Some qualitative properties of sampled-data control 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.

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.

Stability and sensitivity of nonlinear sampled data systems

&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;

Multirate, sampled-data control systems are analyzed in the frequency domain, taking the inter-sample behavior into account. The focus of the analysis is both on the rejection of disturbances within a certain frequency region, and on the robust stability properties. Due to the periodic behavior of such systems, a distinction is made between the performance frequency response (PFR) and the robust frequency response (RFR). The RFR is related to current frequency response approaches for sampled-data systems.

Analysis of performance criteria in sampled-data fault detection

STABILITY AND SENSITIVITY OF NONLINEAR SAMPLED DATA SYSTEMS

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.

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

An optimal dual-rate digital redesign method is proposed that can be applied to continuous-time and fast-rate discrete-time control systems. The paper presents a technique, which relies on the solution of a dual-rate H2 discrete-time control problem, to convert such systems to either a slow-rate or a dual-rate sampled-data control system while guaranteeing closed-loop stability and performance in the discrete-time H2 sense. The proposed technique results in sampled-data control systems providing satisfactory closed-loop performances over an extended range of sampling rates, as compared with other widely used methods of digital redesign. Furthermore, the proposed digital redesign technique is useful in practice since it allows the designer to constrain the complexity of the digital controllers, thus resulting in low-order digital controllers easily implementable in software code and free of causality and real-time problems. Numerical examples provide a comparison of the proposed digital redesign technique with well-known approaches.

The paper proposes a method for optimizing sampled-data systems over a set of reduced order controllers. The method is based on the concept of parametric transfer function and finding a subset of solutions for polynomial Diophantine equation with the order not exceeding the preset number. The method is applied to optimization of H2-norm of sampled-data submarine motion control system.

The robust stability criterion for sampled-data control systems with a sector nonlinearity was presented in our previous papers (1996, 1998). Although it is applicable only to the sampled-data control system of a certain class, a usual discrete-time control system belongs to this type of class. The criterion contains the robust stability condition in regard to the nonlinear allowable band (sector) for continuous-time systems and the linear allowable gain band (interval set) for discrete-time systems. The paper focuses primarily on the concept of robust stability in order to analyze a nonlinear element by the linear gain band, in other words, the validity of Aizerman's conjecture extended into discrete-time systems.

We present a new method for the automated synthesis of digital controllers with formal safety guarantees for systems with nonlinear dynamics, noisy output measurements, and stochastic disturbances. Our method derives digital controllers such that the corresponding closed-loop system, modeled as a sampled-data stochastic control system, satisfies a safety specification with probability above a given threshold. Our technique uses a fast solver and an optimization method to search for candidate controllers, which are then formally evaluated in closed-loop with the system in question by a verified solver. Unstable candidate controllers are discarded by efficiently checking a sufficient condition for Lyapunov stability of sampled-data nonlinear systems. We evaluate our technique on three case studies: an artificial pancreas model, a powertrain control model, and a quadruple-tank process.

The decentralized \({\mathscr{H}}_{\infty }\) sampled-data control problem is investigated for a class of continuous-time large-scale networked nonlinear systems with interconnection. Each nonlinear subsystem in the considered large-scale system is represented by a Takagi–Sugeno model and is closed by a communication channel with transformed time delay. Our objective is to design a decentralized sampled-data fuzzy controller such that the resulting fuzzy control system is asymptotically stable with an \({\mathscr{H}}_{\infty }\) performance. Firstly, using an input delay approach, the sampled-data control system is formulated into the system with time-varying delay, and a two-term approximation method is proposed such that the delayed system is reformulated into an interconnected framework with input and output. Then, we introduce a Lyapunov–Krasovskii functional that all Lyapunov matrices are no longer required to be positive definite. Combined with the scaled small gain theorem, the less conservative solutions to the decentralized \({\mathscr{H}}_{\infty }\) sampled-data control problem for the considered system are derived in the form of linear matrix inequalities. Finally, the effectiveness of the proposed methods is illustrated by two numerical examples.