Pole Placement Algorithm Research Articles

Proportional-retarded control of a quasi-zero-stiffness vibration isolator

This paper explores the control design and performance analysis of an active quasi-zero-stiffness vibration isolator utilizing the proportional-retarded (PR) control architecture. The PR architecture replaces the conventional “derivative” term in the proportional-derivative (or displacement-velocity) controller with the novel “retarded (time-delayed)” term, which is a new and effective way of active vibration suppression. Comprehensive gain-delay conjoint regulation strategies are developed for the strengthened isolation performance. For impact excitations, a complete stability analysis is conducted near the equilibrium position. Furthermore, a parameterized dominant pole placement algorithm is proposed to optimize the transient response of the PR-actuated isolator. Focusing on the rectangular pulse and long-duration step impacts, the algorithm adjusts the dominant poles to optimize the transient performance metrics, including the maximum displacement overshoot, steady-state displacement overshoot, and settling time. Regarding harmonic excitations, the delay-coupled effect is scrutinized for better low-frequency isolation performance, including the resonance frequency, nonlinear steady-state amplitude, multiple steady-state bands and nonlinearity elimination, equivalent active damping and stiffness, and absolute displacement transmissibility. In the case of random excitations, we demonstrate the superiority of the PR structure over the passive system.

POLE PLACEMENT OF LINEAR MULTIDIMENSIONAL SYSTEMS USING UNLIMITED RANK OUTPUT FEEDBACK

The problem of placing poles in linear multidimensional systems using a feedback matrix of unlimited rank is considered. The effect of output feedback of indefinite rank of the characteristic polynomial of a system with several variables is studied. The results are then used to obtain a recurrent pole placement algorithm without any restrictions on the rank of the output feedback matrix used. The algorithm is based on the pseudo-inverse concept of obtaining solutions to systems of linear equations using the least squares method and is computationally efficient.

Sterowanie układem lewitacji magnetycznej w warunkach zakłóceń stochastycznych

This paper presents the possibility of reducing impact of stochastic disturbances on the quality of control by implementation of state estimation using the extended Kalman filter algorithm. Experiments were carried out on the Inteco magnetic levitation laboratory system, which mathematical model is nonlinear. A control method with the use of a state vector and a pole placement algorithm was adopted for the model which was linearized at the selected working point. For different levels of noise in the measurement signal, the operation of the system with a feedback from the measured and estimated state was tested. In order to assess the regulation, the quality of the algorithm was verified for both implementations of the feedback. The obtained time plots of each state variable were compared and the calculated integral quality indices, based on the control error, were compared. The quality of the estimation was assessed on the basis of the following mean square error and based on the errors between estimation and measurements indices. The controller was synthesized on thebasis of the continuous model, and then its discrete form was numerically implement as the extender Kalman filter algorithm. The executive blocks were synchronized with the selected sampling period. The results of the performed research allow to conclude about the advantage of control in the system in which the information about the state vector from the estimation is taken, in comparison with the direct feedback without Kalman filtering.

Soft variable structure control of linear fractional-order systems with actuators saturation

In this paper, a new method of soft variable structure control for Fractional-Order System (FOS) is proposed to achieve faster response while the control signal is continuous and satisfies actuators’ constraints. Our proposed method, by describing a desired commensurate FOS, with the help of a pole placement algorithm and applying an optimization routine, in the form of a procedure, leads the system to the desired character. The routine is done by solving an optimization problem subject to a control signal constraint qua we obtain the fastest response possible in the sense of stability region. The sufficient condition of stability of the control system is developed based on the stability theory of Fractional Order (FO) linear differential equations, and attributes of the Mittag-Leffler function. Finally, an example and corresponding numerical simulations are presented to show the efficiency of the proposed method. In the proposed method, a new control strategy for the FOS is presented, a complex problem is solved in a simple way, and it can exploit the benefits of using FOS in the modeling and control of complex physical phenomena.

State-Space PID: A Missing Link Between Classical and Modern Control

PID control is widely applied in industry. However, it is classified as a classical control technique, in that transfer function method is used to represent the ideal and/or practical PID controller. Modern control concepts, such as state feedback, observer, are seldom found in PID research. This paper proposes a state-space PID structure to fill the gap. The classical ideal PID is first shown to be a state-feedback control structure with the plant output and its derivative and integral as the states, and then a model-independent observer is proposed to estimate the states, thus approximate the ideal PID as a observer-based state feedback control structure (state-space PID). Then it is shown that the proposed state-space PID structure is the dual of the linear active disturbance rejection control structure, and it is a general-purposed control structure in that any strictly-proper linear controller with integration can be implemented via the proposed structure. The design of the state-space PID can be done via the well-known pole placement algorithm in modern control. Simulation and experiment results show that state-space PID structure is a practical implementation of ideal PID, which naturally integrates the noise reduction that is separated from PID tuning, and it is a natural generalization of the classical PID to high-order cases.

