The Root Locus Plot

The pole assignment problem for distributed parameter systems governed by analytic semigroups is discussed. Introducing unbounded feedback operators, we can solve the problem under a weaker restriction on the separation of the open-loop and the closed-loop poles. These types of feedback systems inherit the spectrum determined growth assumption of the open-loop systems. We first present a characteristic equation whose roots are the poles of the closed-loop system. Next we give a feedback element which realizes the desired pole assignment of the closed-loop system. We show an interesting result that an infinite number of the open-loop poles can be uniformly moved by means of a suitable linear feedback. We apply the results -to a heat system and a flexible structure for the cases of distributed controls and boundary controls.

Abstract: Implantable closed-loop epilepsy controllers require ideally both accurate epileptic seizure detection andlow power consumption. On-chip oscillators can be used in implantable devices because they consume less powerthan other oscillators such as crystal oscillators. In this study, we investigated the tolerable error range of a lowerpower on-chip oscillator without losing the accuracy of seizure detection. We used 24 ictal and 14 interictal intrac-ranial electroencephalographic segments recorded from epilepsy surgery patients. The performance variations withrespect to oscillator frequency errors were estimated in terms of specificity, modified sensitivity, and detection timingdifference of seizure onset using Generic Osorio Frei Algorithm. The frequency errors of on-chip oscillators wereset at ± 10% as the worst case. Our results showed that an oscillator error of ± 10% affected both specificity andmodified sensitivity by less than 3%. In addition, seizure onsets were detected with errors earlier or later than with-out errors and the average detection timing difference varied within less than 0.5 s range. The results suggest thaton-chip oscillators could be useful for low-power implantable devices without error compensation circuitry requiringsignificant additional power. These findings could help the design of closed-loop systems with a seizure detector andautomated stimulators for intractable epilepsy patients.Key words: implantable biomedical devices, low power, on-chip oscillators, performance evaluation, seizure detector

The aim of this paper is to investigate the application possibilities of a self-tuning control method to a pressurized-water reactor (PWR) nuclear power plant. A self-tuning control algorithm which incorporates pole assignment into the generalized minimum variance strategy with a particular form of cost function is employed. This algorithm enables closed-loop system stability characteristics to be readily specified and facilitates reference following. The control system design is based on a second-order linear model with unknown, time-varying parameters. To ensure that this low-order model describes the complex real dynamics well enough for control purposes, control parameters are updated on-line with a recursive estimation sequences of the extended least-squares method. Weighting polynomials are also adjusted on-line to keep closed-loop poles at the desired location and to satisfy the zero steady-state condition and disturbance rejection. The purpose of this control system is to hold the average coolant ...

Of all the closed-loop poles of feedback control systems, the three or sometimes two closed-loop poles in the neighbourhood of the cross-over frequency ωc at which the open-loop transfer function, G(s) reduces to unity in magnitude plays the decisive role in shaping the major form of the transient response of the system. However, the evaluation of the closed-loop real poles of higher-order feedback systems in the vicinity of the cross-over frequency ωc (without use of a digital computer) is highly time-consuming and tedious. This paper presents a procedure entitled “Iterative deviation averaging method” for the rapid evaluation of the real-closed loop poles in the neighbourhood of ωc, The procedure is illustrated with a simple example.

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.

Several magnetically levitated transport systems have been constructed, tested and constantly improved. Various technologies for the magnetic levitation system are also being developed and some of them use electromagnets for the vehicle levitation. In this work, an electromagnetically levitated vehicle prototype is studied. The vehicle levitation is achieved through the control of the gaps of these electromagnets. The constructed prototype will have independent levitation and propulsion systems; this paper considers only the magnetic levitation system. The resultant system is open loop unstable and highly nonlinear with a very restrictive equilibrium region. A SISO analytical model and closed loop identification experiments are also presented. The emphasis in this paper is related to design procedures of H/sub 2/ and H/sub /spl infin// controllers applied to the electromagnetic levitation system. For the designs of these controllers, a weighting function is employed to attenuate a resonance peak at low frequencies in the closed loop system. The results show that closed loop system responses with the H/sub 2/ and H/sub /spl infin// controllers are very similar but with better performance than the response obtained with a classical theory controller.

This paper formulates an original hierarchical self-tuning control procedure to enhance the disturbance-rejection capability of under-actuated rotary pendulum systems against exogenous disturbances. The conventional state-feedback controllers generally make a trade-off between the robustness and control effort in a closed-loop system. To combine the aforementioned characteristics into a single framework, this paper contributes to develop and augment the baseline Linear-Quadratic-Regulator (LQR) with a novel “adjustable degree-of-stability design” module. This augmentation dynamically relocates the system's closed-loop poles in the stable (left-half) region of the complex plane by dynamically adjusting a single hyper-parameter that modifies the constituents of LQR's performance index. The hyper-parameter is adaptively modulated online via a pre-calibrated hyperbolic-secant-function that is driven by state-error variables. The performance of the proposed adaptive controller is benchmarked against fixed-gain controllers via credible hardware experiments conducted on the standard QNET Rotary Pendulum setup. The experimental outcomes indicate that the proposed controller significantly enhances the system's robustness against exogenous disturbances and maintains its stability within a broad range of operating conditions, without inducing peak servo requirements.

