授業/制御工学特論2010

Advanced Automation†

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[lecture #1] 2010.9.2 review of classical control theory (given by Prof. Kimura)†

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[lecture #2] 2010.9.9 CACSD introduction†

introduction of Matlab and Simulink
- Basic usage of MATLAB and Simulink used for 情報処理演習及び考究II/Consideration and Practice of Information Processing II: Advanced Course of MATLAB

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[lecture #3] 2010.9.16 CACSD introduction†

review of clasical control theory
1. transfer function
2. Bode diagram
3. characteristics of 2nd-order system
4. Nyquist stability criterion
5. gain margin and phase margin
review of modern control theory
1. state-space representation

[lecture #4] 2010.9.30 Intro. to Robust Control†

H infinity norm
1. robust stabilization
2. performance improvement

ex21.m

ex22.m

s = tf('s')
G = 1/(s+1)
norm(G, 'inf')
P = 1/(s^2 + 0.2*s + 1)
K = 1
nyquist(P*K)
help impulse
impulse(P)
T = 1/(1 + P*K)
impulse(T)
sqrt(2)/(2*pi)
1/ans
step(T)
ex21
ex22

[lecture #5] 2010.10.7 Introduction to Robust Control (cont.)†

H infinity norm
1. robust stabilization <--
2. performance improvement

[lecture #6] 2010.10.14 norm, vector space, normed linear space†

H infinity norm ... {robust stabilization, performance improvement}
norm
- size of {number, signal, system}
- defined on vector space (linear space)
  - ---> normed linear space
  - ... optimization

[lecture #7] 2010.10.21 eigenvalue, eigenvector, singular value decomposition†

H infinity norm : scalar (SISO) ---> matrix (MIMO)
- absolute value ---> maximum singular value
- background: mixed sensitivity problem {robust stabilization and performance improvement are simultaneously considered}

norm2.pdf

A = [2, 1; 0, 1]
[X, L] = eig(A)
X*L/X - A
[U, S, V] = svd(A)
U*U'
V*V'
U*S*V'
U*S*V' - A
sqrt(eig(A'*A))
S

[lecture #8] 2010.10.28 state space representation of connected system, state space representation of generalized plant for various control problem, mixed sensitivity problem†

[lecture #9] 2010.11.4 robust control design example: Robust Control System Synthesis for Pneumatic Systems (given by Prof. Kimura)†

see RubustControlOfPneumatic-e.pdf in Prof. Kimura's homepage for detail

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[lecture #10] 2010.11.11 robust control design example (cont.)†

Design H infinity controller with Eqs.(41)-(47) and generalized plant depicted in Fig.3 in the pdf file.
1. Confirm the following m-file for design:
  pneum.m
  
  pneum_ans.m
2. Derive the generalized plant by hand and correct the m-file.
3. Run the m-file to find controller.
Simulation
simu_pneum.mdl

simu_pneum_noise.mdl

simu_pneum
plot(t, y, 'r', t, r, 'b');

simu_pneum_noise
plot(t, y, 'r', t, n, 'b')

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[lecture #11] 2010.11.18 robust control design example (cont.) (given by Prof. Kimura)†

Exercise

step response
noise response (noise type: step, sinusoidal wave 1Hz, 50Hz, 500Hz)
initial response (x(0) = [1;0;0]）

whiteboard #1

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[lecture #12] 2010.11.25 Speed control of two inertia system with servo motor (1/3)†

simulation (cont. from Nov.18)
Problem setup
apparatus.pptx
Modelling (frequency response experiment)

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[lecture #13] 2010.12.2 Speed control of two inertia system with servo motor (2/3)†

~~reduced-order controller design~~ (will be given by Prof. Kimura using with the robust control design example)
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whiteboard #2
Problem setup
- Objective for control system design
1. speed tracking
2. robust against inertia-load variation
  setup.pdf
Modelling
- frequency response experiment results:
  frdata_offset0_small.dat
  
  frdata_offset0_large.dat
  
  frdata_offset5_small.dat
  
  frdata_offset5_large.dat
  
  frdata_offset10_small.dat
  
  frdata_offset10_large.dat
- example of m-file
  freqresp.m
  
  nominal.m
  
  weight.m
```
>> freqresp
>> nominal
>> weight
```
Controller design (mixed sensitivity problem)
- example of m-file
  cont.m
```
>> cont
```
- design example 1 (wt1 = 2*pi*50 is set in weight.m)
  cont1.dat
  
  cont_order1.dat
  
  cont1.mat
  
  result_small1.dat
  
  result_large1.dat
- design example 2 (wt1 = 2*pi*20 is set in weight.m)
  cont2.dat
  
