Position Control Of Dc Servo Computer Science Essay

Published Date: 02 Nov 2017

INTRODUCTION

POSITION CONTROL OF DC SERVO MOTOR- SOME ASPECTS

Introduction

1.2 LITERATURE SURVEY

1.3 PROBLEM FORMULATION

1.4 OBJECTIVES

1.5 ORGANIZATION OF THESIS

Motivation

Automatic control systems permeate life in all advanced societies today. This development has evolved more complex systems in which nonlinearities need to be more effectively addressed in the design process. Such systems act as catalysts in promoting progress and development propelling society into the next century. Technological developments have made it possible for high-speed bullet trains; exotic vehicles capable of exploration of other planets and outer space; safe, comfortable and efficient automobiles; sophisticated civilian and military aircraft; efficient robotic assembly lines; and efficient environmentally friendly pollution controls for factories. The successful operation of all of these systems depends on the proper functioning of the large number of control systems used in such ventures [1, 5]. Engineering deals with understanding and harnessing the forces of nature for the benefit of mankind while maintaining an ecological balance and a safe planet for us to live. Control engineering is concerned with understanding the plant under operation, and obtaining a desired output response in presence of system constraints. The purpose of feedback in control systems is to ensure that the response of a plant is to be controlled in way that satisfies desired specifications. These specifications are given in terms of closed-loop system. The feedback control system generates an input to the plant based on a comparison of the required and the actual closed-loop response of the system. In the feedback control design process, the task for the control system is to use information about the plant system to design a feedback control system and then to achieve the given specifications [2, 3, 4, 5, 6, 7, 8, 9, and 10].

Feedback is used in control systems for two reasons: First, to change the dynamics of the system -usually, to make the response stable and sufficiently fast. Second, to reduce the sensitivity of the system to uncertainty -both signal uncertainty (disturbances) and model uncertainty. The process of designing a control system usually makes many demands of the engineer or engineering team. These demands often emerge in a step by step design procedure as follows:

Study the system (plant) to be controlled and obtain initial information about the objectives of control.

Model the system mathematically and simplify the model, if necessary.

Analyze the resulting model and determine its properties.

Decide which variables are to be controlled i.e. controlled outputs.

Decide on the measurements and the manipulated variables and the sensors and actuators that will be used and where they will be placed.

Select the type of control configuration.

Decide on the controller to be used.

Take a decision about performance specifications, based on the overall control objectives.

Design controller.

Analyze the resulting controlled system to see that the specifications are satisfied or not; and if the specifications are not satisfied modify the specifications or the type of the controller.

Simulate the resulting controlled system, on a computer or on a pilot plant.

Repeat from step 2, if required.

Choose hardware and software based on the availability and implement the controller.

Test and validate the controlled system, and tune the controller on line, if required [8].

Due to the large use of Proportional Integral Derivative (PID) controllers in process industry, there always have been serious efforts to obtain effective PID controller design methods to meet certain design criteria and provide system robustness. I am inspired by the fact that the modern control engineering deals with improving stability, performance and efficiency among others.

In this research, mainly two methods of designing the position control of DC Servo Motor are discussed. The first method is Quantitative feedback theory and the second method is graphical representation method of PID controller design to obtain the gains to achieve stability. These two techniques are based on the frequency response of the plant (DC Servo Motor). The controller design methodology is used to determine if the uncertain plant remains stable for the entire uncertainty set. The frequency domain application of these design techniques reduces the complexities of plant modeling. These controller design methods are applied to a DC Servo Motor model. PID (PD, PI) controller gains are found to make the system robust and stable.

