State Space Feedback Research Articles

Attenuation of disturbances introduced by dynamic links in precision motion systems using model-based observers

This paper presents an extension to the Unknown Input Disturbance Observer (UIDO) and the Disturbance Estimation Filter (DEF). This extension enables the inclusion of the mechanics of dynamic links to the observer model, in order to attenuate the specific disturbances introduced by those dynamic links. A design method of the state space feedback gain based on the dynamics, and an observer gain based on basic Kalman filter theory is given. It is shown how the observer is designed for a practical example; the cable schlepp within the wafer stage of a lithography machine. Using a simple model of the cable schlepp the disturbance observer design has been validated with an experiment on an actual machine.

Analysis of a Position Control Extension on the Model of a Servo-Screw-Press

Currently, the achievable feedback control performance for servo-screw-presses is limited by its elastic structure. A possible approach to compensate this limitation is the extension of the velocity controller. This structural extension has the potential to improve the controller performance significantly due to a better damping of low frequencies. In this paper, the extension of the control structure by a state space feedback in the velocity control loop is examined. Considering that, the velocity control extension is investigated at a test rig which consists of a servo axis and a two mass system. Furthermore, a simulation model for the test rig is designed. The results of the simulated and experimentally obtained results of the test rig are presented and evaluated in order to make a prediction for the transferability to the simplified model of the servo-screw-press.

Beam Position and Energy Monitoring in Compact Linear Accelerators for Radiotherapy

The experimental verification of a novel sensor topology capable of measuring both the position and energy of an electron beam inside a compact electron linear accelerator for radiotherapy is presented. The method applies microwave sensing techniques and allows for the noninterceptive monitoring of the respective beam parameters within compact accelerators for medical or industrial purposes. A state space feedback approach is described with the help of which beam displacements, once detected, can be corrected within a few system macropulses. The proof-of-principle experiments have been conducted with a prototype accelerator and customized hardware. Additionally, closed-loop operation with high accuracy is demonstrated.

Space-state robust control of a Buck converter with amorphous core coil and variable load

Pulse-width modulation is widely used to control electronic converters. One of the most frequently used topologies for high DC voltage/low DC voltage conversion is the Buck converter. These converters are described by a second order system with an LC filter between the switching subsystem and the load. The use of a coil with an amorphous magnetic material core rather than an air core permits the design of smaller converters. If high switching frequencies are used to obtain high quality voltage output, then the value of the auto inductance L is reduced over time. Robust controllers are thus needed if the accuracy of the converter response must be preserved under auto inductance and payload variations. This paper presents a robust controller for a Buck converter based on a state space feedback control system combined with an additional virtual space variable which minimizes the effects of the inductance and load variations when a switching frequency that is not too high is applied. The system exhibits a null steady-state average error response for the entire range of parameter variations. Simulation results and a comparison with a standard PID controller are also presented.

Modeling and control of a PEM fuel cell system: A practical study based on experimental defined component behavior

In this contribution, the dynamical behavior of a polymer electrolyte membrane (PEM) fuel cell system is modeled; related control approaches are developed. The system model used for experimental and modeling purposes describes a 1.2kW PEM fuel cell stack and an air blower. Due to the dynamical fuel cell–blower interaction the fuel cell stack and the blower model are validated to real systems respectively. Additionally, a feedback based on PI-control is used for hydrogen pressure control with an anode inlet valve. This controller is able to eliminate a stationary error between the anode and cathode pressures. For principal investigations three control approaches, a classical static feed-forward control approach, a state-space feedback control, and a novel gain-scheduling approach are developed, applied, and compared. As result, it can be shown that the feed-forward approach lacks in performance recovering the excess oxygen ratio to the desired level. The state-space feedback control shows stationary error. The introduced gain-scheduling control approach leads to a fast excess oxygen ratio recovery without stationary deviations.

Shaping the Ship Yaw Response by the State-Space Feedback Gain

Ship autopilots are usually designed based on PID controller because of the simplicity and the ease of construct. However its performance in various environmental conditions is not as good as desired. This disadvantage can be decreased by designing a linear state space feedback controller. This paper presents the utility of the state-space feedback controller to stabilize the system and shaping its response as desired. The simulation results for a 4DOF ship with real parameters show the effectiveness of the feedback controller in comparison with ordinary PID ship autopilots.

A Control Systems Approach to Input Estimation with Hydrological Applications

This paper demonstrates the feasibility of a new approach to system inversion and input signal estimation based on the exploitation of non-minimal state space feedback control system design methods that can be applied to non-minimum phase and unstable systems. The real and simulated examples demonstrate its practical utility and show that it has particular relevance in a hydrological systems context.

Modelling and control of a zero current switching high-voltage resonant converter power supply for radio frequency sources

This study presents the design, modelling, control and implementation of a `long-pulse` three-phase resonant converter. A d - q equivalent circuit model of the resonant tank system is established first. Based on that, a model of the whole power supply and a state-space multivariable feedback control has been developed. The soft switching, zero current switching, is achieved by combining frequency and phase control together. An experimental prototype was designed and developed on a small scale. Experimental results confirm the expectations from the simulation study and validate the feasibility of the converter.

