16 - Design of feedback controls

6 - Design and Performance of Feedback Controllers

Active electroacoustic systems are commonly employed to transmit sound from one location to another. For example, consider the following configuration: a person talks into a microphone, which produces an electrically amplified signal for driving a loudspeaker, and the loudspeaker induces an output acoustic signal allowing someone else at a more distant location to hear the person talking. Unfortunately, such system designs typically do not consider acoustic feedback, which can destabilize the system and result in “howling.” In contrast, a feedback control system can transmit sound from one location to another using collocated microphone/loudspeaker transducers without the risk of howling. We design feedback controllers that model positive real (i.e., passive) systems, such as a spring and a gyrator. The spring controller essentially binds the diaphragms of the two transducers together. We relate the spring controller to the string connecting two tin cans together in the classical tin can telephone. Measurements are performed on a real feedback control system with two transducers. Because the feedback controller models a passive system, it is stable in any (passive) acoustic environment. [Sennheiser Electronic Corporation helped support this work.]

Circle Condition-Based Robust Feedback Control Against Plant Perturbation

Modeling, monitoring and control strategies for high temperature short time pasteurization systems — 1. Empirical model development

It is well-known that phase-shifting controllers used for active combustion control must be manually adjusted in order to maintain control over a broad range of operating combustor operating conditions. If one assumes that the thermoacoustic instabilities are linearly stabilizable, then what is needed is a method to determine, and ultimately predict, the frequency response of the plant for any range of operating conditions, so the controller design can be automatically updated to track the changing plant gain/phase relationships that are observed with changing heat release. A unique test-based, design process has been proposed to predict the gain/phase characteristics required of a proportional, phase-shifting controller that can stabilize the thermoacoustic instabilities. In this paper, that process is used to automate the design of a fixed-gain feedback controller that limits the amplitudes of any feedback induced instabilities (to some pre-specified level) while providing the best control of the targeted limit cycling pressure oscillations. The paper describes how a neural network was trained, using the suggested design process, to predict the frequency response of the thermoacoustics in a tube combustor at frequencies adjacent to the limit cycle frequency using certain operating conditions that included a sparsely-sampled temperature profile, total air/fuel flow rate, and equivalence ratio. The neural net training was performed using complex valued, open-loop frequency response function data as the desired signal with the previously mentioned operating conditions as the input signals. (The open loop data was collected for a narrow frequency range surrounding the limit cycle instability by performing a sine dwell at discrete frequencies). Once the neural network was trained, it was used to predict the approximate phase and gain margins as a function of temperature and flow conditions. The margins were then used to automatically update and design a fixed shape feedback controller having the proper phase and magnitude to ensure stability and control in the face of changing operating conditions. A companion paper describes the methodology that underlies the automated design of the feedback controller gain and phase delay.

This work is concerned with the problem of designing stable invariant subspaces for the construction of discontinuity surfaces of variable structure control systems (VSCS). A new method of analyzing and designing the closed loop systems, such as the model following control systems and VSC systems with sliding mode, having desirable behavior in tracking or regulation is developed in this paper. The study has been motivated by the observation that a basic operator associated with the assignment of dynamics in feedback control system qualifies as a projector. Projector theory provides a neat method for analysis and design of VSCS to construct the sliding manifolds in class of differentiate manifolds. Reducibility and invariance properties of projections make them very attractive to decompose a dynamic system into lower order two subsystems decoupled from each other, so we get deep insight into problems in analysis and design tasks of control systems and more information about dynamics incorporated with "modes" and eigenvectors represent intrinsic properties of dynamical systems

In the last few decades, the stabilization in stationary states has emerged as a new auspicious campaigner in chaos theory and found a celebrated place through various control techniques such as predictive control, delayed feedback control, constant proportional feedback control and oscillating feedback control system. Generally, it is accepted that the superiority of control systems is not only to quash the irregular distribution of stationary states, but also to illustrate its basin of attractions as large as possible depending on the numerical as well as analytical observance. In this article, the universal stabilization in unstable stationary states is studied through superior fixed point feedback control system for a family of one-dimensional maps. Further, it is interesting to know that the novel system provides freedom in the control parameter γ due to which the stabilization increases more rapidly for the lager range of parameter γ in [0,1]. The analytical as well as numerical simulations are demonstrated to examine the behavior of parameter γ for which the unstable stationary state admits universal stability.

