![transfer latexit into latex transfer latexit into latex](https://expressionsvinyl.com/product_images/uploaded_images/printable-heat-transfer-vinyl-how-to-1.jpg)
Draw the bode plot of the pre-filter (5 pts)Īnd explain how to realize it ( Transfer function of pre-filter, 2. Push the gain below 30 Hz as close as possible to 1). That the feedback controller cannot be changed, design a good pre -filter to reduce this effect (to It is seen that the gain is not 1 at all frequencies below the bandwidth. The complementary sensitivity obtained for a mass-spring-damper based positioning system is.Integrator can also be added but it is not the best choice since you may require more than one integrator. Then the error is: c) an anti-notch controller with Q of 10. Solution: a) tracking happens at low frequency so sensitivity at low frequency can be simplified to S=1/(1+L) and L=kp/ms 2, hence S=e/r= ms 2 /kp b) maximum bandwidth to achieve the 30degree phase margin is almost 400 rad/s where the phase of the actuator goes below -20 degree (phase of the system with actuator is - 200 degree).
![transfer latexit into latex transfer latexit into latex](https://www.bbraunusa.com/content/dam/catalog/bbraun/bbraunProductCatalog/S/AEM2015/en-us/b1/pinnacle-tpn-transfersets6-lead.jpeg)
(7 pts)Ĭ) What needs to be added to the controller to reduce the error by 10 times.
![transfer latexit into latex transfer latexit into latex](https://i.ytimg.com/vi/9kFtKR1c6EA/hqdefault.jpg)
Hint: Use electrical model of actuator to find the transfer function F/I. Assume a tamed PD provides 50 - degrees phase lead.There is no requirement for modulus and gain margins.The phase margin requirement is at least 30 degree.Inductance and resistance of the actuator. Consider a Lorenz actuator with motor constant of k = 1 and L =1mH and R = 1 ohm are.To follow a 2 mm displacement at 5rad/s with the error of 30 nano-meter? (5 pts)ī) In presence of actuator dynamics as shown in the figure below, find the error of the system Consider a mass system with mass of 100 grams controlled with a tamed PD (lead) controller:Ī) Following the rule of thumb what is the desired bandwidth (defined as crossover frequency).Solution: a is more robust since the differentiation has large band i “a” is larger than the rest. Which of them is more robust against the gain variation of the system (3 pts)? In order to provide a phase lead of 80 degree three lead controllers (, ).Since after the phase lag after the second resonance is -360 degree and it cannot be compensated by differentiator. Why controlling a non-collocated double mass spring system is more difficult than collocated Mechanical compression produces voltage between the piezostack electrodes. Piezostack behaves electrically like a capacitor and mechanically like a high-stiffness spring.ī. Are the following statements true or false?Ī. Zero in the transfer function reduces the slope of the transmissibility function to -1 at high frequencyĬonsider a piezoelectric stack transducer (piezostack). Solution: Transmissibility has one zero and a double pole while compliance only has a double pole. Consider a single mass-spring-damper system, what is the difference between transmissibilityĪnd compliance of the system? Draw the bode plot of both systems ( 6 pts).