Infinite horizon MPC with non-minimal state space feedback

In the MPC literature, stability is usually assured under the assumption that the state is measured. Since the closed-loop system may be nonlinear because of the constraints, it is not possible to apply the separation principle to prove global stability for the output feedback case. It is well known that, a nonlinear closed-loop system with the state estimated via an exponentially converging observer combined with a state feedback controller can be unstable even when the controller is stable. One alternative to overcome the state estimation problem is to adopt a non-minimal state space model, in which the states are represented by measured past inputs and outputs [P.C. Young, M.A. Behzadi, C.L. Wang, A. Chotai, Direct digital and adaptative control by input–output, state variable feedback pole assignment, International Journal of Control 46 (1987) 1867–1881; C. Wang, P.C. Young, Direct digital control by input–output, state variable feedback: theoretical background, International Journal of Control 47 (1988) 97–109]. In this case, no observer is needed since the state variables can be directly measured. However, an important disadvantage of this approach is that the realigned model is not of minimal order, which makes the infinite horizon approach to obtain nominal stability difficult to apply. Here, we propose a method to properly formulate an infinite horizon MPC based on the output-realigned model, which avoids the use of an observer and guarantees the closed loop stability. The simulation results show that, besides providing closed-loop stability for systems with integrating and stable modes, the proposed controller may have a better performance than those MPC controllers that make use of an observer to estimate the current states.

Fast Worm Containment Using Feedback Control

In a computer network, network security is accomplished using elements such as firewalls, hosts, servers, routers, intrusion detection systems, and honey pots. These network elements need to know the nature or anomaly of the worm a priori to detect the attack. Modern viruses such as Code Red, Sapphire, and Nimda spread quickly. Therefore, it is impractical if not impossible for human mediated responses to these fast-spreading viruses. Several epidemic studies show that automatic tracking of resource usage and control provides an effective method to contain the damage. In this paper, we propose a novel security architecture based on the control system theory. In particular, we describe a state-space feedback control model that detects and control the spread of these viruses or worms by measuring the velocity of the number of new connections an infected host makes. The mechanism's objective is to slow down a worm's spreading velocity by controlling (delaying) the number of new connections made by an infected host. A proportional and integral (PI) controller is used for a continuous control of the feedback loop. The approach proposed here has been verified in a laboratory setup, and we were able to contain the infection so that it affected less than 5 percent of the hosts. We have also implemented a protocol for exchanging control-specific information between the network elements. The results from the simulation and experimental setup combined with the sensitivity analysis demonstrate the applicability and accuracy of the approach.

Linear State Space Feedforward and Feedback Structures for Blind Source Recovery in Dynamic Environments

Blind Source Recovery (BSR) denotes recovery of original sources or signals from environments, which may include convolution, temporal variation, and even non-linearity--without necessarily performing explicit environment identification. This paper presents two separate multiple-input multiple-output (MIMO) structures for dynamic linear Blind Source Recovery (BSR) of multiple stochastically independent source signals. We propose linear state space models for both the mixing environment and the demixing (or the recovering) adaptive network. The demixing network may assume either the feedforward or the feedback state space configuration. Separate algorithms have been derived for the adaptive estimation of the feedforward and the feedback demixing/recovering network's parameters. These algorithms are based on the multivariable optimization theory and utilize the Riemannian contra-variant gradient (or the natural gradient) search under the constraints of a state space representation. Auxiliary conditions for the convergence of these algorithms have also been derived and discussed. Illustrative simulation examples have been included to demonstrate the successful adaptation results for both proposed demixing network structures in the case of an infinite impulse response (IIR)-type mixing environment for example source statistical distributions.

ABOUT REDUCING CONSERVATISM IN ROBUST CONTROL DESIGN OF DISCRETE-TIME SYSTEMS: THE NON STATIONARY CASE

The paper addresses the problem of stabilizing discrete-time systems subject to time varying polytopic uncertainty. Non stationary quadratic Lyapunov functions are derived for synthesis in a Poly-Quadratic Lyapunov function concept which avoids in a large extent the conservatism linked with the classical single Lyapunov function quadratic approach. The state space feedback synthesis problem is addressed. The results are extended to cope with two particular problems: ℋ∞ performance analysis and synthesis problem as well as state feedback design while maximizing the size of the uncertainty domain.

Robust torque control design for induction motors: The minimum energy approach

This paper presents two different aspects concerning the control design laws for induction motors: (1) it derives state operating points (steady-state values for currents and fluxes) parameterized in terms of the desired motor torque, defining minimum-energy operation conditions for the electrical motor. (2) It gives a state-space feedback control design methodology based on Lyapunov analysis which renders the minimum-energy operating points invariant. Several controllers are proposed: P-type control, observer-based P-type control, PI-type control and observer-based PI-type control. The PI-structure and the observer-based control are introduced to deal with motor parameter uncertainties, and the absence of flux measurements, respectively. Stability of all these control schemes is studied. Experimental results are also presented.

