Control System Design Guide Using Your Computer To Understand And Diagnose Feedback Controllers 4th Edition George Ellis - Solutions

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Assume that over 1 second, the inertia of a system falls according to the equation J = 0.002 0.001t. Further, assume the speed starts at zero and accelerates at a rate of 2000 rad/sec2. At what maximum velocity will the variation be “slow”; here, slow variation is defined as when ω × dJ/dt
Design the gain scheduling for the following variation of inductance with current:Assume nominal gain is defined as the gain when i = 0. L(i) 1 mH, i < 2A =2mH/i, 2A
a. For a resolver with a 3-min-1 (1-min-1 = 1/60 degree) error at four times per revolution, what is the magnitude of velocity ripple on the sensed signal as a percentage of motor speed?b. Use Experiment 14B to verify. Solver 0 Command EA < < < >>> 7.2 KVP 100 KVI 2 < < > Err Mag (arc-min)
a. Run Experiment 14B.Measure the torque ripple as a function of velocity loop bandwidth for KVP = 1, 2, 5, 10, and 20. Note that you can set KVI = 0 to ensure stability.b. Compare this with the ripple estimated by Equation 14.13. What conclusions can you draw?EQUATION 14.13 0 Solver < < < >>> 7.2
Is the instability demonstrated by Experiment 16A caused by tuned resonance or inertial reduction? What evidence is there for your answer? Vc V Scale1: 10 (Off: 10 Scale2: 10 (Off 10) Time: 0.005
Repeat Question 1 for Experiment 16B.DATA FROM QUESTION 11. Is the instability demonstrated by Experiment 16A caused by tuned resonance or inertial reduction? What evidence is there for your answer? 0000 Command Ve 5 KVP 100 KVI Scale1 10(ON: 10 Seal 100 10 800 Time 0.005 Vc Scale Time: 0.005
Investigate the effects of increasing motor inertia on inertial-reduction instability using Experiment 16B.Tune the system setting the motor inertia to the following four values: 0.0018, 0.0045, 0.009, and 0.018 kg-m2. Using the step response for tuning systems subject to inertial-reduction
Using Experiment 17A, practice tuning by first setting KVP as high as possible with the velocity loop responding to a square wave without overshooting. Retune KVI and KPP as discussed in Section 17.1.2. Be sure to turn the “Position Loop” off when tuning or measuring the velocity loop.a. What
Transfer the values from Question 1a into Experiment 17B. Set the feed-forward gains to the maximum values without generating overshoot in response to the default trapezoidal command in the experiment.a. What are the values of KVF and KAF?b. What is the position loop bandwidth with
Transfer the values from Question 1a into Experiment 17B. Set the velocity feed-forward gain to 0.5 and the acceleration feed-forward gain to zero. Reduce position loop gain to eliminate the overshoot caused by velocity feed-forward.a. What are the values of KVF and KPP?b. What is the position
Use Experiment 17B to investigate the sensitivity of the P/PI loop concerning changing inertia.a. Tune the system without feed-forward, as in Question 1.data from question 11. Using Experiment 17A, practice tuning by first setting KVP as high as possible with the velocity loop responding to a
Verify that at the first phase crossover (200 Hz), the gain margin of the observer in Experiment 18B is set almost entirely by the value of the integral gain, KIO. Vc V Scale1: 10 (Off: Scale2 10 Time: 0.001 H. 201
Use Experiment 18A to compare the disturbance response of observer- and non-observer-based systems with identical control law gains.Compile and run the model. Change the input from command to disturbance as follows. Double-click on “Command Wave Gen” and set the amplitude to 0.0001 (this is set
Using the Live Scope displays at the bottom of Experiment 18A, compare the noise sensitivity of the two velocities’ signals. Enable resolution by double-clicking on the Live Button “Use Res?” so it displays “ON”. Command Dist Dea 850 KV 4.2 1200 Current Loop BW Vm 1/ Td Disturbance Dist
Use Experiments 18A and 18C to evaluate the robustness of an observer-based system in the presence of fluctuations of total inertia (JT).data from Experiment 18adata from experiments 18ca. Find the PM of the encoder system of Experiment 18A with nominal parameters, using VO as feedback.b. Repeat
Use Experiment 18E to study the relationship between acceleration feedback and system sample time.Use the Live Scope display to see instability caused by excessive values of KAFB.a. Make a table that shows the relationship between the maximum allowable KAFB with the system-observer sample time
a. For a sample time of 0.001 s, what is the transfer function of a single-pole low-pass filter with a bandwidth of 20 Hz?b. What is the time-domain function?c. Run the first four samples for RN = 1, N > 0.d. What is the DC gain of this filter?
