Lead lag compensators example with design so that dominant closed loop poles are at the sse is 0. Method design a lead compensator to place the dominant poles at the desired places while neglecting the effects of the lag compensator. Execute time response analysis of a second order control system using matlab 2. Validate your compensator design by simulating the nonlinear simulink model with the tuned controller parameters. Finally, the result of phase lead and phase led compensator is presented by using matlab gui. You may also find the control system designer tool helpful for designing the compensator. Lead or phaselead compensator using frequency response. Design example 1 design a lead compensator for the digital control system below so that the pm is 50, the gm is at least 10 db. Control system design by frequency response using matlab. Compensator design to improve transient performance using. Root locus lead compensator design example polezero. The transfer fcn lead or lag block implements a discretetime lead or lag compensator of the input. Responses can be overlaid on matlab using the overlaymany. The instantaneous gain of the compensator is 1, and the dc gain is equal to 1z1p, where z is the zero and p is the pole of the compensator.
If damping ratio alone is given then draw the root locus and draw line from origin at an angle to intersect the root locus, the point of intersection is the dominant pole. The implementation of classical experiments as matlab m files is described. Design a feedback compensator to reduce the settling time by a factor of 4 while continuing to operate the system with 20% overshoot. Reviews the impact of a lead compensator on the bode diagram and hence shows how this affects the margins. There is a guideline to design digital lead and lag compensators. Laser guided missile control system can be designed to gain insight into a variety of concepts, including stabilization of unstable systems, compensation properties, nichols. Various values of the sample period t will be used to show the effect that varying t. Analysis of phase lead compensator design for laser. Lec30 compensator design using root locus plots duration. Compensator design to improve transient performance using root locus prof. Webb ese 499 3 introduction consider the following unityfeedback system assume. A known nonlinear compensator design approach is adapted to allow design of nonlinear lead andor lag compensators, and a number of matlab functions are developed that automate the compensator design procedure. Achieve your design goals by manually editing compensator poles, zeros.
Laser guided missile control system can be designed to gain insight into a variety of. We can interconnect this compensator c s with a plant p s using the following code. Phase lead compensator design using bode plots, a slightly di. In the root locus design approach presented here, these two tasks are approached separately. Pdf design of a leadlag compensator for position loop. Lag lead compensator is an electrical network which produces phase lag at one frequency region and phase lead at other frequency region. Phase lead compensators are used in feedback control, usually to improve gain margins and add additional damping to a system.
Design of phase lead and phase lag compensator for pitch. Run the command by entering it in the matlab command window. Knowing these constants, the corresponding errors are easily found by using formulas 6. In the control system designer preferences dialog box, on the options tab, select a compensator format. A proportional controller design for 8% overshoot use root locus to determine. A lead compensator design example is worked based on improving transient time domain specifications. Implement discretetime lead or lag compensator simulink. A number of matlab function are developed for the compensator design method. With this design tool, control engineers would be able to rapidly design nonlinear lead andor lag compensators. Pdf computer aided design of lead compensator using root.
The steps to design the lead compensator are with root locus are. This function provides an easy way to construct a phase lead compensator with specified centre frequency and lead. Using these editors, you can interactively tune the gain, poles, and zeros of the compensator, while simultaneously visualizing the effect on the set of plants. Margin 11 the affect of lead compensators on margins. Analyze and interpret stability of the system through root locus, bode plot and nyquist plot. Create a new m file and add the following matlab code.
The proposed phase lead and phase lag compensator design can be used for any system that the mathematical model have been known to meet desired specifications. In this page, you will learn how to design digital lead and lag compensators using the rootlocus design method. Examples functions and other reference release notes pdf documentation. This insight is used to develop good and bad practice in lead compensator design. The output buffer is normally present only when resistive loads needs to be driver. From given specifications determine the damping ratio and the natural frequency.
