Noriyuki Hori

A new perspective for discrete-time models of a continuous-time system

A new perspective of the invariant and mapping discrete-time models for a continuous-time system is presented. More specifically, these models are re-classified as the direct and indirect models and are interpreted in terms of the system structure and the hold device. This concept provides for a better understanding of various discrete-time models. In addition, by extending this concept of direct and indirect models, new types of mapping models may be created and this is shown for the new indirect model case.

Convergence of sampled-data models in digital redesign

This note proposes sufficient conditions that guarantee uniform-in-time convergence, as the sampling period approaches zero, of the control input to and the controlled output of a plant under sampled-data control to those corresponding signals of the same plant under continuous-time control. Sampled-data control systems exhibiting such behavior are formally defined as sampled-data models, which can be very convenient in the analysis and design of sampled-data systems since they can warn the engineer if a known limiting closed-loop behavior is likely to be violated. This practical consideration often occurs in digital redesign, where an analog control law is implemented digitally, with the objective of preventing intersample ripples.

State-space forms for higher-order discrete-time models

This paper presents a fundamental study of the connection between continuous- and discrete-time systems. Provided is a definition for discrete-time models, that is discrete-time systems with a continuous-time counterpart, whose order can be higher than that of the continuous-time system. This definition is based on a comparison in a certain sense on the time responses of continuous- and discrete-time systems. A theorem is presented for relating the higher-order discrete-time models to their continuous-time counterparts, which is an extension of a previous theorem for models with order equal to that of the continuous-time system. State-space forms are derived for models obtained through the use of a certain class of hold elements and through the use of mapping models, and these discrete-time systems are shown to be valid according to the definition. Special cases are models obtained using first-order and slewer hold devices, whose convergence to a continuous-time counterpart has not been shown mathematically before, and mapping models corresponding to two-step linear multi-step methods, which have not previously presented in the state-space form. The derived state-space forms provide a convenient way to implement these models for purposes of analysis, design, and implementation of discrete-time systems and finds applications in such areas as digital signal processing, digital simulation, and digital control.

On a Discrete-Time System Expressed in the Euler Operator

The Euler operator ¿ = (z-l)/T plays an important role in the analysis and synthesis of discrete-time systems. A number of properties pertaining to discrete-time systems which are expressed by the Euler operator approach those of continuous-time systems as the sampling frequency increases, and include those of discrete-time systems expressed by the z operator The stability criteria and some of the positive realness of a real rational function are among them However, there may be some properties which are different from the continuous-time counterpart even if the sampling frequency is increased. One such example is the relative degree condition of the positive real function.

Application of a new multivariable model-following method to decoupled flight control

A new model-following controller for multivariable, linear, time-invariant systems is described and applied to the decoupled longitudinal control of a control-configured-vehicle-type aircraft. The controller is composed of an input dynamics compensator and a state feedback block. This approach enables decoupling and control of systems that cannot be done by state feedback alone. The key concept is that of system augmentation by utilizing a unimodular matrix to assure the nonsingularity of a control matrix. Two methods of generating the control input are described. In the first, the control input is synthesized by explicitly using the plant state variables. In the second, the input and output of the plant are used.

New PWM schemes based on the principle of equivalent areas

It is shown that the concept of discrete-time models of an analog system can be applied to the principle of equivalent areas (PEA), which is noncausal in its exact form. The proposed method makes possible the development of various algorithms for implementing online the PEA for control purposes. From this viewpoint, the existing PEA as applied to the pulse-width-modulation (PWM) can be viewed as the case where the zero-order-hold is used. Moreover, with the proposed approach, an infinitely many formulae can be derived for the conversion of a servo signal into a PWM signal. Four such formulae are shown; two are single-rate formulae and the other two are dual-rate ones. These methods are compared numerically using an open-loop first order example.

Order Reduction of PIM-based Digital Flight Control Systems

Abstract A global digital redesign technique known as the plant input mapping (PIM) method is used in the design of a digital flight control system. Three methods to solve the Diophantine equation associated with the PIM design are studied, including the proposed order reduction technique. Numerical simulations show that the reduced-order PIM-based digital flight control system has superior performance to flight control systems obtained with the classical local digital redesign methods.

On a comparative study of digital redesign methods

Compares the performances achieved with the conventional digital redesign techniques with those obtained with the modern global digital redesign methods such as the plant input mapping methods and the optimal digital redesign approach. The study based on a benchmark control system reveals that the reduced-order plant input mapping method, and not the optimal approach, offers what practicing control engineers are really looking for: simple controllers having a superior behavior in face of finite wordlength effects and over a relatively large band of sampling frequencies.

Digital redesign methods based on plant input mapping and a new discrete-time model

The digital redesign approach is to obtain discrete-time controllers which realize a digital control system approximating some characteristics of the predesigned continuous-time control system. This paper describes a digital redesign method for linear time-invariant continuous-time control systems of the 1-DOF type and the state-feedback type. It is a closed-loop method that takes account of the closed-loop characteristics of the predesigned continuous-time control system. Generally, such methods provide better closed-loop stability and closer approximation to the underlying continuous-time control system for a wider range of sampling periods. The proposed method is based on mapping of the closed-loop control inputs and the transfer function matrix from external inputs to control inputs is discretized as a discrete-time model which generates average continuous-time system outputs for constant inputs. The discrete-time controller or the feedback/feedforward gain matrix is determined so that the discretized closed-loop transfer function matrix can be realized. The redesign is carried out using the state-space approach; thereby the method can be applicable to MIMO systems. To illustrate the methods effectiveness, numerical examples are shown.

A methodology for the potential improvement of gas-turbine engine digital control systems

Proposes new techniques for the digital control of a gas-turbine engine. The methods have the particularities of (i) providing satisfactory responses for a wider spectrum of sampling frequencies than that obtained with the conventional techniques, (ii) resulting in fixed-order and fixed-structure control laws, and (iii) presenting superior performances than the conventional approaches when subjected to quantization effects. The design steps as well as the simulation results are presented for the control of the gas-generator subsystem of a turboshaft engine.