Pole Placement Technique Research Articles

Multi-input shaping design for vibration reduction

The performance of many flexible systems can be improved by employing command shaping techniques to reduce machine vibration. The input shaping technique, in particular, has proven to be highly effective for a wide class of systems. While most real systems are multi-input systems, however, the method has primarily only been developed for single-input systems. This paper presents an approach for designing multi-input shapers using an s-plane pole placement technique. Slightly more information about the system model is taken into account than has been traditionally done with input shaping designs. The input shaping sequences for all system inputs are solved for simultaneously, and the resulting designs lead to shorter impulse sequences than solving for input shaping sequences for each input independently of each other.

A simple optimal pole location technique for structural control

An optimal pole placement technique is proposed for the vibration control of a structure modeled as a single-degree-of-freedom system subjected to a white noise ground excitation. The objective of the proposed technique is to shift the closed-loop poles into a prescribed region in the complex plane using the smallest amount of control force variance. The Kuhn-Tucker necessary condition and the second order necessity and sufficiency theorem are used to solve for the control gain and the corresponding optimal pole locations in the prescribed region. Using independent modal space control theory, the algorithm is extended to the control of a multiple-degree-of-freedom system with incomplete state measurements using limited number of sensors. The performance and stability of the control algorithm are numerically verified on the control of two buildings. Two control devices, active tendon and active mass driver, are used to demonstrate the implementation of the current development. The results show that the technique provide an alternative design methodology for these two control devices to mitigate structural response due to earthquake excitation.

Extended pole placement technique and its applications for targeting unstable periodic orbit

In this paper we extend the pole placement technique in the case of one adjustable system parameter. The extended technique allows a more general choice of feedback forms, so it can improve the performance of the control system in many aspects. As an example of the application, we show how to target the unstable orbit from the corresponding stable one in the vicinity of a tangential bifurcation point without the need of knowing the location of the unstable orbit in advance. This technique can be used to obtain the unstable output related to bistability from an experimental device.

Robust digital control using pole placement with sensitivity function shaping method

SUMMARY It is shown in this paper that based on identified discrete-time models a robust digital linear controller can be designed using the pole placement method combined with sensitivity function shaping in the frequency domain. Two di⁄erent design techniques are presented. The first one is based on the shaping of the sensitivity functions using the fixed parts in the controller and the auxiliary poles of the closed loop while keeping the dominant poles in the desired places. The main idea of the second one is to determine a weighting filter for the output sensitivity function in an H = optimization approach which assures partial pole placement and desired performances. In this technique the weighting filter is interpreted as the inverse of the desired output sensitivity function and is computed using a constrained optimization program. The application of this technique on a flexible transmission system is presented. ( 1998 John Wiley & Sons, Ltd. The controller design methodology considered in this paper is based on pole placement combined with the shaping of the sensitivity function. The computation of the controller in the pole placement technique requires the specification of the desired closed-loop poles (the nominal stability problem) and of some fixed parts of the controller for the rejection of disturbances at various frequencies (the nominal performance problem). However, this is not enough to guarantee the robustness of the design with respect to the plant model uncertainties (the robust stability and robust performance problem). A robust controller design requires also the shaping of the sensitivity functions. The sensitivity functions, particularly the output sensitivity function, are key indicators for the nominal and robust performance as well as for the robust stability of the closed-loop system. The inverse of the maximum value of the output sensitivity function, i.e., the inverse of its H = norm, gives the minimum distance between the Nyquist plot of the open-loop system and the critical point [!1, j0]. This quantity, called the modulus margin, is a much more significant robustness indicator than the phase and gain margins. On the other hand, conditions for assuring a certain delay margin which is also a very important robustness indicator, particularly in the high frequency region, can also be expressed in terms of the shape of the output sensitivity function. It seems therefore reasonable to combine the pole placement with the shaping of the output

Stability and control of a parametrically excited rotating system. Part II: controls

In Part-I of this paper, the stability of a parametrically excited rotating system was analyzed. In this part the design of a feedback controller and an observer for the same mechanical system is considered. First, the time periodic system equations are transformed to a time invariant form which is suitable for an application of the standard techniques of linear control theory. A full-state feedback controller is designed in the transformed domain using the pole placement technique. Next, a Luenberger observer is constructed for estimating the unmeasurable states. Robustness of the observer is tested under the assumption that white noise is present in the measured states. Simulations for several combination of excitation and rotation parameters are provided.

Improving the robustness of H/sub ∞/-PSSs using the polynomial approach

This paper proposes a new design procedure of H/sub /spl infin//-PSS (H/sub /spl infin//-optimal PSS) by incorporating high-frequency roll-off into the design using improper weighting function. This design is based on the polynomial approach where the 'numerator-denominator' uncertainty representation is used for practical uncertainty representations. Furthermore, to improve the dynamic and transient stabilities of the control system, the partial pole placement technique is employed to reassign dominant poles at suitable locations in the left-half s-plane. The effectiveness of using /spl Delta//spl omega/ (shaft speed) input and /spl Delta/P/sub e/ (electrical power) input H/sub /spl infin//-PSSs to damp local oscillation modes is also investigated by comparing the performances of these H/sub /spl infin//-PSSs. Simulation results show that the proposed approach is effective in improving the performance and robustness of the system.