Transient Behaviour Analysis and Design for Platoons with Communication Delay

A novel approximation-based dominant eigenvalue computation and pole placement algorithm for platoons with communication delay is presented in this paper. The proposed approximation method is based on a smallness inequality, which the communication delay and the control system gains have to satisfy. The proposed approximation method creates a system of ordinary differential equation which has the same degree as the system of delay differential equation model and has the same eigenvalues as the dominant eigenvalues of the original system, with a given precision. A control design approach is proposed for platoons with communication delay using the obtained approximation model, which ensures the stability of the controlled platoon with prescribed dynamics. The proposed algorithms are validated with simulations considering a platoon of small size, mobile robots.

Samopodesivi regulator baziran na kaskadnom upravljanju temperaturom kod egzotermne reakcije mešanog sredstva u rezervoaru reaktora

In the process of chemical industries production, an exothermic stirred tank reactor permits the reaction to release the heat due to mixing of substances. The release of heat due to the exothermic process in the stirred tank makes the system nonlinear and uncertain unless it is not regulated properly. In order to regulate the heat release, the self-regulated cascade control model of reactor temperature plant is developed with reference to material and energy balance model of exothermic stirred tank reactor. In this paper the recursive least square algorithm is used for self-tuning regulator cascade control online temperature plant and its controller parameters estimation and also the temperature plant output has been simulated in the presence and absence of a primary self-tuning controller. The use of the secondary loop PI controller will respond rapidly to the flow rate of cooling jacket plant that in turn cascade with the disturbance variables like inlet feed concentration and cooling water temperature. The reactor temperature is monitored to the desired steady state level and becomes stable for further steady state value of parameters. The parameters of the temperature plant will also be stable with online parameter estimating loop of the control system. The designing of master controller and desired plant model using minimum degree pole placement algorithm is highlighted. With the developed SIMULINK design of self-tuning controller, the better comparative results have been achieved over Internal Model Control (IMC), Model Predictive Control (MPC) and conventional based temperature controller plant.

Adjustment of Pole Placement Algorithm Based on Vulnerability Reduction of Skewed Bridges

Skewed bridges due to the specific dynamic characteristics have shown vulnerability in recent strong earthquakes. In this study, an active control strategy is employed to optimize the seismic performance of a typical model of such structures. As the control algorithm, the pole placement method has been used, of which the key factor is selection of desired poles to achieve desired dynamic responses. A performance index (PI) was defined as a function of displacement and rotation of a bridge deck. The desired poles for the algorithm were extracted by optimizing this index. A previously presented and approved simplified model of a skewed bridge with the three degrees of freedom was selected as a typical model, and the methodology was applied on this model. The optimization of PI was carried out by a series of time-history analysis. Ten far-field ground-motion records presented in FEMA-P695 were used for this purpose. The PI was calculated for a range of damping ratio and frequency of the system, and the desired poles were selected for the optimum values of PI. The results show that the control of the model using the selected pole by this method could effectively reduce the displacement and rotation of the bridge model.

Multistage Angular Momentum Management for Space Station Attitude Control

A multistage attitude control and momentum management (ACMM) control strategy is proposed for space stations. The ACMM, which includes closed-loop angular momentum feedback (CAMF) and torque equilibrium attitude (TEA) tracking, is achieved using the gravity gradient and an aerodynamic torques. The CAMF is employed as the normal flight mode, and TEA tracking is used to unload the angular momentum after attitude stabilization. Hence, the angular momentum imparted by the attitude control device does not need to be unloaded using thrusters during the entire operating phase. The system performances, especially the relationship between the environmental torques and the attitude, are analysed. The internal model principle is utilized to suppress the attitude fluctuation during the CAMF mode, and a quintic polynomial is utilized to realize TEA tracking. The pole placement algorithm, which can obtain the feedback matrix in the linear quadratic regulator (LQR) without choosing a weight matrix, is introduced to design the LQR controllers. This approach is demonstrated for a future Chinese space station, and the simulation results verified the effectiveness of the proposed control algorithm.