  cont_order2.dat
  
  cont2.mat
  
  result_small2.dat
  
  result_large2.dat
- example of m-file to compare designed controllers
  compare.m

report

design your controller so that the system performance is improved compared with the given example above
Draw the following figures and explain the difference between two control systems:
1. bode diagram of controllers
2. gain characteristic of closed-loop systems
3. time response of control experiment
Why is the performance of your system improved(or unfortunately decreased)?
- due date: 28th(Tue) Dec 17:00
- submit your report(pdf or doc) by e-mail to kobayasi@nagaokaut.ac.jp
- You can use Japanese
- maximum controller order is 20
- submit your cont.dat and cont_order.dat to kobayasi@nagaokaut.ac.jp not later than 24th Dec

program sources for frequency response experiment
freqresp.h

freqresp_module.c

freqresp_app.c
- format of frdata.dat file
  - 1st column: frequency (Hz)
  - 2nd column: gain
  - 3rd column: phase (deg)
program sources for control experiment
hinf.h

hinf_module.c

hinf_app.c
- format of result.dat file
  - 1st column: time (s)
  - 2nd column: motor speed (rad/s)
  - 3rd column: motor torque (Nm)
  - 4th column: reference speed (rad/s)
configuration of control experiment
- reference signal is generated as described in hinf_module.c:
```
if((t > 3)&&(t < 7)){
  r = 10.0;
}else{
  r = 5;
}
```
- two inertia-load discs (small and large) are used

Difficulties of our plant: As motor speed is approximately calculated by using difference for one sampling period in hinf_module.c like
```
thetaM_rad = (double)read_theta(1) / (double)Pn212 * 2 * M_PI;
speedM_rad = (thetaM_rad - thetaM_rad_before) / msg->sampling_period;
thetaM_rad_before = thetaM_rad
```
sampling period should not become too small. On the other hand, sampling period should be chosen as small as possible so that desiged continuous-time controller could be closely implemented by its descretized version. Therefore, we have a dilemma to control our plant. The sampling period 0.25 msec was chosen by traial and error so that noise in measured speed is not too large. The gain in high frequency range of continuous-time controller should be small enough for discretization.

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[lecture #14] 2010.12.9 Speed control of two inertia system with servo motor (3/3)†

Due to a dimension change of the driven shaft, frequency response experiment has been re-conducted. Please use the following fixed files instead of the ones introduced on the previous lecture.

frequency response experiment results:
frdata_offset5_small_fixed.dat

frdata_offset5_large_fixed.dat

frdata_offset10_small_fixed.dat

frdata_offset10_large_fixed.dat
example of m-file
freqresp_fixed.m

nominal_fixed.m

weight_fixed.m

cont_fixed.m
design example 1 (wt1 = 2*pi*20 is set in weight.m)
cont1_fixed.dat

cont_order1_fixed.dat

cont1_fixed.mat

result_small1_fixed.dat

result_large1_fixed.dat
design example 2 (wt1 = 2*pi*5 is set in weight.m)
cont2_fixed.dat

cont_order2_fixed.dat

cont2_fixed.mat

result_small2_fixed.dat

result_large2_fixed.dat

whiteboard #1

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[lecture #15] 2010.12.16 Speed control of two inertia system with servo motor (cont.)†

preparation of your own controller(s)

participant list2010

↑

Advanced Automation†

[lecture #1] 2010.9.2 review of classical control theory (given by Prof. Kimura)†

[lecture #2] 2010.9.9 CACSD introduction†

[lecture #3] 2010.9.16 CACSD introduction†

[lecture #4] 2010.9.30 Intro. to Robust Control†

[lecture #5] 2010.10.7 Introduction to Robust Control (cont.)†

[lecture #6] 2010.10.14 norm, vector space, normed linear space†

[lecture #7] 2010.10.21 eigenvalue, eigenvector, singular value decomposition†

[lecture #8] 2010.10.28 state space representation of connected system, state space representation of generalized plant for various control problem, mixed sensitivity problem†

[lecture #9] 2010.11.4 robust control design example: Robust Control System Synthesis for Pneumatic Systems (given by Prof. Kimura)†

[lecture #10] 2010.11.11 robust control design example (cont.)†

[lecture #11] 2010.11.18 robust control design example (cont.) (given by Prof. Kimura)†

[lecture #12] 2010.11.25 Speed control of two inertia system with servo motor (1/3)†

[lecture #13] 2010.12.2 Speed control of two inertia system with servo motor (2/3)†

[lecture #14] 2010.12.9 Speed control of two inertia system with servo motor (3/3)†

[lecture #15] 2010.12.16 Speed control of two inertia system with servo motor (cont.)†

related links†

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