Advanced Automation

[lecture #1] 2011.9.1 review of classical control theory

[lecture #2] 2011.9.8 CACSD introduction with review of classical control theory

  • introduction of Matlab and Simulink

[lecture #3] 2011.9.15 given by Prof. Kimura cancelled

[lecture #4] 2011.9.22 given by Prof. Kimura cancelled

[lecture #5] 2011.9.29 given by Prof. Kimura cancelled

supplementary lectures will be given by Prof. Kimura.

[lecture #3] 2011.10.6 CACSD introduction with review of classical and modern control theory

  1. relationship between TF and SSR (higher order case)
  2. open-loop stability
    • can be checked by poles of TF and eigenvalues of A-matrix in SSR
  3. closed-loop stability
    • can be checked graphically by Nyquist stability criterion and Bode plot with GM(gain margin) and PM(phase margin)
    • can be checked numerically by poles of closed-loop TF and eigenvalues of A-matrix in closed-loop SSR
%-- 10/6/2011 1:25 PM --%
grid on

[lecture #4] 2011.10.13 Intro. to robust control theory (H infinity control theory)

  • H infinity norm
    1. robust stabilization
    2. performance optimization
  • Example of performance optimization problem : disturbance attenuation problem
    • controller design with trial and error
    • controller design with H infinity control theory
s = tf('s');
G = 1/(s+1);
norm(G, inf)
G = 1/(s^2+0.1*s+1);
norm(G, inf)

[lecture #5] 2011.10.7 Introduction to Robust Control (cont.)

  • H infinity norm
    1. robust stabilization
    2. performance optimization
  1. a class used to represent plant uncertainty and/or perturbation ... H infinity norm
  2. small gain theorem
    • connects the closed-loop H infinity norm and robust stability condition
    • sketch proof ... Nyquist stability criterion
  3. practical example of robust stabilization problem
%-- 10/20/2011 1:41 PM --%
c = 0.8

[lecture #6] 2011.10.27 norm (vector space, normed linear space), singular value, mixed sensitivity problem

  • H infinity norm ... {robust stabilization, performance improvement}
  • norm
    • size of {number, signal, system}
    • defined on vector space (linear space)
      • ---> normed linear space
      • ... optimization
  • H infinity norm : scalar (SISO) ---> matrix (MIMO)
    • absolute value ---> maximum singular value
    • robust stabilization or performance optimization problem ---> mixed sensitivity problem
  • reference
    • Feedback control theory / John C. Doyle, Bruce A. Francis and Allen R. Tannenbaum
      • 2. Norms for signals and systems
      • 3. Basic concepts
      • 4. Uncertainty and robustness ... p.62 Eq.(4.10) H infinity norm condition in mixed sensitivity problem
    • Robust and optimal control / Kemin Zhou, John C. Doyle and Keith Glover
      • 2. Linear algebra (2.7 Vector norms and matrix norms, 2.8 Singular value decomposition)
      • 4. Performance specifications (4.1 Normed spaces, 4.3 Hardy spaces H_2 and H_infinity)
      • 9. Model uncertainty and robustness
      • 16. H infinity control: simple case
      • 17. H infinity control: general case

[lecture #8] 2011.11.10 state space representation of connected system, state space representation of generalized plant for various control problem, mixed sensitivity problem (by Prof. Kimura)

see Prof. Kimura's page

[lecture #9] 2011.12.1 robust control design example: Robust Control System Synthesis for Pneumatic Systems (given by Prof. Kimura)

[lecture #10] 2011.12.8 Speed control of two inertia system with servo motor (1/3)

  • report
  1. design your controller(s) 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 (your controller and the example above):
    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(Wed) Dec 17:00
    • submit your report(pdf or doc) by e-mail to
    • You can use Japanese
    • maximum controller order is 20
    • submit your cont.dat, cont_order.dat, and cont.mat to not later than 23th(Fri) 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
    • reference signal is generated as described in hinf_module.c:
      if((t > 3)&&(t < 7)){
        r = 10.0;
        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(0) / (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.
%-- 12/8/2011 1:22 PM --%
load result_small.dat
plot(result_small(:,1),result_small(:,2), 'b', result_small(:,1),result_small (:,4),'r')

[lecture #11] 2011.12.15 Speed control of two inertia system with servo motor (2/3)

  • explanation of design example (cont. from the previous lecture)
  • preparation of your own controller(s)
%-- 12/15/2011 1:06 PM --%
help hinfsyn
Ktf = tf(K)
bode(K, 'r', Ktf, 'b')
legend('ss', 'tf')
help fitsys

[lecture #12] 2011.12.22 Speed control of two inertia system with servo motor (3/3)

  • preparation of your own controller(s)

participant list2011

supplementary lectures will be given by Prof. Kimura.

  • example for changing ws = 2 pi 0.1 -> 2 pi 0.01

    #ref(): The style ref(filename,pagename) is ambiguous and become obsolete. Please try ref(pagename/filename)

%-- 12/22/2011 1:20 PM --%

related links

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Last-modified: 2011-12-22 (木) 14:18:25 (2103d)