Closed-loop Step Response Research Articles

Software for Comparative Studies of Phase Lead Compensator Design

Abstract The paper describes a new software package developed for designing phase lead/lag controllers for a given system. The package has been developed in the MATLAB environment with a powerful graphical user interface. It incorporates several phase lead/lag controller design methods based on the frequency domain technique some of which require a computational approach for a system of any complexity. Considerable education benefit can be obtained from studying the different design approaches which can be compared using loop frequency and closed loop step response plots. Two examples are given to demonstrate this.

Time-domain method for the design of optimal linear controllers

The paper presents a time-domain method for designing optimal linear controllers based on minimum error criteria for discrete single-input single-output (SISO) systems. The paper concentrates on using the approach to obtain optimum parameters for a PID controller and, in particular, for the case of a closed-loop step response with no overshoot. The method is also shown to be applicable for simple realistic constraints on the control signal and for continuous controller design.

Development And Verification Of A Mathematical Model For Robot Force Control Via Measuring An Output/Input Relationship And Force Control Experiments

This paper describes the development and verification of a mathematical model for a force control system consisting of a PUMA 560 manipulator, force sensor, and environment. Its main contribution is to present an argument that explicit open-loop dynamic models of manipulation systems used for force control are of little relevance or use. Identification techniques are used to model the system as a "black box," measuring only an output/input relationship. The explicit dynamics of the mechanical, hardware, and software elements of the manipulator are neglected; they are considered as parts of the measured output/input relationship. P+D (PD) loops are closed around each joint of the manipulator before identification to reduce uncertainties, to overcome nonlinearities, and thus to linearize the system. Close correspondence between the experimental and the simulated Bode plots for frequencies below 30 Hz indicates that the developed model is accurate enough to analyze and design a force control strategy for hard-on-hard contact applications, such as robotic drilling. A force control strategy based on a PI law for a hard-on-hard application is designed and evaluated in terms of the step response and achievable bandwidth to further validate the mathematical model of the force control system during contact. The simulated and experimental closed-loop step responses and Bode plots from the PI law prove that the mathematical model developed reflects the low-frequency features of the force control system accurately enough for design and implementation of a force control strategy for a real task.

A technique for optimal digital redesign of analog controllers

Digital control design is often accomplished by discretizing existing analog controllers. For this purpose, a new digital redesign technique is presented in this paper. It is based on optimal matching of the continuous-time closed-loop step responses of both the analog and discretized systems. The optimization problem is solved by application of the recent sampled-data control theory. The proposed technique is applied to discretization of a conventional power system stabilizer for a single-machine power system and the simulation results show that the new optimal digital redesign technique outperforms the conventional discretization methods.

Optimal Digital Redesign with Application to Control Of Power Systems

Digital control design is often accomplished by discretizing existing analog controllers. For this purpose, a new technique is presented in this paper based on optimal matching of the continuous-time closed-loop step responses of both the analog and discretized systems. The proposed technique is applied to discretization of a conventional power system stabilizer for a single-machine power system and the results show that the proposed optimal digital redesign technique outperforms the conventional methods for discretization.

EXPERIMENTAL RESULTS FOR THE SMALL-SIGNAL STUDY OF THE PWM BOOST DC–DC CONVERTER WITH AN INTEGRAL-LEAD CONTROLLER

An experimental verification of previously derived small-signal low-frequency open- and closed-loop characteristics and step responses of a voltage-mode-controlled pulse-width-modulated (PWM) boost DC–DC converter is presented. The Bode plots of the voltage transfer function of the control circuit, the converter and the PWM modulator, the open-loop control-to-output and input-to-output transfer functions, the loop gain, and the closed-loop control-to-output and input-to-output transfer functions are measured. The step responses to the changes in the input voltage, the duty cycle, and the reference voltage are measured. The theoretical results were in good agreement with the measured results. The small-signal model of the converter is experimentally verified.

System identification based on closed-loop step response data

This paper presents a new identification algorithm for processes operating in closed-loop. The algorithm involves fitting two Laguerre models directly to the control signal and the process output signal generated by a step change in the setpoint. The algorithm does not require any prior assumptions about the structure of the process model. The method generates an estimate of the process model in the frequency domain, and then transforms this frequency domain estimate into a continuous-time Laguerre model. Simulation results are used to illustrate the accuracy of the algorithm.

Aircraft flight controls design using output feedback

An approach is given for designing compensators of specified structure for shaping the closed-loop step response that uses linear quadratic output-feedback techniques. This approach results in controllers that take advantage of the wealth of experience in aircraft controls design. The correct initial conditions for determining the output-feedback gains are not uniformly distributed as is traditionally assumed, but are shown to be explicitly given in terms of the step command magnitude. Arbitrary systems are treated, not only those with integrators in the forward paths, by adding a term to the performance index that weights the steady-state error. Necessary conditions are derived that may be used in a gradient-based routine to determine the optimal control gains.

