Method and apparatus for hybrid resetting states proportional-integral-derivative and lag controllers

• US 8,200,347 B2
• Filed: 01/22/2009
• Issued: 06/12/2012
• Est. Priority Date: 01/22/2009
• Status: Expired due to Fees

• Current Assignee: Mitsubishi Electric Research Laboratories, Inc. (Mitsubishi Electric Corporation)
• Original Assignee: Mitsubishi Electric Research Laboratories, Inc. (Mitsubishi Electric Corporation)
• Inventors: El-Rifai, Khalid, El-Rifai, Osamah
• Primary Examiner(s): Chaki, Kakali
• Assistant Examiner(s): Booker, Kelvin
• Application Number:
  US12/357,589
• Publication Number:
  US 20100185304A1
• Time in Patent Office: 1,237 Days
• Field of Search: 700/72, 700/28, 700 41- 45, 327/552, 327/556
• US Class Current: 700/45
• CPC Class Codes: G05B 11/42 for obtaining a characteristic which is both proportional and time-dependent, e.g. P. I., P. I. D.
• CPC Class Codes: G05B 2219/42076 Hybrid, digital control sets reference, coefficients for quick analog, pid, control

Abstract

A controller includes a feedforward module to produce a feedforward component az_r, where a is a high frequency gain, a proportional module is to produce a proportional component K_pvz, where K_pv is a proportional gain, and an integral or lag module with state resetting to produce an integral or lag component. The feedforward component az_r, the proportional component K_pvz, and the integral component K_ivz_c are combined as an input u for the system to be controlled.

Claims

1. A controller for controlling a system, comprising:

a feedforward module to produce a feedforward component az_r, where a is a high frequency gain;

a proportional module to produce a proportional component K_pvz, where K_pv is a proportional gain;

an integral or lag module to produce respective integral or lag components, wherein the feedforward module and the proportional module and the integral or lag module form a controller having a state, and the integral or lag module is capable of resetting the state; and

means for combining the feedforward component az_r, the proportional component K_pvz, and the integral or lag components to produce an input u for the system to be controlled, wherein the feedforward module is provided with a reference signal r and an error signal e, and wherein where the error signal is a difference between the reference signal and an output y of the system, and the error signal is also provided to the proportional module.

2. The controller of claim 1, wherein the feedforward component

is ż

_r={dot over (r)},

for order n=1, and

ż

_r={umlaut over (r)}+K_ppė

,

for order n=2, and wherein K_pp is a gain, z=−

(d/dt+K_pp)^n-1e.

3. The controller of claim 1, wherein the input is

u=−

K_pvz−

K_ivz_c+aż

_r,

where a is a high frequency gain, K_iv is an integral gain, and the integral component is

ż

_c=z, if zz_c≧

0

z_c⁺=0, if zz_c<

0,

such that the controller operates as a hybrid resetting controller.

4. The controller of claim 1, wherein the input is

u=−

K_pvz−

K_ivz_c+α

ż

_r.

where a is a high frequency gain, K_iv is an integral gain, and wherein the lag component is

ż

_c=z−

a_cz_c, if (z−

a_cz_c)z_c>

0

z_c⁺=0, if (z−

a_cz_c)z_c≦

0, and

where a_c is the lag pole, such that the controller operates as a resetting lag controller.

5. The controller of claim 1, wherein the input is

6. The controller of claim 1, wherein the input is

u=−

K_pvz−

K_iv1z_c1−

K_iv2z_c2+aż

_r,

where a is a high frequency gain, and

ż

_c1=z, if zz_c1≧

0

z_c1⁺=0, if zz_c1≦

0

ż

_c2=z

where K_iv1>

0 is the integral gain corresponding to state z_l1, and K_iv2>

0 is a non-resetting integral gain corresponding to state z_l2.

7. The controller of claim 1, wherein the input is

u=−

K_pvz−

K_ivz_c+aż

_r,

where a is a high frequency gain, K_iv is an integral gain, and

ż

_c=z, if zz_c≧

0

z_c⁺=a_d(t)z_c, if zz_c≦

0

where a_d is a resetting tune varying gain that can allow for switching the resetting off based on a time or state threshold condition, and t is time.