Active absorption of acoustic waves using state-space model and optimal control theory

The work presented in this paper regards modeling, synthesis, and simulation of an active acoustic field control system under state-space feedback control approach. The active system is supposed to absorb an incident sound energy so that the reflection off an acoustic boundary is diminished. To illustrate the concept, a simple model describing transient sound reflection and transmission in an unbounded, one-dimensional space is derived in a state-space form. The distributed parameter system is approximated with a finite dimensional model using a standard discretization technique with special boundary treatments. Based on the state-space model, a feasible feedback control algorithm is synthesized using optimal control theory (LQG). Numerical simulation of the closed-loop response of an active control system including two sensors and one actuator is presented, which shows a broadband reflection (echo) reduction.

On‐line gas analysis in animal cell cultivation: I. Control of dissolved oxygen and pH

To monitor gas reaction rates in animal cell culture at constant dissolved oxygen concentration (DO) and constant pH it was necessary to develop improved control methods. Decoupling of both controllrs was obtained by manipulation of molar fractions of oxygen and carbon dioxide in the gas phase. Two pairs of DO and pH controllers were designed and tested both in simulation and exprimental runs. The first controller pair was developed for headspace aeration only, whereas the second controller pair was designed for bubble aeration using a microsparger and flushing the headspace with helium. pH was controlled by a conventional discrete PID controller in its velocity form. For DO control two linear state space feedback controllers with parameter adaptation were established. In these controllers the oxygen uptake rate (OUR) was considered as a disturbance and was not included in the mathematical model. The feedback gain adaptation was based on the difference between the actual molar fraction of oxygen at time step n and the initial molar fraction. This difference is related to OUR and was used to increase or decrease the state feedback controller gain (k and k(1), respectively) in a slow manner. With these controllers it was possible to get an excellent online estimate of OUR. In the case of bubble aeration a simple gas phase mass balance was sufficient, whereas during the headspace aeration a liquid phase balance was required. It has been shown that determination of OUR using gas balance requires a significantly better controller performance compared to just keeping DO and pH within reasonable limits. (c) 1995 John Wiley & Sons, Inc.

Robust pole placement in discrete-time systems

The problem of robust pole placement via a state-space feedback is discussed for discrete-time systems. It is assumed that a discrete-time system is described in terms of state-space equation x(k+1)=Ax(k)+bu(k), y(k)=c/sup T/x(k)+eu(k) with uncertain entries of matrices (c, A, b, e). A feedback matrix f is calculated such that the real stability radius of the characteristic polynomial of the closed loop system is possibly maximal.

Robust Torque Regulation for Induction Motors: The Minimum Energy Approach

This paper presents two different aspects concerning the control design laws for induction motors: (1) It derives state operating points (steady-state values for currents and fluxes)parameterized in terms of the desired motor torque, defining minimum energy operation conditions for the electrical motor. (2) It gives a state space feedback control design methodology based on Lyapunov analysis which renders the minimum energy operating points invariant. A PI-type control is here proposed. The PI-structure is introduced to deal with motor parameter uncertainties. Stability of this control schemes is studied.

Adaptive control of robot manipulators via velocity estimated feedback

An approach for designing robot controllers using state-space feedback is presented. The robot model parameters are assumed to be unknown and velocity measurements are assumed not to be available. This asymptotically stable control scheme combines an adaptive control law with a sliding observer and does not need additional assumptions on the variation of the inertia matrix eigenvalues. State observation and parameter adaptation are performed simultaneously. The adaptation law, the observer gains, and the control law are designed on the reduced order manifold which results from the invariance of the switching surface.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A hierarchical expert system for computer process control

This paper reports on the design and implementation of an expert system for computer process control (HESCPC). The complexity of the expertise necessary for computer process control applications requires that the expert system architecture be structured into a hierarchy of classes of specialized experts. The architecture of HESCPC integrates four classes of expert systems: operator/manager companion expert class, control system algorithm design expert class, hardware expert class, and software expert class. The paper is concerned with the design and implementation of the general system architecture, an operator adviser expert for a nuclear power plant and a control system designer expert using a state space feedback approach. Although the design and implementation aspects of all experts are discussed, the emphasis is on the latter. At this stage of the HESCPC development, the declarative knowledge represented by 423 metarules and 1261 rules is distributed on a hierarchical structure among 20 experts on different levels of the hierarchy which are able to communicate among themselves to solve difficult control problems. Examples of control system design sessions of linear mono and multivariable systems using feedback state space approach are given. A run time of an operator-adviser data-driven expert system for a nuclear plant is also presented.

Divisors of polynomial matrices: Theory and applications

In this paper divisors G(s) of a given polynomial matrix N(s) are discussed. The paper deals with the following problems: extraction of a greatest right (left) divisor of N(s), computation for a given state-space system (C, A, B) a state-space feedback making the system (C, A + BF, B) maximally or appropriately unobservable and determination for a given system (C. A, B, O, W, O) a disturbance rejection feedback F. The developed methods are very simple from computational point of view and can be easily implemented in the software via existing computer library procedures.