a. For a sample time of 0. 00025 s, what is the transfer function of a two-pole notch filter with a bandwidth of 200 Hz and a ζ = 0.2?b. Evaluate this transfer function at the following frequencies: 150 Hz, 180 Hz, 195 Hz, 200 Hz, and 205 Hz.
Retune the proportional controller of Experiment 6 A with the power converter bandwidth set to 100 Hz. Use the criteria of Chapter 6 (no overshoot for proportional gain, etc.). Measure the overshoot, peaking, and bandwidth of the closed-loop system; measure the PM and GM of the open-loop system. E
For the system of Experiment 7A:a. Slow the sample rate to 1 kHz (T Sample = 0.001). Retune the system for max KVP causing no overshoot and KVI causing 10% overshoot. What are the new values of KVI and KVPt . Set the velocity command to 40 RPM. Since both waveform generators are set to 10 Hz, the
Run Experiment 7B using the gains of Question 4a.DATA FROM QUESTION 4Aa. Slow the sample rate to 1 kHz (T Sample = 0.001). Retune the system for max KVP causing no overshoot and KVI causing 10% overshoot. What are the new values of KVI and KVPt? When tuning this model, the disturbance waveform
For the system of Experiment 8A:a. Set the sample rate at 1 kHz (TSample = 0.001) and zero feed-forward. Tune the PI controller so KVis at the maximum value without overshoot and KI causes about 10%overshoot to a square wave. What are the gains?b. What is the bandwidth? Note: Since the controller
For the system of Experiment 8A, install the values of gains from 4a.a. What is the maximum feed-forward gain that causes no more than 20% overshoot?b. What is the bandwidth?c. Compare the results of adding feed-forward to raising the sample rate. S/H www 1/K < >> 0 At 500 0 d/dt GEst KF (%) < < >>
Design the following analog filters:a. Two-pole low-pass with a break frequency of 500 Hz and ζ = 1.0.b. Two-pole notch with a break frequency of 500 Hz and ζ = 1.0.c. Three-pole Butterworth low-pass with a break frequency of 200 Hz.
Which of the following are IIR filters?a. CN = 0.1RN + 0.4RN-1 + 0.1 RN-2b. CN = CN-1 + 0.1 RN + 0.4RN-1 + 0.1 RN2c. CN = - 0.2CN-1 + 0.2CN-2 + RN.
