Performance and robust frequency response for multirate sampled-data systems

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.

A frequency domain approach to fault detection in sampled-data systems

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.

&lt;div class="htmlview paragraph"&gt;In this work we study the stability of digital controls of flexible/Vibratory aerospace/automobile systems by the graph norm technique, occurring in sampled-data control systems due to sampling period variations. To do so, this work tries to establish regions (graphs) of stability and instability in a Banach Space, the distances (norms) between them and a given design to detect analytically and/or numerically its margins of stability or conditions of instability. Based on that, we sketch the first steps for a design methodology of stable digital controllers of flexible/vibratory systems embedded in a sampled-data system with adjustable sampling periods of A/D and D/A converters. A short tutorial about the graph norm technique is also given and some theoretical results as well numerical results are shown. This work was done in two folds to unmask the stability secrets hidden in a general sampled-data control system, until today not revelated. The first part we have used the graph norm and at the second part we made use of the Liapunov stability theory.&lt;/div&gt;

Analysis of performance criteria in sampled-data fault detection

This paper is concerned with new discretization methods of continuous-time controllers taking account of the intersample behavior of the resulting sampled-data systems. We first state how to evaluate the controller discretization error based on the Hilbert-Schmidt norm of the sampled-data frequency response, and introduce what we call the desirable frequency response of the discretized controller. We then show that the desirable frequency response can be determined in a closed form in terms of the state-space representations of the original continuous-time controller and the frequency-domain weight. We further discuss some important properties of the desirable frequency response, whereby we propose a heuristic method for controller discretization. We further propose a more sophisticated method, and the effectiveness of these proposed methods is demonstrated by numerical examples. The relationship of the proposed methods with (as well as difference and advances from) similar existing studies are clarified from the viewpoint of the modern theory on the frequency response of sampled-data systems, and the roles and choice of the frequency-domain weight are discussed for better recovery of control performance.

Participation of wind energy along with conventional fuel sources in power generation is progressively rising in many countries. Due to continuous development of large-scale wind farms, some synchronous generators are being economically displaced from generation schedule. Modern wind turbine generators do not generally provide frequency control support after a disturbance, while during a fault they usually generate a current, which is close to their rated current value. Thus, presence of substantial wind generation in a system may impose a challenge in maintaining adequate frequency response. Moreover, it may result in low short-circuit ratio at the grid connection point of wind farms. Inadequate frequency response and low short-circuit ratio may create a concern for secured operation of a power system. Both frequency response and short-circuit level primarily depend on the number of committed synchronous generators. Hence, there may be a certain relation between these two system performance indicators. This paper investigates a correlation between frequency response and short-circuit performance due to high penetration of wind power. A case study of an Australian power system is presented.

This paper is concerned with the digital implementation of the linear quadratic controller in the case of the sampled-data system. By applying the bilinear transformation, a way of computing a stabilizing suboptimal digital controller which does not require the resolution of the discrete Riccati equation is proposed. Corresponding values of the optimal and suboptimal discrete-time cost functions are estimated with respect to the sampling period and the degradation is evaluated. A simple numerical example is given to support the theoretical results.

The introduction of the root-locus method in the z-plane simplifies the investigation of sampled-data control systems, by demonstrating the correlation between transient response and the location of the roots. It is shown that by establishing the correlation between frequency locus and the root locus, the correlation between frequency and transient response of sampled-data systems can be demonstrated.

Approximation of frequency response for sampled-data control systems

TRANSPORT LAG in sampled-data control systems influences their stability. If this influence is studied as the function of transport lag and other system parameters, the design procedure becomes cumbersome. This paper, which applies Mitrovi?'s algebraic method,1?3 presents a new way to analyze and synthesize various sampled-data control systems such as the cyclic variable-rate, multirate, and those with nonsynchronized samplers. Other related problems are greatly facilitated by this method also.

Bifurcation and Chaos in Nonlinear Sampled-Data Control Systems

Sampled-data based discrete and fast load frequency control for power systems with wind power

To ensure frequency stability of low inertia power systems, VSC needs to provide frequency response (FR) service. Limited by predicting grid inertia/damping and disturbances that are difficult to measure, the FR performance is greatly restricted. Besides, excessive response under certain conditions results in several consequences, including 1) energy waste, and 2) the VSC power frequently and excessively deviating from steady-state points, thereby reducing the component’s life, lowering system safety/reliability, and increasing the risk of VSC overcurrent faults. To solve these issues, this paper proposes the frequency trajectory planning (FTP) based FR strategy, with the fundamental idea to actively plan the frequency trajectory with necessary safety margin in accordance with the grid code. Specifically, if the system frequency locates within the range of planned one (suggesting frequency indexes satisfying the requirement), VSC remains at the steady-state point to avoid excessive FR service; otherwise, the FR service is required, and the FTP control is enabled to closely track the planned trajectory. By fulfilling the tracking purpose, the requirement on system frequency indexes is met, frequency stability is guaranteed, and the over-response is avoided. Namely, the planned trajectory can characterize whether the system requires FR service and whether the provided FR service is sufficient or excessive. Additionally, the method needs no measurement of inertia/damping and disturbances of the system, and can be directly integrated into the commonly used VSC control systems. Finally, experiments prove the effectiveness and advancement of the FTP strategy.

Droop control, inertia control, and PD control are three typical frequency response (FR) strategies of grid-tied inverters interfaced renewable energy sources (RES) to restrain the power system frequency indicators, i.e., frequency deviation ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \omega $ </tex-math></inline-formula> ) and the rate of change of frequency (RoCoF). Due to the highly limited inverter capacity, the FR performance in power systems with high RES penetration should be optimized. To this end, this paper first analyzes the impact of high-penetration renewable energy injection on power system frequency stability, and derives the system frequency expressions in the absence of an FR scheme, and in the presence of droop/inertia/PD controls that are representative for various virtual synchronous generator-based FR schemes. Under the same constraint of available FR capacity, control parameter ranges of these FR schemes are obtained, and their optimal conditions for restraining the maxima of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \omega $ </tex-math></inline-formula> and RoCoF are identified and compared analytically. Comparison conclusions are finally proved by the provided experiment and simulation results.