The dc gain, again is the ratio of the magnitude of the steadystate step response to the magnitude of the step input, and for stable systems it is the value of the transfer function when. If pis a pole it follows that yt ept is a solution to the 6. Files supplied with the srv02 position control experiment. For example, suppose we know two steady states for an input, u, and an output, y. Breaking up the system into different frequency bands is especially useful when plotting the bode of more complex systems. A pv controller in essence is a pd controller without the. The tf model object represents transfer functions in polynomial form.
The following topics are covered in this laboratory. The steady state gain of a system is simply the ratio of the output and the input in steady state. The transfer function model notation assume, for now, that the target variable yt is stationary i. The dynamics between the angle of the servo load gear and the position of the ball is described by transfer function p bb s. In this lab, students are asked to tune the transfer function parameters and do some basic model fitting. Obtain srv02 transfer function using a frequency response experiment. And the transfer function is only valid when the system is linear, not when it is slewing. Find the closedloop srv02 position control transfer function.
The basic srv02 units comes with an potentiometer sensor that can. As we shall see in the next section, the transfer function represents the response of the system to an exponential input, u est. Find find the control gains k p and k d in terms of n and. Speed control lab experiment adapted from student workbook, quanser srv02 base unit. Transfer functions are a frequencydomain representation of linear timeinvariant systems. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. Every laboratory chapter in this manual is organized into four sections. Introduction the objective of this experiment is to develop a feedback system that controls the position of the rotary servo load shaft. Motor heat loss rises with both v and i and motor t accelerates wear, while bearing wear rises exponentially with rpm. Objectives the objective in this experiment is to introduce the student to the fundamentals of control using the pid family of compensators. Find the transfer function vo vi of the rc circuit in fig.
In the next few sections, the timebased motion equations are developed and, from these equations of. Ten modules to teach controls from the basic to advanced. If a, it will give, the transfer function of this linear system thus will be rational function, note that, as and bs are given above as polynomial of system. Laboratory described in appendix a to get familiar with using quarcrwith the srv02. Srv02 position control specifications the time domain specifications for controlling the position of the srv02 load shaft are, e ss 0 11 t p 0. On completion of this tutorial, you should be able to do the following.
Using the proportionalintegralderivative pid family, a compensator is designed to meet a set of specifications. Closed loop transfer function the proportionalvelocity pv compensator to control the position of the srv02 has the structure where kp is the proportional control gain, k, is the velocity control gain. How to mathematically model the servo plant from first principles. Assuming that the the input and the output of the system. Transfer functions the roots of the polynomial as are called poles of the system and the roots of bs are called the zeros of the system. Srv02 ball and beam control laboratory student manual 1. The zpk model object represents transfer functions in factorized form. Transfer function from unit step response for each of the unit step responses shown below, nd the transfer function of the system. The srv02 ets system includes a slip ring assembly that allows the modules to be rotated the full 360 degrees. The basic unit is equipped with a potentiometer to measure the outputload angular position. Quanser srv02 system there are two srv02 options available.
It is difficult to estimate swrps because of the spatial and temporal variability of the soil hydraulic properties in the field. At the end of this session, you should know the following. Implementation of pv and piv control for position control of. Frequency response method to derive transfer function of. Srv02 ball and beam control laboratory student manual. Statespace computation of the h 2 norm rather than ev aluating the in tegrals 2. This function has three poles, two of which are negative integers and one of which is zero. Srv02 et speed control experiment 1 objective the objective in this experiment is to design a feedback controller that would regulate the speed of the output shaft. Yildiz technical university department of mechanical. Desired position control response the block diagram shown in figure 1 is a general unity feedback system with a compensator cs and a transfer function representing the plant, ps.
