Hypertracking and Hyperrejection: Control of Signals Beyond the Nyquist Frequency

In conventional hard disk drives, a control system compensates for the vibration in which frequency is higher than the Nyquist frequency by using a multi-rate filter that can decrease the gain above the Nyquist frequency. However, such a control system can only avoid instability that results from mechanical vibrations and cannot suppress the vibrations. In response to these problems, we proposed a design method for a sampled-data control system that decreases vibrations in which frequencies are higher than the Nyquist frequency. Our method can easily design a control system and can calculate the norm of the sensitivity function in a sampled-data system by using frequency responses of a controlled object. When the method was applied to the head-positioning system of a hard disk drive, we found that the control system can suppress the disturbance in which the frequency was higher than the Nyquist frequency

Basing on lifting technology, this paper researches a design method for multirate sampled-data control system in the background of flight control system design, which consummates the theory of multirate sampled-date control system design for further steps, and provides a method to design multirate sampled-data controller. As the reason of uncertainty in the aircraft model and the need of different sampling frequencies in different control loops, H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> -optimal multirate sampled-data control is considered. First, multirate sampled-data control system is outlined, and then the signal description are presented. Because of multirate sampled-data system is time-variant, the direct digital controller design becomes difficult. The equivalent discrete time-invariant systems can be converted from the linear time-variant systems through lifting technology. Then the H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> discretization of multirate sampled-data systems is researched. After the sampled-data control system was lifted, the equivalent L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> [0, h) -induced norm is proven. Base on the above, the method of H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> -optimal multirate sampled-data control is summarized. A height control is simulated using a simplified aircraft model to illustrate the design. The simulation shows that the multirate Sampled-data control system can achieve the satisfactory objective accurately and optimally.

REGULATOR BY SLIDING MODES WITH EXPONENTIAL HOLDER FOR LINEAR SYSTEMS

One of the problems of the theory of management of objects with a high degree of uncertainty of behavior is solved: the development of theoretical foundations of analysis, modeling methods and improvement of bio cybernetic systems, their algorithmic and software necessary to improve the efficiency of the management process is proposed. To solve this problem, it is proposed to use the mathematical apparatus of information theory, on the basis of which the information characteristics of the control signal transmission channel from the source to the control object through the external environment are calculated, taking into account the noise of the ecosystem of the control object. The existing systems using monomodal control signals that do not carry a semantic load are analyzed, and the disadvantages and limited possibilities of improving the control systems under consideration are described. Using the example of one of the insect behavior control systems with a trichromic view, a comparison of the results obtained using various technical means used as control signal sources was performed. For improving the efficiency of control systems, which use a multimodal control signal structure, proposed various algorithms for constructing control systems using a multimodal control signal structure are considered, namely: serial and parallel circuits, combined, combining serial and parallel algorithms for using control signal sources. As a method for further improving the efficiency of control systems for biological objects with a high degree of uncertainty, it is proposed to use biological signals containing a large semantic load for the control object, which determines its behavioral response. The directions of further research are formulated in order to maximize the amount of information transmitted to the control object.

W e st udy the solution of the so-called maximum speed problem of a linear control system, in which, unlike the classical optimal speed problem with a relay-type control, a linear control algorithm is determined for a linear object that provides the maximum speed of the system. It is of practical importance due to the widespread practical application of linear co ntrol laws. The problem is formulated in relation to continuous, one-dimensional high-order control objects described by the corresponding transfer function or an equivalent system of ordinary differential equations in a certain phase space. The time of the transition process t tp of the designed system is understood in the sense of the classical theory of automatic control and is determined using the zone D = s pr 4,321 %, equal to the given (desired) value of the overshoot of the synthe si zed s ystem. This overshoot corresponds to an oscillatory link with a damping coefficient √ 2/2 — the Butterworth filter of the second order. Accordingly, the maximum performance problem is put in the following formulation: it is required to fi nd a linear feedback algorithm that provides the closed control system with a given astatism order n a and transferring the control object from the initial state to the final one, determined by the constant signal of the regulator’s task, with the minimum value of transient time t tp and set value overshoot s = s pr when performing a constraint on the control signal |u(t)| m u max . At present, this problem has been solved by an approximately algebraic method of synthesizing linear control systems in determining the desired transfer function of a projected closed system based on typical (reference) normalized transfer functions (NTF). The approximate nature of the decision is determined by the fact that the NTF used in the synthesis of high-speed systems are established empirically. This paper proposes a mathematically sound solution to the problem of maximum speed using the theory of analytical design of optimal controllers (ADOC). The maximum speed and set limits on the overshoot and the value of the control signal in the synthesized system are provided by the proposed method for selecting the weights of the quadratic quality functional. We emphasize that the proposed method for the synthesis of high-speed systems, in contrast to the algebraic method, is applicable to a wider class of control objects: both minimal-phase and non-minimal-phase, as containing zeroes, and not. The method is illustrated by an example of the synthesis of a high-speed fourth-order control system containing the results of its simulation.