An Extended Self-Tuning Multivariable PI Controller

Several issues of practical extended self-tuning PI control of a multivariable process with n inputs and n outputs are discussed using a simplified ARX model. The controller is tuned to yield satisfactory closed loop step responses with small interactions, reasonable rise times and/or gain (phase) margins while taking into account bounds of control input increments. The controller has a small number of tuning parameters, the choice of which is not difficult. The controller is extended to have facilities for simple process diagnostics. Its gains can be used in fault detection and set point testing that require only marginal additional computations. A few propositions are made for practical applications. The use of update techniques in the control algorithm is treated. An iteration of the simplified extended controller (controller + diagnostics) requires 0(n2) floating point operations. The control algorithm is tested in control of a laboratory scaled process that simulates the “head box” of a paper machine.

A magnetic bearing system using capacitive sensors for position measurement

A capacitive sensor system for use in a bearingless induction motor is presented. Details of the circuit design are presented, and a theoretical step response is calculated and compared with experimental results. It is shown that one-dimensional position stability of an induction machine rotor can be obtained by controlling the currents in diametrically opposed conventional stator windings. In the case considered, the weight of the rotor was supported by a state current of 33% of the rated value. A margin is therefore available for the addition of a rotating component of current. The rotor of this machine has been reduced during development of the position sensor. It is anticipated that the system could be implemented with a smaller airgap and consequently a smaller steady-state current. The position signal was satisfactorily obtained using a simple airgap-mounted position-sensing system. An approximate model of the nonlinear system is sufficient for predicting the closed-loop step response for small perturbations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A Concept of Industrial Adaptive Control Based on Robust Design Principle and Multi-Model Approach

The discussed concept of industrial control strategy for single loop temperature control in plastics extrusion contributes to problem solutions according to computer aided or automatic proper tuning of a standard PID-Type controller. The adaptive feature is realized by a controller parameter scheduling. The scheduling depends on actual plant characteristics identified during start-up phase or after significant set-point changes. The available controller parameter sets {KP, TI, TD} are gained by a systematic search of the best compromise of a multiple performance description of simulated closed loop step response. Robustness of each controller parameter set is met using a family of plant models representing a nominal, an upper, and a lower boundary of plant step response data. The multi model plant description results from least square identification. No changes of the standard PID controller structure is necessary; a tuning loop only superimposes the well known digital control loop leading to a more easy to use PID control device which behaves robust and adaptive.

On a Class of Adaptive PID Regulators

Based on some relations discovered between the deterministic servo regulator and the PID design a simple design role is presented for stable processes to ensure 5% relative overshoot for the closed loop step response. The adaptive solution is based on the explicit identification of a second order process model with time delay. Extending the PID regulator by an appropriate correcting term the poorly damped or inverse unstable process zero is allowed to be a zero of the closed loop system, as well. Additional pole placement is also available.

Design of a longitudinal ride-control system by Zakian's method of inequalities

In this paper, Zakian's method of inequalities is applied to the design of a ride-control system for a STOL aircraft. The purpose of the controller is to reduce the normal acceleration experienced by both passengers and crew. The method is based on the synthesis of a controller such that a set of performance specifications and constraints is satisfied. Controllers are designed on the basis of the characteristics of both the closed-loop step response and the closed-loop error response. It is shown that the design of a single-input, single-output controller by the method of inequalities is straightforward, and can be achieved by using a sequence of formulations until the designer is satisfied that no further improvement is necessary.

Loop Frequency Response Design for Prescribed Step Response Bounds

A loop frequency response design procedure for achieving prescribed closed loop step response bounds is described. This procedure is based on the Horowitz sensitivity criterion which specifically deals with large plant parameter variations and is essentially frequency domain orientated. The variations in the closed loop system frequency response are represented by polygonal plots in the complex plane at a number of frequencies and the overall loop frequency response is adjusted until these plots are seen to lie in or close to corresponding specified polygonal plots which represent bounds on the system step response. The advantages of this technique compared with others using the Horowitz criterion are that it is ideally suited to computer assisted design when use is made of a visual display unit and it provides an effective and natural way of specifying the step response bounds. Any preferred method can be used to construct the required loop frequency response function although that suggested here permits a very rapid initial design since essentially only one parameter need be varied. Thus trade-offs between loop gain-bandwidth and system sensitivity can be quickly established.

Computer-aided design of parallel compensated closed-loop control systems

A method is described whereby linear, single-input, single-output control systems can be designed by a computer-aided design process in which the inverse Nyquist diagram of the system is displayed automatically on a cathode ray oscilloscope coupled to the computer. The designer communicates with the computer using his intuitive understanding of the high order processes with or without distance/velocity (transportation) lag in the feedback loops. The design method is augmented by another program which gives the cathode ray display of the closed-loop step response of the compensated system. The article includes two numerical examples in which the parameters of the control systems containing parallel compensating devices are selected by the computer-aided design process to give a specified performance.