm and self-tuning poleplacement control were implemented to adapt the controller parameters to meet the desired performances. In self-tuning using iterative learning algorithm, its learning mechanism will automatically find new control parameters. Whereas the self tuning pole-placement control uses system identification in real time and then the control parameters are calculated online. It is observed that self-tuning using iterative learning algorithm does not require accurate model of the plant and control the vibration based on the reference error, but it is unable to maintain its transient performance due to the change of physical parameters. Meanwhile, self-tuning poleplacement controller has shown its ability to maintain its transient performance as it was designed based on the desired closed loop poles where the control system can track changes in the plant and disturbance characteristics at every sampling time. Overall results revealed the effectiveness of both control schemes in suppressing the unwanted vibration over conventional fixed gain controllers.

Tuning rules for a quick start up in Dynamic Matrix Control

Abstract: This paper pretends to offer design rules for the parameters adjustment of the Dynamic Matrix Control (DMC) to allow an easier starting up. The effect on the time response of each algorithm parameter that can be tuned by the user is studied in an unconstrained system. To this aim, the position of the closed loop poles of the equivalent system is calculated. To simplify the study and to obtain more direct conclusions the number of poles will be limited using a First Order Plus Death Time simplification of the real plant. Design rules proposed in this study are tested in some simulated benchmarks and in a real plant.

On Transfer Functions Realizable with Active Electronic Components

Abstract: In this work, we characterize transfer functions that can be realized with standard electronic components in linearized form, eg those commonly used in the design of analog amplifiers (including transmission lines) in the small signal regime We define the stability of such transfer functions in connection with scattering theory, ie in terms of bounded reflected power against every sufficiently large load In the simplest model for active elements, we show that unstable transfer functions exist which have no pole in the right half-plane Then, we introduce more realistic transfer functions for active elements which are passive at very high frequencies, and we show that they have finitely many poles in the right half-plane Finally, in contrast to the ideal transfer functions studied before, the stability of such "realistic" transfer functions is characterized by the absence of poles in the open right half-plane and the positivity of the real part of the residues of the poles located on the imaginary axis This report is written in a way which is suitable to the non-specialist, and every notion is defined and analyzed from first principles

PM diagram of the transfer function and its use in the design of controllers

Abstract: This paper presents the graphical chromatic representation of the phase and the magnitude of the transfer function G(s) of a system and its educational use in the design of the most typical controllers. The magnitude is represented in decibels and the phase is represented by colours. This representation permits to put a face to the transfer functions, deepening our intuitive understanding of transfer functions. An important characteristic of this diagram is that permits to read the phase and the gain margins directly and the imaginary axis cut represents the Bode diagram. It permits to see intuitively the connexions among the different diagrams. It is also possible to put the grid with damping ratio ζ and frequency ω n . In summary, this PM diagram can be useful, especially in Control Education because improves the intuition about transfer functions, and it can be used in a Classical Control Course to complement the design of controllers using the Root Locus diagram.

State Derivative Feedback Control Application for Pole Placement Problem

Abstract: The pole placement is one of the most important methods for designing controller for linear systems. In this paper work a procedure for solving the pole-placement problem for a linear time-invariant single-input/single output (SISO) systems by state-derivative feedback is described. Pole placement design to place all closed-loop poles at desired locations. In this paper, we shall prove that a necessary and sufficient condition that the closed -loop poles can be placed at any arbitrary locations in the s-plane is that the system be completely state controllable. Then we shall discuss methods for determine the required state feedback gain matrix (12). Keywords—Characteristics Polynomial, Feedback gain matrix, Pole placement, State Derivative feedback.

Comparing 2DOF PI and DO-FPI controllers for the first-order plants

Abstract: The paper compares a traditional two-degree-of-freedom PI controller (2DOF PI) with a disturbance observer based filtered PI control (DO FPI) with scalable filtering properties. Analytical tuning of both control loops is based on specifying position of their double real dominant poles. As in the papers [1], [2], a core structure of a filtered P controller (with adjustable filtering properties) is augmented to the DO FPI controller with an integral action based on an load (input) disturbance reconstruction using inversion of the plant dynamics. Thereby, the introduced filters may take arbitrary order by simultaneously keeping fixed position of the double dominant closed loop pole which enables noise attenuation adjustment without a necessity to repeat analysis of the optimal P controller tuning. This new simple modular approach is compared with the traditional 2DOF PI controller with an equally specified double real dominant pole. This one-parameter tuning procedures illustrated by an example of an optical plant control show possibilities of a significant increase of the closed loop performance by simultaneously remaining to be simple and transparent enough.