Two Applications for Hybrid H∞-Control: Generalised Sampled-Data and Loop-Shaping

TRACKING METHODOLOGY WITH ZEROS VARIATION AND DISTURBANCE REJECTION APPLIED TO UNCERTAIN SYSTEMS

A method is presented for processing multi-channel seismic data that recovers, simultaneously and unambiguously, signal frequencies above and below the temporal Nyquist of the input data, By exploiting signal stationarity and redundancy, I show that the sample interval of a single input channel does not uniquely determine the maximum recoverable frequency. The method is tested using normal moveout (NMO) and stack on synthetic model data. Frequencies of 10 to 225 Hz are recovered from input data sampled at 4 ms. I then apply the method to real data. The results demonstrate that antialias strategies based on the one-dimensional Shannon-Whittaker sampling theorem (l) impose an unnecessary limit on the ability to recover high frequencies and maximize signal resolution. The method is applicable wherever the trajectory of the signal to be imaged irregularly intersects the sampling grid. It is appropriate for resolving both temporal and spatial aliasing concerns. Introduction Since the inception of digital signal processing, concerns about signal aliasing have played a major role in determining useable signal bandwidth and the cost of obtaining that bandwidth. For example, the authors of a 1991 article in The Leading Edge observed that "..the major use of Nyquist's work in geophysics is the elimination of alias frequencies on digitally recorded seismic data. The Nyquist frequency is the highest frequency that can be obtained for a given sampling interval." (2). Such concerns have led the seismic industry to systematically restrict potential signal frequencies to below the Nyquist frequency by the application of antialiasing filters based on the Whittaker-Shannon sampling theorem. This paper describes a simple methodology for the recovery of signal components in excess of the Nyquist limit predicted by the one-dimensional Whittaker-Shannon sampling theorem. With this method, an optimum balance of image bandwidth and signal-to-noise ratio may be achieved by simple processing parameter choices. The methodology is applicable whenever the signal trajectory is irregularly intersected by a sampling grid of two or more dimensions. Aliasing It is generally accepted that the digital sampling interval and the upper limit of the recoverable signal spectrum are inexorably linked. Authors usually cite the one-dimensional Whittaker-Shannon sampling theorem which states that the maximum recoverable frequency (? Nyq) in an evenly-sampled function is given by:(mathematical equation)(available in full paper) where ?t is the sampling interval (in seconds). Frequencies in the input function prior to sampling, which are in excess of this Nyquist frequency, are, if not removed prior to sampling, said to be aliased (or folded) in the sampled output. Aliasing is generally understood to mean that those frequencies above ? Nyq are irretrievably lost due to being "mixed" with those below ? Nyq. Commonly, aliasing has been dealt with by one or both of two methods: Alias reduction method #1 Antialias filtering is almost always used to significantly reduce contamination by aliased frequencies whenever analog data are sampled (e.g., during field recording) or whenever the sampling interval is increased. While usually successful in preventing anticipated aliasing problems, this filtering can result in a loss of valuable signal both above and below ? Nyq. Also, additional equipment and/or processing costs are usually incurred.

Many of nonlinear control systems are sampled-data system, i.e. the continuous-time nonlinear plants are controlled by digital controllers. So it is important to investigate that if the solution of the discrete-time output regulation problem is effective to sampled-data nonlinear control systems. Recently a feedforward neural network based approach to solving the discrete regulator equations has been presented. This approach leads to an effective way to practically solve the discrete nonlinear output regulation problem. In this paper the approach is used to sampled-data nonlinear control system. The simulation of the sampled-data system shows that the control law designed by the proposed approach performs much better than the linear control law does.

Robust guaranteed cost control of uncertain fuzzy systems under time-varying sampling

Power flow control in multi-terminal DC grids can be accomplished through the connection in series of a controlled voltage source converter to a line. Having finite energy, the voltage source requires a means for either power recycling or additional source of power to regulate its voltage. An interline dual full bridge current flow controller (CFC) provides the capability to recycle power from one line to another through the voltage source in addition to controlling the power flow on either line. This paper proposes a control methodology that fulfils both control objectives. A double modulation controller (DMC) implements one modulating signal and two control signals to control the duty ratio of the converters simultaneously. The first control signal is proportional to the required reduction in the line current. The second control signal is implemented to regulate the voltage to either a set average value or to a value that is proportional to the amount of reduction in current.