Compare the rise time of observer- and non-observer-based systems to a step command.a. Open Experiment 10A and retune the system for reasonable margins of stability (e.g., find maximum KP without overshoot and maximum KI for 30% overshoot to step).b. What is the settling time?c. Repeat parts a and
Retune an observer for a lower bandwidth.a. Open Experiment 10G and retune the system starting with KDO ζ 0.05, KPO ζ 0, and KIO ζ 0. For limits allow 15% overshoot with KPO and slight ringing with KIO. b. What is the bandwidth of the observer?c. Using Experiment 10C, place the values of part a
Using hot connection on the Live Scope in Experiment 10C, compare the plant output (C) with the sensor output (Y).a. Are they similar?b. If so, does this imply sensor phase lag is not a significant factor in closed-loop performance? 1.5 30 KP KI < < >>> 50 0 Gc Gpc K Gp Gs Command R Solver 60 KPO
Show that having the exact value for the estimated sensor bandwidth is not required for the experimental process to find KEst discussed in Section 10. 4.3.4. In Experiment 10E, corrupt the value of the sensor bandwidth by changing it from 20 to 30 Hz (top node of GSEst block); be careful to restore
Provide the modeling equations for the following figure. Assume an analog PI controller (GC(s)), a single-pole low-pass filter with a break frequency of 200 Hz for the feedback filter (H(s)), and a model of a single-pole low-pass filter with a break frequency of 100 Hz for the power converter (GPC
What is the gain and phase of a single-pole low-pass filter(a) at its bandwidth and(b) at 1/10 its bandwidth?(c) Repeat for a two-pole low-pass filter with ζ = 0.7
a. Using Experiment 3A, what is the gain margin with the default settings? What is this on the linear scale?b. What gain of KP would cause instability?c. What gain of KP will yield 3 dB of GM? Install this gain and comment on the step response. How much peaking does this cause? d. What conclusion
a. Using Experiment 3A, what is the gain margin with the default settings? What is this on the linear scale? b. What gain of G would cause instability?c. What gain of G will yield 3 dB of GM? Install this gain and comment on the step response. How much peaking does this cause?d. Compare Questions
Using Experiment 3A, follow the zone-based tuning procedure of Section 3.5 using a square wave command with the following criteria: For KP, allow no overshoot. For KI, allow about 10% overshoot.a. What are KP and KI?b. Repeat Question 1a, but inject extra phase lag in the loop by reducing the
a. Using the DSA in Experiment 4A to generate open-loop Bode plots, what is the phase margin when the sample time is set to its default (0.00025 sec)?b. Repeat with a sample time of 0.0005 sec.c. Repeat with a sample time of 0.001 sec.d. What conclusion could you draw? 100 < > 65 KVI Wave Gen TCalc
a. In Experiment 4A, set the sample frequency to 50 msec and measure the phase margin.b. Compare this with the phase margin with a 1-msec sample time (same as Question 1c).(DATA FROM QUETION 1C)c. Repeat with a sample time of 0.001 sec.c. Assume that a 50-msec sample time in Experiment 4A is short
Provide the ideal gain scheduling for Figure 12.16 as a function of Q.DATA FROM FIGURE 12.16 Assume inertia varies with theta as follows:where JM is the motor inertia, JL is the load inertia, and R is the length of both arms connected to the elbow. Assume that the nominal gain is defined as the
Continuing Question 5, turn off the lag filter and use a notch filter to improve the performance. Simultaneously adjust Notch Freq and KVP to maximize KVP without inducing peaking in the closed-loop Bode plot.DATA FROM QUESTION 5Using Experiment 16C, improve the performance of a system with reduced
Assume a gain margin of 20 dB and a plant with a nominal gain of 50/sec. Assume also that the minimum GM of the system is specified to 10 dB. To what maximum value of gain can the plant climb under all operating conditions?
Correcting for reversal error correction and deadband compensation are special cases of what general technique?
Name three benefits of using software R/D conversion compared with hardware R/D converters.
For a 2000-line encoder sampled at 5 kHz, what is the speed resolution absent filtering?
a. What are the two advantages of resolvers over encoders?b. What are the two advantages of encoders over resolvers?
What servo drive configuration is the least intelligent? And the most intelligent?
Why do servomotors produce less torque at high speeds with the same current?
Why does the torque constant of a servo motor fall at a high current?
For a modulated power transistor on a 330-VDC bus, if the transistor is on 30% of the PWM cycle, what is the average output voltage?
Which commutation method provides the smoothest output torque d sine-wave or sixstep?
For brushless permanent-magnet motors, what is the primary advantage of DQ control over phase control?
What sensors are typically used to commutate six-step motors? Why are these sensors not used for sine-wave commutation?
