![]() There is a method to do this with the rlocfind command in MATLAB. The root locus near the zeros and percent overshoot line. Need the cancellation of poles and zeros near the imaginary axis, so we need to select a gain corresponding to a point on ![]() Overshoot and a fast response, we need to select a gain corresponding to a point on the root locus near the real axis andįar from the imaginary axis or the point that the root locus crosses the desired damping ratio line. Recall that we want the settling time and the overshoot to be as small as possible. Now that we have moved the root locus across the 5% damping ratio line, we can choose a gain that will satisfy the design Now let's change the axis to see the details of the root locus. In your m-file add the following lines of code: Poles at 30 and 60 and the zeros at 3+/-3.5i. It seems that a notch filter (2-lead controller) will probably do the job. We'll also need two poles placed far to the left to We will probably need two zeros near the two poles on the complex axis to draw the root locus, leading those poles to theĬompensator zeros instead of to the plant zeros on the imaginary axis. ![]() We will put another two poles further to the left on the real axis to get fast response. Two zeros very close to the two poles on the imaginary axis of uncompensated system for pole-and-zero cancellation. Make all of the poles and zeros move into the left-half plane as far as possible to avoid an unstable system. These poles and zerosĪre almost on the imaginary axis, they might make the bus system marginally stable, which might cause a problem. ![]() The command sgrid is used to overlay the desired percent overshoot line on the close-up root locus you can find more information from commandsįrom the plot above, we see that there are two pair of poles and zeros that are very close together. Note from the specification, we required the maximum overshoot,, to be less than 5% and damping ratio,, can be found from the approximate damping ratio equation. In your m-file, add the following command and then run the file, you should Let's first view the root locus for the plant. By adding zerosĪnd/or poles to the original system (adding a compensator), the root locus and thus the closed-loop response will be modified. The main idea of root locus design is to estimate the closed-loop response from the open-loop root locus plot. Therefore, the dominant poles are the roots -0.1098+/-5.2504i, which are close to the imaginary axis with a small damping We are now ready to design a controller using the root locus design method.įirst let's see what the open-loop poles of the system are: R = roots(denp) The system model can be represented in MATLAB by creating a new m-file and entering the following commands (refer to the main problem for the details of getting those commands).ĭenp= ĭen1= Step, the bus body will oscillate within a range of +/- 5 mm and will stop oscillating within 5 seconds. For example, when the bus runs onto a 10-cm (X1-X2) has a settling time less than 5 seconds and an overshoot less than 5%. We want to design a feedback controller so that when the road disturbance (W) is simulated by a unit step input, the output From the main problem, the dynamic equations in transfer function form are the following:Īnd the system schematic is the following where F(s)G1(s) = G2(s).įor the original problem and the derivation of the above equations and schematic, please refer to the Suspension: System Modeling page.
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