The lag lead compensator circuit in the s domain is shown in the following figure. The transfer function of the lag compensator network is given by. Analysis of phase lead compensator design for laser guided. For this example, graphically tune your compensator using the root locus editor and openloop bode editor, and validate the design using the closedloop step response. Compensator design for a set of plant models matlab. To open the compensator editor dialog box, in control system designer, in an editor plot area, rightclick and select edit compensator. Root locus lead compensator design example polezero cancellation duration. The examples and plots presented here are all done. The twostage refers to the number of gain stages in the opamp. However if the compensator is in the form with the closed loop char. Design of a lead lag compensator for position loop control of a gimballed payload.
To interactively shape the openloop response using control system designer, use the bode editor. Chang 2004 used phaselag and phase lead compensators to control servo control systems 3. Design the lag compensator to satisfy the improvement in steady state performance. It is an excellent example to illustrate many important design concepts that area also directly applicable to other designs. The instantaneous gain of the compensator is 1, and the dc gain is equal to 1z1p, where z is the zero and p is the pole of the compensator the block implements a lead compensator when 0 compensator when 0 design compensator using automated pid tuning and graphical bode design. Depending on the effect desired, one or more lead and lag compensators may be used in various combinations. Change the nominal model to change the nominal model, in the app, click multimodel configuration. In the editor, you can adjust the openloop bandwidth and design to gain and phase. Lead, one pole and one zero on the negative real axis, with the zero having a. Ece 422 zplane root locus design george mason university. Design lag, lead, lead lag compensators and verify experimental results using matlab. Add the following commands to the above m file and rerun it in the matlab command window. You can add dynamics and modify compensator parameters using the compensator editor or using the graphical bode editor, root locus editor, or nichols editor plots compensator editor.
Design via root locus elec304alper erdogan 1 1 lecture. Control design using bode plots performance issues synthesis. This example shows how to design and analyze a controller for multiple plant models using control system designer. Design of lead compensator for process control using. Analyze toque speed characteristics of dc and ac servomotors. By default, the compensator transfer function displays in the time constant format. Students will have the knowledge on matlab and scilab tools. The lag compensator is expressed in the same form as a lead compensator. On the control system tab, you can select a compensator tuning method, and create response plots for analyzing your controller performance. Interactive educational tool for the design of compensators using. Bode diagram design is an interactive graphical method of modifying a compensator to achieve a specific openloop response loop shaping. This paper introduce the lead,lag,lag lead compensator design of root locus using single composite matlab programme. Implementation and simulation of digital control compensators from continuous compensators using matlab software. Pdf implementation and simulation of digital control.
To add poles and zeros to your compensator, in the compensator editor, rightclick in the dynamics table and, under add polezero, select the type of polezero you want to add. There are three generic compensators as phase lab compensator phase lead compensator notch filter phase lead compensator transfer function phase contribution example open loop transfer function of a system is design a control system for the following specifications 1. Getting started with the control system designer matlab. We will start from the frequency domain design using bode plot. It is a combination of both the lag and the lead compensators. However, design method described there generally applies for improving the. The purpose of compensator design generally is to satisfy both transient and steadystate speci. In matlab a phaselead compensator in root locus form is implemented using the following commands where kc, z, and p are defined. Pdf a root locus design matlab simulation lead and lag compensator to improve the steady state error and overshoot with settling time find. Evaluate the steady state performance of the lead compensated system to. Use matlab to compare the responses with a simple gain design, a lag design and a. After you have done that, use the matlab function rlocfind to select the desired closedloop poles and obtain a corresponding additional gain k. State space root locus sketching rules negative feedback rule 1.
Introduction to matlab lag compensator with bode plot lag compensator with root locus so far we have seen the design of lag compensators, now we move on to lead compensators which help in improving the transient response. Many variables have already been defined for you, and you should not change these. Pdf root locus, lead, lag, lag lead commentator using matlab with. Lead compensation tutorial resources in control education. This example illustrates the root locus design process in the zplane to obtain a discretetime compensator.
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