Table 17.3 shows that the gains resulting from the tuning procedures of Chapter 17 turned out to provide nearly equivalent transfer functions for P/PI, PI/P, and PID position control. This could also have been done analytically.data from table 17.3a. Using the relationships shown in Table 17.1,
a. Provide the transfer function for an accumulator (Euler’s integrator) assuming a sample time of 0.01s.b. What is the time-domain function?The z-Domain 95c. Repeat 1a) with trapezoidal integration.DATA FROM REPEAT 1Aa. Provide the transfer function for an accumulator (Euler’s integrator)
For a sample time of 0. 005 s,a. evaluate z at 10 Hz.b. Repeat for 20 Hz.c. Repeat for 50 Hz.
a. For a system sampling at 0. 05 s, where does aliasing start?b. What frequency components are indistinguishable from DC?
a. What is the DC gain of a 14-bit A/D converter with a span of10 V?b. Repeat for a 16-bit ADC.c. Repeat for a 14-bit D/A converter with a span of5 V.DATA FROM REPEAT A14-BIT D/Aa. What is the DC gain of a 14-bit A/D converter with a span of10 V?
For the tuning procedures used in Questions 1 e4, list two steps you could take to make the tuning more aggressive (that is, producing smaller margins of stability).
In the power supply of Figure 7.5, what is the primary means of improving disturbance response at very high frequency?DATA FROM FIGURE 7.5What would the equivalent means be for a motor controller? And for a temperature controller? U-{s) K S Kp l-(s) LPF Cel(s) ILOAD(S) lg(s) + (s)L?V + |al- Gp(s)
What is the most common way to achieve ideal disturbance response to DC disturbances?What is the most common problem encountered when trying to implement disturbance decoupling?
a. If the power converter and feedback signals are ideal, what is the command response of a control system using full feed-forward?b. Why is full feed-forward impractical in most systems?
For the given simplified control loop:a. What is the ideal feed-forward function if GC(s) is a PI control law?b. What if GC(s) is a PID control law? GF(s) 1 R(s) Ge(s) C(s) Ls
What is the effect of full feed-forward gains on disturbance response? And on phase margin and gain margin?
An input that is sampled at 5 kHz is corrupted with a noise input with a frequency of 194 kHz. What frequency will the noise alias to?
What is the approximate relationship between settling time and bandwidth when settling to 0.5% of the final value?
a. Estimate the frequency of ringing in Figure 2.13b.DATA FROM FIGURE 2.13Bb. Estimate the frequency of maximum peaking in Figure 2.14b, the corresponding Bode plot.DATA FROM FIGURE 2.14Bc. What conclusion do you draw by comparing a and b? Command Feedback 45% Overshoot Scale1: 10 (Off: 20) Scale2:
Which of the following functions are not linear, time-invariant (LTI)? For those that are not, state at least one of the LTI rules they violate:a. Integrationb. Differentiationc. Additiond. Subtractione. Multiplication of a variable by a constantf. Multiplication of a variable by itself
a. For Question 3a, what is the phase margin and gain margin?DATA FROM QUETION 3Aa. What are KP and KI?b. Repeat for Question 3b.DATA FROM QUETION 3Bb. Repeat Question 1a, but inject extra phase lag in the loop by reducing the feedback filter break frequency to 100 Hz.c. Repeat for Question 3c.DATA
a. For Question 3a, what is the bandwidth?DATA FROM QUESTION 3Aa. What are KP and KI?b. Repeat for Question 3b.DATA FROM QUETION 3Bb. Repeat Question 1a, but inject extra phase lag in the loop by reducing thefeedback filter break frequency to 100 Hz.c. Repeat for Question 3c.DATA FROM QUETION 3Cc.
The first row of Table 4.2 provides “aggressive” assumptions. Using Experiment 4A, examine the meaning of “aggressive” in this context.DATA FROM TABLE 4.2a. Validate the entry in Table 4.2 for “aggressive, position-based motion systems.” Use parameter settings from Section 4.4.2.b. What

Control System Design Guide Using Your Computer To Understand And Diagnose Feedback Controllers 4th Edition George Ellis - Solutions

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