### [lecture #2] 2010.9.9 CACSD introduction †

• introduction of Matlab and Simulink

### [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
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}
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 #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

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

1. 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:
2. Derive the generalized plant by hand and correct the m-file.
3. Run the m-file to find controller.
2. Simulation
simu_pneum
plot(t, y, 'r', t, r, 'b');

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

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

Exercise

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

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

• report
1. design your controller so that the system performance is improved compared with the given example above
2. 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
3. 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
• 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;
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.

### [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.

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

• preparation of your own controller(s)

participant list2010