Partial pole placement in LMI region

Abstract: A new approach for pole placement of single-input system is proposed in this paper. Noncritical closed loop poles can be placed arbitrarily in a specified convex region when dominant poles are fixed in anticipant locations. The convex region is expressed in the form of linear matrix inequality (LMI), with which the partial pole placement problem can be solved via convex optimization tools. The validity and applicability of this approach are illustrated by two examples.

Optimized tuning method of stationary frame Proportional Resonant current controllers

Abstract: This paper presents an optimized tuning method of Proportional Resonant (PR) current controllers implemented in the stationary frame. The approach consists of defining three operation regions based on behavior of the closed loop poles, and of determining simplified tracking and disturbance transfer functions for each of these regions. Charts of proportional and resonant normalized gains versus settling time and overshoot are then built, allowing the designer to easily visualize the influence of these gains on the transient response. It is shown that the disturbance response performance is more significant than the tracking one, and that minimum settling time and overshoot for this case are obtained if the resonant gain is set equal to the controller resonant frequency, providing a simple and efficient rule-of-thumb for the designer. Simulation and experimental results are presented to validate the method.

Direct adaptive regulation in the vicinity of low damped complex zeros — Application to active vibration control

Abstract: The adaptive feedback approach is now widely used for the rejection of multiple narrow band disturbances with unknown and time varying frequencies in Active Vibration Control (AVC) and Active Noise Control (ANC). The approach is based directly or indirectly on the use of the Internal Model Principle and the Youla-Kucera parametrization combined with an adaptive law. All the algorithms associated with the approach make the assumption that the plant zeros are different from the poles of the disturbance model in order to achieve disturbance compensation. However in practice the problem is more intricate since it is not clear what happens if the plant have very low damped complex zeros (often encountered in mechanical structures) and the frequency of the disturbance is close to the anti-resonance frequency (the resonance frequency of the plant zeros). A recent international investigation on adaptive regulation in the presence of unknown time varying disturbances [16] has considered such a situation for a benchmark example. Several solutions have been proposed and the most successful has been based on the appropriate choice of the desired closed loop poles to be achieved by the Youla-Kucera central controller [5] using a Q FIR filter with the minimum number of parameters. Recently in [12] it was suggested that over parametrization of the Q (FIR) filter can enhance the robustness of the linear and adaptive scheme in the vicinity of plant complex zeros. The present paper compares these two approaches using the same benchmark example as in [16]. The results from simulations and real time experiments used to evaluate the two approaches are presented.

Controller order reduction with pole region constraint

Abstract: The problem of finding a low order output feedback dynamic controller for multi-input multi-output linear systems is considered. The resulting closed loop poles are placed within a pre-specified region in the complex plane. The matrix fraction descriptions of the plant and controller are parameterized using the eliminant matrix. The non-convex constraints imposed by the regional pole placement requirement on the resulting polynomial matrices, are convexified using a well known LMI based inner approximation method for polynomial stability region. The approximated convex problem is shown to be a semidefinite program solvable by standard optimization tools.

Eigenvalue structure of the predictor feedback for discrete-time LTI systems

Abstract: The discrete-time predictor feedback system was designed to compensate for constant input delays based on d-step ahead state predictions in discrete-time linear time-invariant systems. The entire spectrum, initially investigated by numerical computation, shows that aside from the eigenvalues of A + BK, there are other eigenvalues located about the origin. Existing literature only focuses on the spectrum coinciding with that of A + BK, but, in this study, we extended previous results by considering the full state of the system to obtain the eigenvalues mathematically. In contrast to the continuous-time case, it is important to note that the discrete-time delay system is finite-dimensional. From this viewpoint, we started our analysis from the state space representation to construct a proof that derives the poles of the closed-loop system. Furthermore, as a preliminary step, we attempt a frequency domain analysis by considering nonzero initial conditions in taking the Z-transform of the system with an example.

Design and implementation of RST controllers for a nonlinear system

Abstract: This paper aims at developing an efficient controller for a nonlinear system. This necessitates identifying a near accurate model using the data acquired through real time experimentation conducted on the laboratory level process. An offline parametric estimation method is used to obtain discrete-time models for various operating regions. Three different digital polynomial controllers are designed and implemented to achieve the desired dynamics of the reference model. In order to obtain further improvement in the desired performance closed loop poles are relocated by Pole placement technique. The objective of this work also includes a comparative analysis of performances of the chosen system when implementing all these four strategies under different operating regions. The design and simulation studies are carried out in MATLAB/SIMULINK platform.