This work is concerned with the existence of asymptotically stable 2-D (2-dimensional) systems by means of a feedback control model represented by the system of partial difference equations and their Lagrange solutions. Thus, the goal is to establish a controller that provides a feedback control system with state variables depending solely on its Lagrange solution in the sense that the solution to the variable state is not a linear combination of other Lagrange solutions. Roughly speaking, the results showed that, to achieve such a control system, the controller has to diagonalize the block matrices of the matrices composing the system description model. Finally, a numerical example is presented to show how the controller is designed in order to generate a stable feedback control with given Lagrange solutions.

The dynamics of a web transport system are coupled and interactive among spans of web and rolls/rollers. As the process speed or variation of the speed is high, system friction and inertia of rotation of rolls could cause problems in implementation of observer techniques for tension estimation and control. In the author's previous study (see IEEE International Conference on Industrial Electronics, Control and Instrumentation, Denver, Colorado, USA (2001)), an observer-based tension feedback controller with friction and inertia compensation was proposed. However, the gains of observer and controller were determined based on the trial-and-error approach. This paper continues the author's previous study and presents an analytical approach for the gain design of observers in the time domain but design of controllers in the frequency domain. The linearization and decentralization techniques are implemented. Design of tension observers and feedback controllers with friction and inertia compensation is studied. Approaches for the gain design are discussed, and summarized procedures are given. The proposed analytical approach for design of tension observers and feedback controllers has been proven to be adequate by experiment.

Feedback control design by Lyapunov's direct method

In the present paper, we examine the Model Feedback Control System. Since the Model Feedback Control System is simple, the ModeI Feedback ControI System has been applied to many applications such as the trajectory control of robot manipulator, level control of serially connected tanks and so on. Since the control structure of the ModeI Feedback Control System has constrained, it is likely that the Model Feedback Control System can not represent all of stabilizing controllers for the plant. Nothing has been reported whether or not, the ModeI Feedback Control System can represent all of stabilizing controllers. The purpose of the present paper is to give a solution to the question whether or not, all of stabilizing controllers for the plant are written as the Model Feedback Control structure. Since Model Feedback Control System is applied to many minimum phase systems, in the present paper, we especially clarify the relationship between the ModeI Feedback Control System and the parametrization of all stabilizing controllers for the minimum phase system. First, the relationship between the Model Feedback Control system and the parametrization by Glaria and Goodwin is clarified. Next, for the strictly proper system, the relationship between the Model Feedback Control System and the parametrization by Yamada and Moki is presented. Simple design method of the Model Feedback ControI System to specify control characteristics is shown.

Multiple DSP system for real time parallel processing and feedback control on fusion experiments