1.2 DC Servo Motor

A DC servo motor is usually a DC motor of low power rating. DC servo motors have a high ratio of starting torque to inertia and therefore they have a faster dynamic response. A DC servo motor is used as an actuator to drive a load. DC Servomotors are permanent magnet type or separately excited DC Servo Motors. Permanent magnet type DC Servo Motors are constructed using rare earth permanent magnets which have high residual flux density and high coercivity. As no field winding is used in Permanent Magnet DC Servo Motors, the field copper losses are zero due to which the overall efficiency of the motor is high. The speed torque characteristic of this motor is flat over a wide range, as the armature reaction is negligible. Moreover speed is directly proportional to the armature voltage for a given torque. Armature of a DC servo motor is specially designed to have low inertia. In some application DC servo motors are used with magnetic flux produced by separate field windings. The speed of Permanent Magnet DC motors can be controlled by applying variable armature voltage. These are called armature voltage controlled DC servo motors. Wound field DC motors can be controlled by either controlling the armature voltage or controlling the field current [2, 4, 6, and 10].

1.3 Literature Survey

There are several PID tuning techniques used today: Ziegler-Nichols, frequency domain tuning, tuning using optimization, relay based tuning, internal model control tuning and other methods [26].

Traditionally, the controllers have been tuned experimentally by the method of Ziegler and Nichols. This method called "continuous cycling method’ has been known as a fairly accurate procedure to determine good settings of PID controllers for a wide range of common industrial processes. The controller parameters were obtained in the following way: set and increase until a periodic oscillation occurs in the output. The value of at this point is called the ultimate gain () and the oscillation period is called the ultimate period (). The final step is to compute the controller parameters based on the following three formulas:

(1.1)

However, very little emphasis is given to measurement noise, sensitivity to process variation and set point response that can cause the closed-loop system to be poorly damped and to have poor stability margins.

Without bringing the system close to instability a new experimental method was introduced by Astrom and Hagglund using a relay to generate an oscillation for measuring the ultimate gain and ultimate period. This was done by employing the configuration shown in Figure 1.1, where the relay is adjusted to induce a self-sustaining oscillation in the loop [27].

Figure 1.1: Block diagram of relay feedback.

In earlier work based on the Buckingham’s pi-theorem, the application of dimensional analysis in tuning of PI controllers for first order systems with delay was introduced [29]. This analytical method was based on defining and gains in terms of the three parameters of the plant function: plant gain, time delay and the coefficient of the first order term in the denominator. The goal was to then to apply the pi-theorem to simplify these functions. The proposed method proved to be advantageous over Ziegler-Nichols method.

In [18] an optimization algorithm is proposed for designing PID controllers, which minimizes the asymptotic open loop gain of a system, subject to appropriate robust stability and performance Quantitative feedback Theory constraints. In [30] a simple optimization algorithm is proposed for designing fixed-structure controllers for highly uncertain systems. The method can be used to automate the loop-shaping step of the QFT design procedure and guarantees robust stability and performance to the feedback loop for all parameters in the plant’s uncertainty set. To avoid over-designing the system, the algorithm can be used to minimize the asymptotic gain, the open-loop crossover frequency or the 3 dB bandwidth of the closed-loop system (nominal or worst case). In [7], an extension of the Hermite-Biehler theorem for quasi-polynomials was used to derive all stabilizing PID controllers. Datta et al. first described the closed-loop characteristic equation as a quasi-polynomial

(1.2)

whereand represent, respectively, the real and imaginary parts of . Then, due to Pontryagin’s results, they were able to find the necessary and sufficient condition that defines the range of such that zeros of and are simple and real. Through further investigation they also showed that for a fixed value of the region defining the stabilizing parameters and is a convex polygon. Similar results were also used to obtain the two-dimensional stabilizing regions in case of PI and PD controllers.

The method introduced in [22] considers decomposing the numerator and denominator of the plant transfer function into their even and odd parts and then obtaining solutions for the stabilizing parameters in terms of such decomposition. Since the solutions are functions of frequency, the author also considers the calculation of the frequency range over which the parameters need to be evaluated.

