Controlling the flow of information in feedback systems with measurement quantization

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.

ABSTRACTIn this study, a command tracking error square control scheme is first proposed for analysis and design of feedback control systems. One of the tracking errors is low‐pass filtered and used in the feedback loop for gain adaptation; the other is used in the forward loop for command tracking control. The overall systems are nonlinear feedback systems, and can be reconfigured to an automatic gain control (AGC) loop with command tracking error input. The stability and robustness of the controlled systems are verified by time response, frequency response, and large parameter variation testing with a simple illustrating example and are finally applied to a complicated electro‐hydraulic velocity servo system with large load disturbance.

Equivalent time constants are obtained for nonoscillatory second-order processes. In analogy with first-order processes, the equivalent time constant is defined to be the time at which the monotonic step-response of the second-order process reaches approximately 63.3 percent of its steady-state value. These time constants can be applied to the analysis and design of feedback control systems in which oscillations cannot be tolerated.

Many practical problems in the field of engineering become so complex that they may be effectively solved only with the aid of a computer. An effective solution depends on the use of an efficient algorithm. Plotting root locus diagrams is such a problem. This thesis presents such an algorithm. Root locus design of feedback control systems is a very powerful tool. Stability of systems under the influence of variables can be easily determined from the root locus diagram. For even moderately complex systems of the type found in practical applications, determination of the locus is extremely difficult if accuracy is required. The difficulty lies in the classical method of graphically determining the location of points on the locus by trial and error. Such a method cannot be efficiently applied to a computer program. The text presents an original algorithm for plotting the root locus of a general system. The algorithm is derived using the combined methods of complex variable algebra and numerical analysis. For each abscissa desired a polynomial is generated. The real roots of this polynomial are the ordinate values for points on the root locus. Root finding methods from numerical analysis enable the solution of the problem to be one of convergent iteration rather than trial and error. Among the material presented is a computer program for solution of the general problem, an example of a completely analytic solution, and a table of solutions for more simple systems. The program inputs are the coefficients of the open loop transfer function and the range and increments of the real axis which are to be swept. The output lists the real and imaginary components of all solution points at each increment of the sweep. Also listed are the magnitude and angle components of the solution point and the value of system gain for which this is a solution. For less complex problems, the method can be applied analytically. This may result in an explicit relation between the real and imaginary components of all solution points or even in a single expression which can be analyzed using the methods of analytic geometry. As with any advance in the theory of problem solving, the ideas presented in the thesis are best applied in conjunction with previous solution methods. Specifically, an idea of the approximate location of the root locus can be obtained using sketching rules which are well known. The method presented

The object of this work is to present computer programs, written using Turbo Pascal version 5.5, which can be utilized for the analysis and design of control systems as required for undergraduate courses. The programs have been designed so that the student uses the computer as a tool for reducing computational drudgery and not as a substitute for engineering analysis. The software, which can be used on an IBM Personal Computer and compatibles, will be made freely available to interested educators. >

A survey is presented of the environment, the hardware, and the system, user interface, and applications software that can make engineering workstations effective tools for the analysis and design of control systems. The hardware discussion covers processors, memory, networks, and diskless workstations. Operating systems, distributed file systems, and software for developing user interfaces are highlighted, along with the most widely used applications packages for control system engineering.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Stability is one of the most important concepts of analysis and design of control systems. Stability analysis of fuzzy control systems has been difficult since fuzzy systems are essentially nonlinear systems. Recently, stability analysis techniques [l]-[6] [13]-[16] based on nonlinear stability theory have been reported. Langari and Tomizuka [2, 6] analyzed stability of fuzzy linguistic control systems. Kitamura [3] realized stability analysis of fuzzy control systems by using extended circle criterion. Farinwata [5] and Kato [14] utilized phase plane analysis type of techniques, tanaka and co-authors [1,3,4] applied Lyapunov approach to fuzzy control systems and recently developed LMI-based designs [10, 17, 28-37], where LMI stands for nonlinear matrix inequality.

While linear covariance analysis is widely used for navigation system design and analysis, it is often overlooked as a tool for closed-loop guidance navigation and control (GN&amp;C) system design and analysis. This article presents an overview of the techniques and methods required to develop a linear covariance analysis tool for a close-loop GN&amp;C system. Then, using a simple nonlinear closed-loop GN&amp;C problem as a guide, the capabilities of linear covariance analysis for the design and analysis of closed-loop systems are demonstrated. It is shown that linear covariance can be accurately applied to a closed-loop system with time-to-go guidance, dead-reckoning navigation, and a Kalman filter for state estimation. The accuracy and efficiency of linear covariance analysis is shown by direct comparison to Monte Carlo analysis results, and the value of linear covariance analysis is highlighted by presenting several analysis capabilities that are often required in the design and analysis of closed-loop GN&amp;C systems. It is also shown how the efficiency of linear covariance enables new design methodologies, one of which is presented in this article, that would otherwise be prohibitive with Monte Carlo analysis.