This work is proposed to continue the discussion of the problems, theoretical foundations and practical features of the construction and synthesis of robust control systems with high gain, allowing us to control multidimensional nonlinear dynamic objects of high dimensional with functional uncertainties. If problems could not be solved at the level where they appeared, it is necessary to rise the level of understanding of the laws of nature, or in the words of master Lui-Shi Chun Qiu (China, 3rd century BC): "The boy of five chi growth leads the bull by the bridle and the bull obeys him in everything. This is because the person in this case follows naturalness" (the laws of nature). The judo philosophy ("soft way") is based on the principles of using the power and energy of the opponent to achieve victory. The purpose of this work is to demonstrate the theoretical aspects and practical features of the methods of synthesis of optimal control systems by the criterion of maximum reproduction accuracy using the example of robust systems, which allow to control dynamic objects with functional uncertainties, including unstable objects, no minimal-phase objects, neutral objects and objects with differentiation properties. The simplicity (at the level of the engineer) and universality, mathematical rigor and physical validity of this approach is based on the judo philosophy: suppressing the dynamics of a functionally uncertain object and external disturbances by the infinitely large gain with the finite control signal and at the same time maintaining sustainability. Theoretically exhaustive solution of the problem of robust control is given by the idea of constructing systems that are stable with an unlimited increase of the gain coefficient. The sustainability properties are valid for optimal systems that were synthesized using quadratic quality functionals that do not explicitly depend on the control signal, and using a restriction on the control signal. It is significant that in contrast to continuous systems with un-measurable disturbances and not well known control object (in which the conditions of invariance imply the use of infinitely large gain), in relay (discontinuous) systems the equivalent effect is achieved with the help of finite control signal. A nice bonus is the highest accuracy which leads to mathematically zero error of regulation, thus all error coefficients (of position, speed, acceleration, acceleration derivative, etc.) is also equal to zero in the presence of external and internal interferences. In fact, the optimal accuracy control system is equivalent to a system with astatism of the n-th order: the regulator contains n serial connected integrators.

This article is devoted to the development of a new method of synthesis a regulators’ transfer functions matrix of an optimal multivariable open-loop control system. The regulator is designed to maximize an accuracy of a nonlinear multivariable control object transition from one steady state to another. It is assumed that disturbances act on the control object and sensors measuring data has inertia and noise. Both disturbances and noises are an additive combination of regular and random components. Random components belong to a class of interconnected stationary processes with rational spectral density matrices. A substantiated method differs from the known one by the fact that during formulation and solution of the problem somebody uses a new block diagram of the control system, which takes into account the results of metrological certification of a sensor dynamics. Synthesis of the regulator is carried out in the frequency domain by the Wiener-Kolmogorov method. A new algorithm, which is obtained as a result of synthesis problem solution, allows you to find the matrix of regulator transfer functions , which provides a minimum of corresponding quadratic quality criteria’s. The first of them is equal to the sum of certain way weighted squared deviations regular repetition errors of the object path and control signals. The second criterion is equal to the sum of the weighted variance of the random error components and the control signals. To execute the proposed algorithm it is necessary to perform the operations of Wiener factorization and separation of rational matrices. The corresponding functions are contained in the freely distributed software package SciLab.

In urban traffic systems, traditional signal control can no longer meet the increasing traffic demand, and local congestion is severe during peak hours. Fixed detector data is characterized by high deployment density, full sample detection and restorable vehicle paths, providing new data support for coordinated signal control. We propose an optimization method for regional coordinated control, with the Changsha road network as the study area. Firstly, based on License Plate Recognition (LPR) data, the road network is divided into sub-networks and combined with the boundary control for regional coordinated control. Then, the critical path is taken as the control object, and the phase coordination rate is introduced as the optimization objective. The particle swarm optimization algorithm improved by the logistic chaotic map is used as the global searcher, and sequential quadratic programming is adopted as the local searcher to solve the optimization strategy for the objective function. Finally, a simulated road network is constructed in VISSIM 6.0 simulation software to verify the effectiveness of the strategy. The results show that the optimization strategy reduces intersection delay and saturation by 20.3% and 19.3% in the critical path coverage area. Road travel time and the average number of vehicle stops are reduced by 21% and 22.1%. This indicates that the regional coordinated control based on the improved particle swarm algorithm can better alleviate the peak hour traffic congestion.

We explore the channel estimation problem in the case of quasi-synchronous users in a DS-CDMA system. Knowledge of the transmit (TX) filter is assumed, and the anti-aliasing low-pass front end receive (RX) filter is designed for critical sampling at the Nyquist rate for the TX filter. It is shown that when the sampling frequency is larger than the Nyquist frequency, the discrete-time representation of the channel is not unique. However, all representations can be treated in a similar fashion once the Nyquist rate is satisfied. On the other hand, fractionally sampling the channel leads to a scenario in which the cut-off frequency can be approached arbitrarily close to the Nyquist rate. In the case of sparse channels, sampling the channel at any rate lends to a small number of non-zero coefficients in the finite-impulse response(FIR) representation of the channel. The structured channel estimation algorithm presented in this paper exploits the sparseness of this model. Results are compared with those of other previously proposed structured methods.