Advanced Automation†
[lecture #1] 2010.9.2 review of classical control theory (given by Prof. Kimura)†
[lecture #2] 2010.9.9 CACSD introduction†
- introduction of Matlab and Simulink
[lecture #3] 2010.9.16 CACSD introduction†
- review of clasical control theory
- transfer function
- Bode diagram
- characteristics of 2nd-order system
- Nyquist stability criterion
- gain margin and phase margin
- review of modern control theory
- state-space representation
[lecture #4] 2010.9.30 Intro. to Robust Control†
- H infinity norm
- robust stabilization
- 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
- robust stabilization <--
- 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 #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
[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.
- Confirm the following m-file for design:
- Derive the generalized plant by hand and correct the m-file.
- Run the m-file to find controller.
- 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
- step response
- noise response (noise type: step, sinusoidal wave 1Hz, 50Hz, 500Hz)
- initial response (x(0) = [1;0;0])
[lecture #12] 2010.11.25 Speed control of two inertia system with servo motor (1/3)†
- simulation (cont. from Nov.18)
- Problem setup
- Modelling (frequency response experiment)
[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)
- Problem setup
- Objective for control system design
- speed tracking
- robust against inertia-load variation
- Modelling
- Controller design (mixed sensitivity problem)
- example of m-file
>> cont
- design example 1 (wt1 = 2*pi*50 is set in weight.m)
- design example 2 (wt1 = 2*pi*20 is set in weight.m)
- example of m-file to compare designed controllers
- 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:
- bode diagram of controllers
- gain characteristic of closed-loop systems
- 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
- format of frdata.dat file
- 1st column: frequency (Hz)
- 2nd column: gain
- 3rd column: phase (deg)
- program sources for control experiment
- 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
[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:
- example of m-file
- design example 1 (wt1 = 2*pi*20 is set in weight.m)
- design example 2 (wt1 = 2*pi*5 is set in weight.m)
[lecture #15] 2010.12.16 Speed control of two inertia system with servo motor (cont.)†
- preparation of your own controller(s)
participant list2010
related links†