Positive force/torque feedback (PFF) can compensate for the detrimental effects of load dynamics and exogenous force/torque disturbances on the tracking performance of motion control systems. With real world nonideal force/torque sensors/actuators, a PFF controller can be designed to accommodate the sensor's/actuator's dynamics and to minimize the impact of load dynamics or external force/torque disturbances upon the motion tracking loop. This brief shows that PFF is an effective method for many practical control problems. It is also shown that the analysis and design of motion control systems with PFF can be put into the /spl mu/ framework and, thus, the tracking controller and the force/torque feedback controller can be synthesized simultaneously using commercially available /spl mu/ tools. Some practical issues, which are independent of design methods, such as the robust stability (RS) of the PFF loop and the bandwidth requirements for the PFF controller, are also discussed. It is concluded that, outside the system's effective tracking bandwidth, it is not wise to use model-based perfect PFF for a big load due to the lack of robustness of the PFF loop against the actuator uncertainties. Experimental results with a UW hexapod strut show that the /spl mu/ design method for PFF is promising.

In this second part of the paper on the analysis and design of uncertain fuzzy control systems, we present a controller design method for a class of uncertain fuzzy control systems. This class of systems can be represented by the discrete-time uncertain fuzzy models discussed in Part I. Since this model representation considers system uncertainties and system disturbance, the controller design problem for this kind of model becomes a H/sub /spl infin// control problem for a nonlinear uncertain system. A new stability analysis and control system design approach are then developed for this kind of uncertain fuzzy model. Furthermore, a constructive algorithm is developed to obtain the H/sub /spl infin// feedback control law.

Network-based control systems have been emerging technologies in control and computer communication fields over the past decade. This paper focuses on the analysis and design of network-based control systems with binary modulation. First, it is shown that different modulations can result in different delays which are inevitable in network-based control systems. The delay can be seen as constant delay when the transmission time is the main consideration. Second, channel noise can result in bit error while bit error is seen as active packet loss in this paper, in this context, the conditions of signal-to-noise ratio (SNR) for binary modulation that can guarantee the stability of systems are obtained according to the proposed algorithm. Third, the system with delay and noisy communication can be modeled as an asynchronous dynamic system (ADS); in addition, the stability is analyzed and controller is designed in terms of Lyapunov function and linear matrix inequality (LMI) scheme. Finally, without loss of generality, numerical simulation demonstrates the effectiveness of the proposed scheme and designed controller based on binary amplitude shift keying (2ASK) modulation.

To help along the analysis and design of nonlinear control systems the NONLINCON package, an acronym for nonlinear control, was developed. This note addresses the usefulness of symbolic computation, and of the NONLINCON package in particular, for the symbolic analysis and design of nonlinear control systems. The symbolic computation program MAPLE is used as computing substratum. Textbook problems show that the NONLINCON package can be used successfully. A larger scale problem is too complex, however, to be solved with the current versions of NONLINCON and MAPLE. The conclusion is that symbolic computation is a viable approach for textbook problems, but not yet for more complex ones. >

Design, Analysis and Real-time Implementation of Networked Predictive Control Systems

In this paper, an unknown input filter is proposed for discrete-time linear systems with quantized measurements. The approach uses a slightly modified model of the system to estimate both the system states and the unknown input simultaneously. Two well-known quantization methods, namely linear and logarithmic, are studied and a specific design procedure is derived for each case. For the linear case, the quantization error is modelled as measurement noise and for the logarithmic case, it is modelled as a norm-bounded uncertainty. In the end, simulation results are used to illustrate the effectiveness of the proposed filter.

Feedback control of functional neuromuscular stimulation has the potential to improve daily function for individuals with spinal cord injuries (SCIs) by enhancing seated stability. Our fully implanted networked neuroprosthesis (NNP) can provide real-time feedback signals for controlling the trunk through accelerometers embedded in modules distributed throughout the trunk. Typically, inertial sensors are aligned with the relevant body segment. However, NNP implanted modules are placed according to surgical constraints and their precise locations and orientations are generally unknown. We have developed a method for calibrating multiple randomly oriented accelerometers and fusing their signals into a measure of trunk orientation. Six accelerometers were externally attached in random orientations to the trunks of six individuals with SCI. Calibration with an optical motion capture system resulted in RMSE below 5° and correlation coefficients above 0.97. Calibration with a handheld goniometer resulted in RMSE of 7° and correlation coefficients above 0.93. Our method can obtain trunk orientation from a network of sensors without a priori knowledge of their relationships to the body anatomical axes. The results of this study will be invaluable in the design of feedback control systems for stabilizing the trunk of individuals with SCI in combination with the NNP implanted technology.