Robust Stability Clearance of Flight Control Law Based on Global Sensitivity Analysis

Abstract: To validate the robust stability of the flight control system of hypersonic flight vehicle, which suffers from a large number of parametrical uncertainties, a new clearance framework based on structural singular value ( ) theory and global uncertainty sensitivity analysis (SA) is proposed. In this framework, SA serves as the preprocess of uncertain model to be analysed to help engineers to determine which uncertainties affect the stability of the closed loop system more slightly. By ignoring these unimportant uncertainties, the calculation of can be simplified. Instead of analysing the effect of uncertainties on which involves solving optimal problems repeatedly, a simpler stability analysis function which represents the effect of uncertainties on closed loop poles is proposed. Based on this stability analysis function, Sobol’s method, the most widely used global SA method, is extended and applied to the new clearance framework due to its suitability for system with strong nonlinearity and input factors varying in large interval, as well as input factors subjecting to random distributions. In this method, the sensitive indices can be estimated via Monte Carlo simulation conveniently. An example is given to illustrate the efficiency of the proposed method.

Investigation of robust stability analysis for interval system

Abstract: The main objective of the present work is to investigate the robustness of the interval system In this paper robust stability analysis of closed loop system is presented using simplified conditions of Arguon's theorem which is comparatively efficient and expeditious than that by Kharitonov's theorem Here it has been shown that even if the closed loop pole lies in the left half of s-plane the system may exhibit unstable response under perturbed condition

Design of the general multi-capacity inertia standard transfer function

Abstract: Standard transfer function based design is a kind of simple and practical approach for establishment of the controllers in industrial applications. Based on Binomial Theorem and Hui Yang Triangle, a kind of general multi-capacity inertia(MCI) standard transfer function with the characteristics of non-overshoot and no limit for the system order is proposed. The type of the MCI standard transfer function is demonstrated to be determined via a simple algebraic operation. Dynamic performance simulations on the step and the ramp response have validated the superiority of the proposed standard transfer function. The inherent relation between the inertia time constant and the settling time is also discussed.

Orthonormal basis functions applied to optimal control design with closed-loop pole location constraints

Abstract: This article proposes an optimal control design technique to ensure that the closed-loop poles are assigned to prescribed locations in the complex plane. A key element in this approach is the usage of orthonormal basis functions to parametrise the main design parameter. This goal is achieved by using a quadratic cost based optimisation approach, considering control effort penalisation as well as cheap control. Youla parametrisation is used, subject to a set of constraints which guarantee stability, zero steady error to constant references and disturbances, and yielding the prescribed set of closed-loop poles.

Centralised Multi-input Multi-output Controllers for Non-minimum Phase Systems

Abstract: In the present work, the method of designing the centralised controllers for the minimum phase multivariable systems proposed by Vijay Kumar et al. is extended to non-minimum phase systems. The controller is designed based on the direct synthesis method. Inverse of process transfer function matrix in the direct synthesis method is approximated based on relative gain array concept. Maclaurin's series is applied to reduce it to a standard proportional and integral form. The method is further improved by using equivalent transfer function matrix derived from relative normalised gain array and relative average residence time array as process inverse transfer function matrix. Effective transfer function is the equivalent transfer function of gij(s) when all other loops are closed. The desired closed-loop transfer function should contain the process right half plane zero. Quadruple tank process with non-minimum phase behaviour is considered to analyse the performance of the proposed centralised controll...

Multi-loop aircraft model cluster flutter restraining composite root locus multistage PID (Proportion Integration Differentiation) robust controller design method

Abstract: The invention provides a multi-loop aircraft model cluster flutter restraining composite root locus multistage PID (Proportion Integration Differentiation) robust controller design method. The method comprises the following steps: directly determining to obtain a model cluster constructed by amplitude frequency and phase frequency features in a full envelope by means of frequency sweeping flight test under the condition that different heights and Mach numbers are given; giving a closed loop pole distribution limitation index under corresponding root locus description through multi-loop model equivalence according to an amplitude frequency margin in the flight envelope and a phase margin military standard requirement, determining the stage number and parameter value of a multistage PID robust controller by adding the multistage PID robust controller, the closed-loop pole distribution limitation index in the full envelope of an air craft and a model identification method in system identification; designing a low-altitude flight aircraft which is accordant with the full envelope, can be used for restraining flutter, has low overshot and is stable on the basis of the concept of closed-loop pole distribution limitation under root locus description.