Bhattacharyya and colleagues used a mathematical generalization of the Hermite-Biehler theorem to find all stabilizing PID controllers for systems with time-delay [7, 9, and 12]. In [16] an innovative controller design method, which did not required complex mathematical derivation, was presented. Much of the early works done in this area concentrated on finding PID controllers that stabilize a nominal plant model. The authors of [16] extended their research by obtaining the entire region of PID controllers that met certain gain and phase margin requirements. In [19, 23], techniques for finding all achievable PID controllers that stabilized an arbitrary order system and satisfied weighted sensitivity, complementary sensitivity, robust stability and robust performance constraints were introduced.

1.4 Problem Formulation

Design of the system to obtain the desired performance is the control problem. The necessary basic equipment is then assembled into a system to perform the desired control function. Although most systems are nonlinear, in many cases the nonlinearity is small enough to be neglected, or the limits of operation are small enough to allow a linear analysis to be used. A basic system has the minimum amount of equipment necessary to accomplish the control function. After a control system is synthesized to achieve the desired performance, based upon the design technique that is chosen, final adjustments can be made in a simulation, or on the actual system, to take into account the nonlinearities that were neglected. A computer is generally used in the design, depending upon the complexity of the system [1].

In this thesis report two techniques are mainly proposed to find the controller gains for the position control of DC Servo Motor. These two techniques which are proposed for the design of position control of DC Servo Motor are the quantitative feedback theory and the graphical representation method. First of all transfer function for the DC Servo Motor is obtained. The gains of the controller are then obtained based on the Quantitative feedback theory. QFT is a unified theory that emphasizes the use of feedback for achieving the desired system performance tolerances despite plant uncertainty and plant disturbances [5]. Then this controller is applied successfully in the feedback loop; with plant as the transfer function of the DC Servo Motor. After that graphical method of controller design is used for the Design of position control of DC Servo Motor model with time delay. Time delay is a big problem in the industry. In the mathematical description of a physical or biological process, it is quite common to assume that the future behavior of the process depends only on the present state, and therefore can be described by a finite set of ordinary differential equations. This is satisfactory for a large class of practical systems. However, such description does not account for important behaviors of many systems that include time delays. Indeed, due largely to the current lack of effective methodology for analysis and control design for such systems, the time-delay elements are often either neglected or poorly estimated, which frequently results in analysis and simulation of insufficient accuracy, which in turn leads to unsatisfactory performance of the system designed. Indeed, it has been demonstrated in the area of automatic control that a relatively small delay may lead to instability or significantly deteriorated performances for the corresponding closed-loop system.

In order to reliably analyze and design feedback control for such systems, it is necessary to consider the fact that the system’s future behaviors depend not only on the current value of the state variables, but also some past history of the state variables. These systems are called time-delay systems. Examples of the systems that cause time delays include: the measurement of system variables (engineering process), the physical nature of some system’s components (hydroelectric power systems; biological and ecological systems, such as population dynamics) or signal transmissions (power and communications systems). To effectively deal with time-delay systems, the engineers in the control fields are faced with three issues: (1) How to mathematically describe such systems in a form which is convenient for analysis and design? (2) How to analyze a given system to extract some fundamental properties? And (3) How to design a PID (PD, PI) controller to achieve stability and satisfy desired performance requirements?

A principal goal of this research is to show that it is possible to design a controller that can be applied to the position control of dc servo motor that stabilizes the nominal system without and with time delay.

1.5 Organization of the Thesis

The remainder of the thesis is organized as follows. In chapter 2, a general overview of the structure and application of feedback control systems is given. In this chapter, the most basic but important robust control concepts of nominal stability, robust stability, and uncertainty modeling are discussed. In chapter 3, DC Servo Motor is discussed. In chapter 4, position control of DC Servo Motor using Quantitative Feedback Theory is described. In Chapter 5, Design of Position control of DC Servo Motor based on Graphical Representation Method is presented. Chapter 6, summarizes the results obtained in this research and highlights future research that can be done in the area of controller design for the position control of DC Servo Motor.