Robust controller design for time-varying systems

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

Optimal causal control of a wave energy converter in a random sea

In this paper, we present robust adaptive controller design for SISO linear systems with zero relative degree under noisy output measurements. We formulate the robust adaptive control problem as a nonlinear H/sup /spl infin// optimal control problem under imperfect state measurements, and then solve it using game theory. By using the a priori knowledge of the parameter vector, we apply a soft projection algorithm, which guarantees the robustness property of the closed-loop system without any persistency of excitation assumption on the reference signal. Due to our formulation in state space, we allow the true system to be uncontrollable, as long as the uncontrollable part is stable in the sense of Lyapunov, and the uncontrollable modes on the jw-axis are uncontrollable from the exogenous disturbance input. This assumption allows the adaptive controller to asymptotically cancel out, at the output, the effect of exogenous sinusoidal disturbance, inputs with unknown magnitude, phase, and frequency. These strong robustness properties are illustrated by a numerical example.

Structural controllability of time-invariant and time-varying systems when the input control sequences have a restricted length k is compared. The dimensions of controllable space coincide in the following three special cases: the input sequences have length k=2; the input sequences have k=n, where n is the size of the system (i.e., the ultimate controllability is the same in both cases); and for every length of input sequences provided that the system has a single input only. It is proved that there may appear a gap for every input length k such that 2 >

An analytical framework is described for the design of feedback control systems to meet specified performance criteria in the presence of structured and unstructured uncertainty. Attention is focused upon the linear time invariant, single-input, single-output problem for the purposes of exposition. The framework provides for control of the degree of the stabilizing compensator or controller.

A systematic control design methodology is introduced for multi-input/multi-output stable open-loop plants with multiple saturations. The idea is to introduce a supervisor loop so that when the references and/or disturbances are sufficiently small, the control system operates linearly as designed. For signals large enough to cause saturations, the control law is modified in such a way to ensure stability and to preserve, to the extent possible, the behavior of the linear control design. Key benefits of this methodology are: (1) the modified compensator never produces saturating control signals: (2) integrators and/or slow dynamics in the compensator never windup: (3) the directional properties of the controls are maintained; and (4) the closed-loop system has certain guaranteed stability properties. The advantages of the proposed design methodology are illustrated by the simulation of an academic example and the simulation of the multivariable longitudinal control of a modified model of the F-8 aircraft. >

In this paper a new systematic switching control approach to adaptive stabilization of linear time-varying (LTV) discrete-time systems is presented.A feature of the localization-based method is its high model falsification capability, which in the case of LTI systems is manifested as the rapid convergence of the switching controller.We believe that the proposed method may help pave the way for design of practical adaptive switching controllers applicable to a wide range of linear time-invariant and timevarying systems.

Approaches to the analysis and design of feedback control systems in which measurement quantization is present are discussed. The author regards a quantized measurement of a real number simply as a partial observation of that number and not as a straightforward approximation with associated error. As a consequence, the results have an information theoretic component that is absent from earlier research, the majority of which deals with measurement quantization by means of signal-plus-noise models and least-squares theory. It is possible to compute an upper bound on the asymptotic accuracy (measured as a mutual information) with which the current state of a linear system can be specified given a long record of quantized measurements. In deriving this upper bound, it is shown how input to the system can be used as information-gathering tools, and an observer-like construction for systems with quantized outputs is obtained. The results have some interesting system theoretic ramifications, and they form the foundation for a theory of observability for state-space systems with piecewise constant output. This theory differs from the usual one in several significant ways, and the utility of its attendant formalism is demonstrated by some simple examples. >

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.

The model of NCS (Networked Control Systems) with state observer is presented when the network-induced random time-varying delays are bounded and the upper bound of which is longer than one sampling period. Thus we established a discrete-time jump system model with Markov delay. Based on this, this paper gave also initial feasible solution of interior-point algorithm to design stabilizing controllers by the optimization method. This paper generalizes previous results on delay-less state observer systems. Theoretical analysis and simulation on a cart and inverted pendulum with random time delay show that feedback control based state observer can make the system stable.

The use of abstract chemical reaction networks (CRNs) as a modelling and design framework for the implementation of computing and control circuits using enzyme-free, entropy driven DNA strand displacement (DSD) reactions is starting to garner widespread attention in the area of synthetic biology. Previous work in this area has demonstrated the theoretical plausibility of using this approach to design biomolecular feedback control systems based on classical proportional-integral (PI) controllers, which may be constructed from CRNs implementing gain, summation and integrator operators. Here, we propose an alternative design approach that utilises the abstract chemical reactions involved in cellular signalling cycles to implement a biomolecular controller - termed a signalling-cycle (SC) controller. We compare the performance of the PI and SC controllers in closed-loop with a nonlinear second-order chemical process. Our results show that the SC controller outperforms the PI controller in terms of both performance and robustness, and also requires fewer abstract chemical reactions to implement, highlighting its potential usefulness in the construction of biomolecular control circuits.

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.

Summary This paper contains a summary description of the way in which interactive C.A.D. of feedback control systems has been introduced into a number of technological degree courses at the University of Reading. It describes the basic hardware/software available, the ways in which the students are taught and the practical work they are expected to perform.

The networked environment presents many new challenges for the design of feedback control systems. A specific problem is that networked control systems (NCSs) are subject to the performance-degrading effects of time-varying, random loop delays. Model predictive controllers are a well-known method for delay compensation, but often exhibit poor performance under these types of loop delay. This paper investigates the use of play-back buffers to remove the uncertainty in the delay. First we study the value of removing all delay uncertainty with comparisons to unbuffered PID control using a bounded- interval delay distribution, and then we explore optimal playback buffer design for bounded-interval and heavy-tailed delay distributions.

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.