Robust Switching Control and Subspace Identification for Flutter of Flexible Wing

Active flutter suppression and subspace identification for a flexible wing model using micro fiber composite actuator were experimentally studied in a low speed wind tunnel. NACA0006 thin airfoil model was used for the experimental object to verify the performance of identification algorithm and designed controller. The equation of the fluid, vibration, and piezoelectric coupled motion was theoretically analyzed and experimentally identified under the open‐loop and closed‐loop condition by subspace method for controller design. A robust pole placement algorithm in terms of linear matrix inequality that accommodates the model uncertainty caused by identification deviation and flow speed variation was utilized to stabilize the divergent aeroelastic system. For further enlarging the flutter envelope, additional controllers were designed subject to the models beyond the flutter speed. Wind speed was measured online as the decision parameter of switching between the controllers. To ensure the stability of arbitrary switching, Common Lyapunov function method was applied to design the robust pole placement controllers for different models to ensure that the closed‐loop system shared a common Lyapunov function. Wind tunnel result showed that the designed controllers could stabilize the time varying aeroelastic system over a wide range under arbitrary switching.

Stabilization of Lossless Propagation Time-Delay Systems

Problem of constructing finite-dimensional stabilizing controllers for a class of linear time-invariant neutral time-delay systems, namely lossless propagation time-delay systems, is considered while the effect of small time-delay perturbations on stability is taken into account. For this purpose, a dynamic output feedback controller design approach which provides more flexible and automated design of the controller than previously proposed design approaches based on the continuous pole placement algorithm is proposed. A design example is also presented, to demonstrate the proposed approach.

Pole placement algorithm for control of civil structures subjected to earthquake excitation

In this paper the control algorithm for controlled civil structures subjected to earthquake excitation is thoroughly investigated. The objective of this work is the control of structures by means of the pole placement algorithm, in order to improve their response against earthquake actions. Successful application of the algorithm requires judicious placement of the closed-loop eigenvalues from the part of the designer. The pole placement algorithm was widely applied to control mechanical systems. In this paper, a modification in the mathematical background of the algorithm in order to be suitable for civil fixed structures is primarily presented. The proposed approach is demonstrated by numerical simulations for the control of both single and multi-degree of freedom systems subjected to seismic actions. Numerical results have shown that the control algorithm is efficient in reducing the response of building structures, with small amount of required control forces.

Decentralized controller design by continuous pole placement for neutral time-delay systems

The stabilizing decentralized controller design problem for (possibly descriptor-type) linear time-invariant neutral time-delay systems is considered. A design approach, based on the continuous pole placement algorithm and the decentralized pole assignment algorithm, is proposed. A design example is also presented, to demonstrate the proposed approach.

Strong Stabilization of Lossless Propagation Time-Delay Systems by Continuous Pole Placement

Stabilizing controller design problem for a class of LTI neutral time-delay systems, namely lossless propagation time-delay systems, is considered. Effect of small time-delay perturbations on the stability is also taken into account. A dynamic output feedback controller design approach, based on the continuous pole placement algorithm, is proposed. A numerical example is also presented to demonstrate the proposed approach.

Decentralized Controller Design by Continuous Pole Placement for Incommensurate-Time-Delay Systems

Decentralized controller design problem for linear time-invariant retarded incommensurate-time-delay systems is considered. A design approach based on the decentralized pole assignment algorithm and the continuous pole placement algorithm is proposed. An example is also presented to demonstrate the proposed design approach.

Mode tuning of a simplified string instrument using time-dimensionless state-derivative control

In recent years, there has been a growing interest in smart structures, particularly in the field of musical acoustics. Control methods, initially developed to reduce vibration and damage, can be a good way to shift modal parameters of a structure in order to modify its dynamic response. This study focuses on smart musical instruments and aims to modify their radiated sound. This is achieved by controlling the modal parameters of the soundboard of a simplified string instrument. A method combining a pole placement algorithm and a time-dimensionless state-derivative control is used and quickly compared to a usual state control method. Then the effect of the mode tuning on the coupling between the string and the soundboard is experimentally studied. Controlling two vibration modes of the soundboard, its acoustic response and the damping of the third partial of the sound are modified. Finally these effects are listened in the radiated sound.