Controlling chaotic dynamical systems

We review the major ideas involved in the control of chaos. We present the Ott-Grebogi-Yorke (OGY) method of controlling chaos, which is a particular case of the pole placement technique, but which is the one leading to the shortest time to achieve the control of chaotic systems. Implementation using only measured time series in experimental settings is also described.

Chaos control with adjustable control times

We investigate a quasi-continuous extension of the Ott, Grebogi and Yorke (OGY) control method [ Phys. Rev. Lett., 1990, 64, 1196]. This extension allows one to raise the control frequency as high as is needed in order to stabilize unstable periodic orbits (UPOs) of high instability. To achieve this, the control requirement has to be chosen such that one can also cope with complex eigenvalues of the linearized flow. For this purpose, we use a variant of the pole placement technique. In a bronze ribbon experiment, we show the feasibility of this quasi-continuous control method. All control vectors are determined solely from the analysis of a scalar measurement signal. Finally, we show how the number of control steps needed can be minimized.

Relation between pole-placement and linear quadratic regulator for discrete-time systems

The relation between the pole placement technique and the optimal regulator technique of discrete time system is presented. It is shown that the closed loop system based on both techniques, and under certain conditions, has a common Lyapunov function. It bridges the gap between these two methods for discrete-time systems, and makes them more understandable.

Laboratory Kit for Heating Liquids Using Advanced Control Strategies

This work presents a laboratory kit designed for the purpose of controlling temperature in liquids. Many different control strategies can be easily evaluated by using this low cost kit. The results of comparative tests with PID controllers designed by two pole placement techniques are presented comprising the following alternatives: a controller with fixed parameters; and an adaptive controller using on-line recursive parameter estimation. These tests show the superior performance obtained with the adaptive strategy. Others interesting experiences comparing alternative control techniques could also be realised by using this inexpensive and useful laboratory kit.

Pole placement self tuning control for packed distillation column

In this paper, we present results from the successful application of pole placement self-tuning control for a packed distillation column in a pilot plant. The steady-state and dynamic behaviour of a binary packed distillation column has been simulated using a back mixing model. The model solution has been obtained employing orthogonal collocation on finite elements. A number of comparisons are made with results obtained both theoretically and experimentally. After a brief description of the pole placement self tuning algorithm the results are compared for the application at a SISO plant. A pseudo-random binary sequence and Bierman algorithm are used to estimate the relevant parameters of the system model. Pole-placement technique is applied to self-tuning proportional-integral-derivative (PID) control. Both experimental and theoretical works were carried out and results were compared.

Pole-Placement Technique for Magnetic Momentum Removal of Earth-Pointing Spacecraft

A linear pole-placement technique is presented for magnetic momentum removal of Earth-pointing spacecraft. First probed are the twomost commonly used momentum removal schemes, linear and bang-bangH £ B schemes (whereH is the excess angularmomentumvector andB is the geomagneticŽ eld vector), bothbased on a comparison between a constant disturbance torque and an averaged magnetic control torque acting on a spacecraft. Through analysis and illustrations, it is shown that these two methods lack a precise technique for determining control gains or strength (in ampere meter squared) of roll, pitch, and yaw electromagnets. As an alternative, a linear, closed-loop, pole-placement technique is devised, which correlates control gainswith the closed-loop pole locations and steady-state amplitudes of roll/yaw and pitch momentum under an orbit-averaged magnetic controller and disturbances. Special cases of lowand high-inclination orbits where pitch and yaw electromagnets, respectively, are ineffective are formulated. This new scheme and the mentioned two classical schemes of momentum removal are compared and illustrated, and generally applicable conclusions are drawn.

A transputer-based adaptive speed controller for AC induction motor drives with load torque estimation

In this paper, we design and implement an adaptive speed controller that can estimate load torque for AC induction motor drives employing a transputer-based parallel processing technique. The adaptive speed controller, which precedes the field-oriented control loop, consists of a two-degree-of-freedom controller and a feedforward load-torque compensator. The two-degree-of-freedom controller is designed by a pole-placement technique with polynomial manipulations. Its parameters are adjusted adaptively in terms of estimated model parameters. Estimating the model parameters entails a second-order least-squares estimator with constant trace to avoid estimator windup. The design of the feedforward compensator is based on an estimated load-torque model. Estimating the load torque entails a first-order least-squares estimator with variable forgetting factor and covariance resetting, the purposes of which are to detect any slow or sudden changes of torque disturbance, respectively. The resulting adaptive controller is implemented in parallel by IMS T800-20 transputers. Experimental results demonstrate the robustness of the proposed control method in contending with varying load and torque disturbance.