Obtaining the srv02 transfer function using a frequency response experiment. Steady state gain the transfer function has many useful physical interpretations. New smith predictor structure used for the control of the. Suppose you want your initial conditions to be zero. Based on these responses and the answers to the questions in the prelab, we will infer the coe. Exam february, answers geng5514 finite element methods. In this lab, students are asked to tune the transfer function parameters and do. It turns out that the form of the transfer function is precisely the same as equation 8. Evaluate a transfer function at a single angular frequency.
The default for compare is to estimate initial conditions from the data. Transfer functions, poles and zeros waterloo maple. Mar 04, 2014 feedback control systems fcs lecture2 transfer function and stability of lti systems dr. Converter transfer functions this is of the following standard form. In the next few sections, the timebased motion equations are developed and, from these equations of motion, its transfer function is obtained. How to find a transfer function that describes th e rota ry motions of the.
Obtaining the srv02 transfer function using a bump test. The rotary servo base unit srv02 is the fundamental element of the quanser rotary control experiments. The model parameters can also be found experimentally. Srv02 base unit flexible link inverted pendulum ball and beam 2 dof inverted multidof torsion pendulum 2 dof robot flexible joint gyrostable platform double inverted pendulum 2 dof ball balancer with the srv02 base unit, you can select from 10 addon modules to create experiments of varying complexity across a. The spaces are called after british pure mathematician g. Description the plant consists of a dc motor in a solid aluminum frame. Download fulltext pdf download fulltext pdf modeling and control of a rotary inverted pendulum using various methods, comparative assessment and result analysis conference paper pdf available. File name description 01 srv02 modeling student this laboratory guide contains prelab and inlab exercises manual.
The tf model object can represent siso or mimo transfer functions in continuous time or. The transfer function of the system is bs as and the inverse system has the transfer function as bs. Pdf modelling of periodic flows in pipelines by transfer. Obtaining the srv02 transfer function using a frequency response. The transfer function can thus be viewed as a generalization of the concept of gain. Instrumentation and control tutorial 3 transfer function manipulation this tutorial is of interest to any student studying control systems and in particular the ec module d227 control system engineering. Pdf modeling and control of a rotary inverted pendulum. The system shown in figure 1 is a linear model of the quanser srv02 dc motor with. Because speed is the derivative of position, these two transfer functions. If we have an input function of x s, and an output function y s, we define the transfer function h s to be. Model the speed of the srv02 using a firstorder transfer function. The parameters, and characterize the behavior of a canonical secondorder system.
The specifications that are needed for the questions can be found in the srv02 user manual in table 3. Closed loop transfer function the proportionalvelocity pv compensator to control the position of the srv02 has the structure. Compare identified model output and measured output matlab. In addition, pedotransfer functions ptf help to convert the. May seem like an odd, arbitrary function now, but well later see why it is very important convolution in the time domain corresponds to. Convolution systems convolutionsystemwithinputu ut0,t transfer functions and convolution 819.
The inverse system is obtained by reversing the roles of input and output. Srv02 base unit experiment for matlabsimulink users ten modules to teach controls from the basic to advanced level abet, inc. Control systems steady state errors tutorialspoint. Second order transfer functions 8 w t norris 2nd order transfer functions monday 3 march 2008 ii the peak is at about 14 db for. If slew limit is involved, or other large signal conditions, then step response is no longer the laplace transform of the transfer function, because the system is no longer linear time invariant. The transfer function method is presented to model periodic flows in water pipelines. Accurate control of flexible link robot arm chalmers publication. The inlab exercises are explained using the quarc software. The solution for this situation is the introduction of a smith predictor structure presented below. Generally in all universities in india and worldwide quanser servo plant with the quanser q4. Laplace transforms are used to transform the governing equations for transient flows and then converted into. That is, the motor has its own internal gearbox that drives external gears. Nov 21, 2017 a transfer function is the ratio of the output of a system to the input of a system, in the laplace domain considering its initial conditions and equilibrium point to be zero. Signalsget step response of continuous transfer function yst.