Feedback control has become a crucial tool in the research on magnetic confinement of plasmas for achieving controlled nuclear fusion. This thesis presents a novel plasma feedback control system that, for the first time, employs a Graphics Processing Unit (GPU) for microsecond-latency, real-time control computations. This novel application area for GPU computing is opened up by a new system architecture that is optimized for low-latency computations on less than kilobyte sized data samples as they occur in typical plasma control algorithms. In contrast to traditional GPU computing approaches that target complex, high-throughput computations with massive amounts of data, the architecture presented in this thesis uses the GPU as the primary processing unit rather than as an auxiliary of the CPU, and data is transferred from A-D/D-A converters directly into GPU memory using peer-to-peer PCI Express transfers. The described design has been implemented in a new, GPU-based control system for the High-Beta Tokamak – Extended Pulse (HBT-EP) device. The system is built from commodity hardware and uses an NVIDIA GeForce GPU and D-TACQ A-D/D-A converters providing a total of 96 input and 64 output channels. The system is able to run with sampling periods down to 4 μs and latencies down to 8 μs. The GPU provides a total processing power of 1.5 x 1012 floating point operations per second. To illustrate the performance and versatility of both the general architecture and concrete implementation, a new control algorithm has been developed. The algorithm is designed for the control of multiple rotating magnetic perturbations in situations where the plasma equilibrium is not known exactly and features an adaptive system model: instead of requiring the rotation frequencies and growth rates embedded in the system model to be set a priori, the adaptive algorithm derives these parameters from the evolution of the perturbation amplitudes themselves. This results in non-linear control computations with high computational demands, but is handled easily by the GPU based system. Both digital processing latency and an arbitrary multi-pole response of amplifiers and control coils is fully taken into account for the generation of control signals. To separate sensor signals into perturbed and equilibrium components without knowledge of the equilibrium fields, a new separation method based on biorthogonal decomposition is introduced and used to derive a filter that performs the separation in real-time. The control algorithm has been implemented and tested on the new, GPU-based feedback control system of the HBT-EP tokamak. In this instance, the algorithm was set up to control four rotating n = 1 perturbations at different poloidal angles. The perturbations were treated as coupled in frequency but independent in amplitude and phase, so that the system effectively controls a helical n = 1 perturbation with unknown poloidal spectrum. Depending on the plasma's edge safety factor and rotation frequency, the control system is shown to be able to suppress the amplitude of the dominant 8 kHz mode by up to 60% or amplify the saturated amplitude by a factor of up to two. Intermediate feedback phases combine suppression and amplification with a speed up or slow down of the mode rotation frequency. Increasing feedback gain results in the excitation of an additional, slowly rotating 1.4 kHz mode without further effects on the 8 kHz mode. The feedback performance is found to exceed previous results obtained with an FPGA- and Kalman-filter based control system without requiring any tuning of system model parameters. Experimental results are compared with simulations based on a combination of the Boozer surface current model and the Fitzpatrick-Aydemir model. Within the subset of phenomena that can be represented by the model as well as determined experimentally, qualitative agreement is found.

This paper presents the characteristics of sediment transport by flood in the Lower Yellow River with the reach from Huayuankou to Gaocun, which is regarded as a typical braided pattern. The Artificial Neural Network Model on Water Use for Sediment Transport (WUST) by flood was established based on the measured data from 1980 to 1998. Consequently, simulations of controlling process of sediment transport by flood were made in terms of the control theory under different scenarios. According to the situation of sediment transport by flood in the Lower Yellow River, Open-Loop control system and feedback control system were adopted in system design. In the Open-Loop control system, numerical simulations were made to reveal the relationship between average discharge of flood and the WUST with varying sediment concentrations. The results demonstrate that sediment concentration has significant influence on the controlling process of flood flow to WUST. It is practical and efficient to control WUST if sediment concentration is less than 20 kg/m3. In the feedback control system, controlling processes of sediment concentration and flood discharge for sediment transport were simulated respectively under given conditions, and it was found that sediment transport process could be controlled completely by sediment concentration and discharge at the inlet of the reach from Huayuankou to Gaocun. Using the same method, controlling processes of sediment transport by flood in other reaches in the Lower Yellow River were also simulated. For the case of sediment concentration being 20 kg/m3, the optimized controlling discharge ranges from 2390 to 2900 m3/s in the lower reach of Huayuankou. This study is also of significance to flood control and flushing sediment in the Lower Yellow River with proper operation modes of Xiaolangdi Reservoir.

In this paper we provide a robust feedback controller and observer design to provide a maximum stability radius. The technique would take into account the performance specifications in the design process. This is done by using the linear matrix inequalities (LMI). The technique is illustrated on a feedback controller and observer design of an inverted pendulum