Controlling chaos in high dimensions

We review the major ideas involved in the control of chaos by considering higher dimensional dynamics. We present the Ott-Grebogi-Yorke (OGY) method of controlling chaos to achieve time periodic motion by utilizing only small feedback control. The time periodic motion results from the stabilization of unstable periodic orbits embedded in the chaotic attractor. We demonstrate that the OGY method, also applicable to high dimensions, is a particular case of the pole placement technique, and we argue that it is the one leading to shortest time to achieve control. Implementation using only a measured time series in experimental situations is described.

Enhancement of power system stability by using controlled series compensation

This paper studies the application of controlled series compensator (CSC) to damp power swings in multi-machine power systems. For the design of CSC damping controllers, a necessary step is the derivation of the linear state equation for the system. In order to consider the dynamics of the CSC, it is important to present the change in the CSC reactance as one of the state variables. In this case, unlike the traditional network representation, the network admittance matrix is no longer a constant matrix. Under this situation, the conventional linearization method for obtaining the linear state equation for the system must be modified. In this paper, a linear dynamic model for a multi-machine power system equipped with controlled series compensators (CSCs) is derived. Based on this linear dynamic model, a state feedback controller is designed for CSC control. The feedback control gains are obtained by using the pole placement technique. Given that CSCs are to be installed in a meshed system, the optimum location for installing CSCs is determined by analyzing the mode controllability. The effectiveness of this controller for damping the oscillations caused by power system disturbances is verified by simulation studies.

Robust indirect adaptive control of the electrohydraulic velocity control systems

A robust version of an indirect adaptive control scheme with self-excitation capability to the problem of controlling velocity of the electrohydraulic servosystems subject to unmodelled dynamics and load disturbances is proposed. The scheme contains an effective gradient least squares estimator using a dead zone technique and a certainty equivalence based adaptive controller. A design procedure for synthesising the adaptive controller is formulated by using the pole-placement technique, where a signal is created and fed back to the control law such that it has self-excitation capability and thus the stability of the closed-loop control system can be achieved. A series of simulations are performed to demonstrate the effectiveness of the proposed scheme. The results show that the proposed scheme is fairly robust to the control systems with uncertainties as well as improved performance characteristics, compared with that of the suboptimal PID control scheme with constant feedback gain and that of the adaptive model following control scheme.

A reduced-order dynamic model for end-effector position control of a flexible robot arm

The dynamic model of a robot arm composed of flexible beams and revolute joints is developed using a Rayleigh-Ritz based substructure synthesis technique and the linear theory of elastodynamics. Low-degree power functions in space variables of each substructure (beam) are adopted as shape functions for the purpose of discretization. Boundary conditions between substructures are then considered in the form of linear constraints of generalized (modal) coordinates and are enforced a posteriori, yielding the assembled dynamic system. This modified approach allows a systematic formulation which is independent of the problem characteristics and analyst's initiative, and allows a simpler reduced-order model with less degrees of freedom than those obtained by other discretization schemes, e.g. the finite element method. Using a pole placement technique and such a model for a robot arm with a revolute joint and a single flexible link carrying a payload, a state feedback controller is designed for the purpose of vibration suppression as well as trajectory tracking. The output signals consist of ''modal'' measurements provided by accelerometers and ''rigid'' angular velocity and position measurements provided by a tachometer and an optical shaft encoder on the motor shaft. Comparison of experimental and simulation results confirms the simplicity and validity of the proposed method.

Input Shaping Design for Flexible Systems with Multiple Actuators

This paper presents an approach for designing multi-input shapers using an s-plane pole placement technique. Slightly more information about the system model is taken into account than has been traditionally done with input shaping designs. The input shaping sequences for all system inputs are solved for simultaneously, and the resulting designs lead to shorter impulse sequences than solving for input shaping sequences for each input independently of each other.

Adaptive Pole-Placement Control with Input Saturations

This paper presents an adaptive pole-placement technique for SISO linear time-invariant stable systems with integrators subject to saturations on both the control variable and its increment. First, an antiwindup scheme is presented and BIBO stability is proven in the non adaptive case. In an adaptive context, BIBO stability is achieved by guaranteeing asymptotic convergence of the estimated parameters to their true values whenever saturations are likely to occurr. This is achieved by injecting a persistently exciting signal of arbitrarily small amplitude and automatically generated by the algorithm. Simulation results are reported to assess the performance of the method.

Adaptive control of nonminimum phase systems subject to unknown bounded disturbances

This paper presents a robust adaptive pole placement control scheme for continuous-time systems with bounded disturbances. The system may possibly be nonminimum phase and unstable. It is shown that for arbitrary bounded disturbances, a global asymptotical bounded-input/bounded-output (BIBO) stability is established through pole placement techniques without either introducing persistent excitation probing signals into the system or assuming any a priori knowledge on the plant parameters. Moreover, the disturbance upper bound is not assumed to be known. The system order is the only a priori knowledge required on the plant. The adaptive control law is free from singularities in the sense that the estimated plant model is always controllable.