Design and stability analysis of adaptive fuzzy feedback controller for nonlinear systems by Takagi–Sugeno model-based adaptation scheme

This paper focuses on the design of a real-time adaptive Takagi---Sugeno (T---S) fuzzy-based dynamic feedback tracking controller to deal with the metallic sphere position control of a magnetic levitation system (MLS), which is an intricate and highly nonlinear system involving plant uncertainties and external disturbances. The dynamic model of this MLS is first constructed based on the concepts of geometry and motion dynamics. The objective of this proposed control strategies is to design a real-time adaptive controller with the help of Takagi---Sugeno type fuzzy-based output feedback techniques and to directly ensure the asymptotic stability of the closed-loop controlled system by Lyapunov stability theorem without the requirement of strict constraints, detailed system information, and auxiliary compensated controllers. Proposed adaptive tracking controller is developed in such a way such that all the states and signals of the closed-loop system are bounded and the trajectory tracking error is as small as possible. In this paper, the controller consists of adaptive and robustifying components whose role is to nullify the effect of uncertainties and achieve a desired tracking performance. Here, separate adaptive control laws have been proposed to automatically take care of external disturbance and uncertainties by designing a two-port controller. The first part stabilizes the nominal plant; without modeling uncertainties. The second part of the controller is to reject modeling uncertainties. The good transient control performance and robustness to uncertainties of the proposed adaptive control scheme for the MLS is verified by numerical simulations and real-time experimental results. These results demonstrate that, the proposed adaptive controller yields favorable control performance superior to that of PID and and Neuro-fuzzy network controller in terms of overshoot, settling time, mean square error and steady-state error and also it can guarantee the system stability and parameter convergence with a pole placement algorithm.

Seismic response of active or semi active control for irregular buildings based on eigenvalues modification

A reduction of the response of irregular structures subjected to earthquake excitation by control devices equipped by suitable control algorithm is proposed in this paper. The control algorithm, which is used, is the pole placement one. A requirement of successful application of pole placement algorithm is a definition-selection of suitable poles (eigen-values) of controlled irregular structures. Based on these poles, the required action is calculated and applied to the irregular structure by means of control devices. The selection of poles of controlled irregular structure, is a critical issue for the success of the algorithm. The calculation of suitable poles of controlled irregular structure is proposed herein by the following procedure: a fictitious symmetrical structure is considered from the irregular structure, adding vertical elements, such as columns or shear walls, at any location where is necessary. Then, the eigen-values of symmetrical structure are calculated, and are forced to be the poles of irregular controlled structure. Based on these poles and additional damping, the new poles of the controlled irregular structure are calculated. By pole placement algorithm, the feedback matrix is obtained. Using this feedback matrix, control forces are calculated at any time during the earthquake, and are applied to the irregular structure by the control devices. This procedure results in making the controlled irregular structure to behave like a symmetrical one. This control strategy can be applied to one storey or to multi-storey irregular buildings. Furthermore, the numerical results were shown that with small amount of control force, a sufficient reduction of the response of irregular buildings is achieved.

Feedback norm minimisation with regional pole placement

This article proposes a convex algorithm for minimising an upper bound of the state feedback gain matrix norm with regional pole placement for linear time-invariant multi-input systems. The inherent non-convexity in this optimisation is resolved by a combination of two separate approaches: (1) an inner convex approximation of the polynomial matrix stability region due to Henrion and (2) a novel convex parameterisation of column reduced matrix fraction system representations. Using a sequence of approximations enabled by the above two methods, it is shown that the constraints on closed-loop poles (both pre-specified exact locations and regional placement) define linear matrix inequalities. Finally, the effectiveness of the proposed algorithm is compared with similar pole placement algorithms through numerical examples.

A Wavelet‐Based Adaptive Pole Assignment Method for Structural Control

AbstractThis article presents a time varying wavelet‐based pole assignment (WPA) method to control seismic vibrations in multi‐degree of freedom (MDOF) structural systems. The discrete wavelet transform is used to determine the energy content over the frequency band of the response in real time. The frequency content was implemented in the Big Bang–Big Crunch algorithm to update the optimum values of the closed‐loop poles of the structural system adaptively. To calculate optimum gain matrix, a robust pole placement algorithm was used. The gain matrix is calculated online based on response characteristic in real time and must not be calculated a priori (offline) choice. The WPA is tested on a 10‐story structural system subject to several historical ground motions. It is observed that the WPA has advantages in some design problems. Numerical examples illustrate that the proposed approach reduces the displacement response of the structure in real time more than conventional linear quadratic regulator (LQR) controller.