An important characteristic of flexible multibody systems containing closed-loop topologies is that the component modes used to describe individual bodies will no longer be independent because of loop closure constraints. Thus, the issue of component modal selection becomes even more complicated. In addition, the foreshortening effect that has been studied extensively in the literature in the context of open-loop topologies will also be present in these constraint equations. Simulation results presented demonstrate the effects of modal selection and foreshortening on the dynamic response of closed-loop flexible systems.

When designing controllers for piezoelectric systems with hysteresis, usually simplified models are used. This can lead to inaccuracies in the closed-loop system response. In this letter, we pose the problem of tracking stabilization of piezoelectric systems using the generalized Bouc-Wen model, a highly non-linear system rarely used to design controllers. Besides, we consider only partially knowledge of one hysteresis system parameter and external disturbances in all the system states. We propose an interconnected control composed of three parts for the solution: an observer, a virtual hysteresis control, and actuator control. It is demonstrated that the closed-loop system converges in finite time. Simulation experiments were carried out, demonstrating the effectiveness of our approach despite exogenous and unknown disturbances.

This paper studies the tracking problem of an uncertain LTI system where both the control input and system state are quantized. The ℒ 1 adaptive controller is designed for the quantized system. Two common types of quantization, logarithmic and uniform, quantization are considered. In both cases, the analysis of the closed-loop system provides a uniform transient performance bound, which depends on the adaptation rate and the quantization densities of the state and the input. By increasing the adaptation rate and improving the state and the input quantization, the closed-loop system response can be rendered arbitrarily close to the reference system output. Finally, the simulations illustrate the theoretical results.

In this paper, we study the problem of robust H? controller design for uncertain continuous-time systems with variance and D-stability constraints. The parameter uncertainties are allowed to be unstructured but norm-bounded. The aim of this problem is the design of an output feedback controller such that, for all admissible uncertainties, the closed-loop poles be placed within a specified disk, the H? norm bound constraint on the disturbance rejection attenuation be guaranteed, and the steady-state variance for each state of the closed-loop system be no more than the prescribed individual upper bound, simultaneously. A parametric design method is exploited to solve the problem addressed. Sufficient conditions for the existence of the desired controllers are derived by using the generalized inverse theory. The analytical expression of the set of desired controllers is also presented. It is shown that the obtained results can be readily extended to the dynamic output feedback case and the discrete-time case.

A resonant current controller for a grid tied inverter connected to the grid through an L filter is presented. The controller allows to arbitrarily assign all the closed loop poles and zeroes of the system. It also allows to achieve the dynamic response of any arbitrary transfer function with relative grade greater or equal than two. A particular assignment of closed loop poles and zeros is proposed, which is used to obtain the response of a second order system without zeroes, for any number of resonances included in the controller.

This paper is concerned with the development of fully Autonomous Underwater Vehicles (AUVs) for deep ocean scientific and commercial applications. Specifically, it is regarding the design of automatic feedback control systems for AUV attitude control. The design method used in this paper formulates the AUV attitude control problem within the framework of the Optimal Control Theory. This approach determines an optimal control law that keeps the state of a dynamic system near a constant reference state while minimizing a quadratic cost functional. This study has developed four optimal control laws based on different performance criteria. First, the standard Linear Quadratic performance index was used to obtain a baseline control design. The LQR control law has been found to be undesirable because it resulted in a closed-loop system with fast and slow dynamics. In order to place the closed-loop eigenvalues close to each other, a pole placement algorithm has been used in connection with the LQR performance index. Two control laws have been designed based on this approach. Finally, a fourth design has been obtained by using a Hilbert Space Norm (also known as H/sub 2/ Norm or Root-Mean-Square) performance index. The main reason for designing a control law based on H/sub 2/ Norm performance index was to minimize the fuel consumption of the AUV for longer endurance. The stability and performance characteristics of the four optimal control laws have been analyzed via computer simulation and frequency response studies. All the closed-loop AUV systems exhibited overdamped response without any overshoot. Because the yaw and pitch channels have right hand zeros indicating the controllers have finite gain margins in these two channels. Hence, stability robustness of the AUV controllers can not be ignored and must be the subject of more detailed investigation in the future.

In this paper a new saturated control design for uncertain systems is proposed. The developed saturated control scheme is based on linear matrix inequality (LMI) optimization to achieve prescribed dynamic performance measures e.g., settling time and damping ratio. In this design, the closed-loop poles are forced to lie within a desired region. The proposed design provides robustness against system uncertainties. The existence of the saturated robust control with regional pole placement is shown using LMI and Lyapunov function analysis. Simulation results of two illustrative examples are given to validate the effectiveness of the proposed controllers. Application to car active suspension to achieve comfortable dynamic performance by pole placement and avoiding actuator saturation is also considered.

In this paper a new design procedure is proposed that combines linear quadratic optimal control (LQ) with pole assignment. In LQ-problems the quadratic weights are usually found by trial and error to get good time behavior. In contrast the proposed method modifies a given state weighting matrix such that all closed-loop poles are located in a specified region of the complex s-plane. It is shown that this can be done with the smallest possible increase of the quadratic performance index under consideration. The procedure is extended to the design of robust control systems where the plant is described by a family of linear systems according to different operational conditions. The control of a F4E aircraft demonstrates the achievements of the new procedure.