The transfer function generalizes this notion to allow a broader class of input signals besides periodic ones. To use zero for initial conditions, specify z for the initialcondition option. For instance, consider a continuoustime siso dynamic system represented by the transfer function syss nsds, where s jw and ns and ds are called the numerator and denominator polynomials, respectively. We know that the transfer function of the system has the generic firstorder system form given in equation 1. Transfer function methodology tfm the transfer function methodology tfm is a dynamic means of accounting for heat transfer. Mimo transfer functions are arrays of siso transfer functions. The transfer function model is described by the following three equations. The srv02 transfer function pss represents the dynamics between the servo input motor voltage and the resulting load angle. It turns out that the form of the transfer function.
The srv02 transfer function p s s represents the dynamics between the servo input motor voltage and the resulting load angle. They can decrease overall performance and may constitute a source of instability of the system, feng 2009. Transfer functions continued ys m k0 bks k n k0 aks k xshsxs in the time domain, the relationship can be complicated in the s domain, the relationship of ys to xs of lti systems simpli. Ball and beam position control lab rotary motion servo. Srv02 position control laboratory student manual file name description table 1. Although there are other methods of accounting for heat transfer, carriers hap program utilizes tfm in its calculations because it extends the analysis to account for specific system behavior to control the air. Srv02et speed control experiment mcmaster university. Wiring and operating procedure of the srv02 plant with the upm and dac device, as discussed in reference 5. Attach the black disc load to the motor with the two bronze screws.
Using the proportionalderivative pd family, a cascade control system is designed to meet a set of specifications. Create an option set to specify the initial condition handling. Before drawing the bode magnitude plot, approximate the lowfrequency gain of the system when. Using the graph, we can estimate the time constant as t 0. Figure 2 below is a simulink block diagram mapping the different stages of the system. Sdient of the ccm of some basic conveners con v buck dr c fundamentals of power electronics chapter 8. Steadystate gain the steadystate of a tf can be used to calculate the steadystate change in an output due to a steadystate change in the input. Multiply the flippedshifted signal and the other signal integrate the result from. Description the quanser srv02 rotary servo plant, pictured in figure 1, consists of a dc motor that is encased in a solid aluminum frame and equipped with a planetary gearbox. The motor has its own internal gearbox that drives external gears. The magnitude of the frequency response of the srv02 plant transfer function given in equation 1. Computation of the modulation transfer function is a mechanism that is often utilized by optical manufacturers to incorporate resolution and contrast data into a single. The srv02 transfer function model is derived analytically in section 4. Control systemstransfer functions wikibooks, open books.
How to design quarc controllers for quansers srv02 system. Then we can calculate the steadystate gain, k, from. This assumption is relaxed for systems observing transience. The dynamics between the angle of the servo load gear and the position of the ball is described by transfer function pbbs. In the position control experiment the motorload transfer function with speed as output found in 5. Yildiz technical university department of mechanical engineering. These are known as the nominal model parameter values. Introduction the objective of the ball and beam experiment is to stabilize the ball to a desired position along the beam. The purpose of this lab is to design a controller using the 2nd order transfer function representation of the form. Transfer function parameters are found using frequency response and the obtained model is used to design a servo position control. The transfer function of a time delay is thus gs e. Actual transfer function requires monitoring v, i and rpm to know lift. R, ft 0 for all t srv02 motorconnector power leads to the srv02 dc motor. Transfer functions laplace transform laplace transform consider a function ft, f.
Inside the piv control subsystem, set the manual switch to the. Recall in the srv02 modeling laboratory, the srv02 voltage. In paddy field, soil saturated hydraulic conductivity k s plays as an important component in the calculation of irrigation requirement of the water balance equation and also for irrigation efficiency. The bb01 transfer function describes the displacement of the ball with respect to the load angle of the servo. Srv02 position control lab rotary motion servo plant. Srv02 position control laboratory student manual 1. Rotary servo base unit srv02 the rotary servo base unit experiment acquaints students with the concept of rotary displacement control, which is integral to such highprecision applications as a cdrom drive.
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