8. The controller of claim 1, wherein the input is

u=−

K_pvz−

K_ivz_c+aż

_r,

where, and a is a high frequency gain, and K_iv is an integral gain.

9. The controller of claim 1, wherein the input is

u=−

K_pvz−

K_ivz_c+aż

_r,

where a is a high frequency gain, K_iv is an integral gain, and the integral component is

ż

_c=z, if zz_c≧

0

z_c⁺=b_d, if zz_c≦

0,

where b_d is a selected offset, and controller operates as a hybrid resetting controller.

10. A controller for controlling a system, comprising:

a feedforward module to produce a feedforward component az_r, where a is a high frequency gain;

a proportional module to produce a proportional component K_pvz, where K_pv is a proportional gain;

an integral or lag module to produce respective integral or lag components, wherein the feedforward module and the proportional module and the integral or lag module form a controller having a state, and the integral or lag module is capable of resetting the state; and

means for combining the feedforward component az_r, the proportional component and the integral or lag components to produce an input u for the system to be controlled, wherein the input is

u=−

K_pvz−

K_ivz_c+aż

_r,

where a is a high frequency gain, K_iv is an integral gain, and the integral component is

ż

_c=z, if zz_c≧

0

z_c⁺=0, if zz_c≦

0,

such that the controller operates as a hybrid resetting controller.

11. A controller for controlling a system, comprising:

a feedforward module to produce a feedforward component az_r, where a is a high frequency gain;

a proportional module to produce a proportional component K_pvz, where K_pv is a proportional gain;

an integral or lag module to produce respective integral or lag components, wherein the feedforward module and the proportional module and the integral or lag module form a controller having a state, and the integral or lag module is capable of resetting the state; and

means for combining the feedforward component az_r, the proportional component K_pvz, and the integral or lag components to produce an input u for the system to be controlled, wherein the input is

u=−

K_pvz−

K_ivz_c+aż

_r,

where a is a high frequency gain, K_iv is an integral gain, and wherein the lag component is

ż

_c=z−

a_cz_c, if (z−

a_cz_c)z_c≧

0

z_c⁺=0, if (z−

a_cz_c)z_c≦

0, and

where a_c is the lag pole, such that the controller operates as a resetting lag controller.

12. A controller for controlling a system, comprising:

a feedforward module to produce a feedforward component az_r, where a is a high frequency gain;

a proportional module to produce a proportional component K_pvz, where K_pv is a proportional gain;

an integral or lag module to produce respective integral or lag components, wherein the feedforward module and the proportional module and the integral or lag module form a controller having a state, and the integral or lag module is capable of resetting the state; and

means for combining the feedforward component az_r, the proportional component. K_pvz, and the integral or lag components to produce an input u for the system to be controlled, wherein the input is

13. A controller for controlling a system, comprising:

a feedforward module to produce a feedforward component az_r, where a is a high frequency gain;

a proportional module to produce a proportional component K_pvz, where K_pv is a proportional gain;

an integral or lag module to produce respective integral or lag components, wherein the feedforward module and the proportional module and the integral or lag module form a controller having a state, and the integral or lag module is capable of resetting the state; and

means for combining the feedforward component az_r, the proportional component K_pvz, and the integral or lag components to produce an input u for the system to be controlled, wherein the input is

u=−

K_pvz−

K_ivz_c+aż

_r,

where a is a high frequency gain, and

ż

_c1=z, if zz_c1≧

0

z_c1⁺=0, if zz_c1≦

0,

ż

_c2=z

where K_iv1>

0 is the integral gain corresponding to state z_l1, and K_iv2>

0 is a non-resetting integral gain corresponding to state z_l2.

14. A controller for controlling a system, comprising:

a feedforward module to produce a feedforward component az_r, where a is a high frequency gain;

a proportional module to produce a proportional component K_pvz, where K_pv is a proportional gain;

an integral or lag module to produce respective integral or lag components, wherein the feedforward module and the proportional module and the integral or lag module form a controller having a state, and the integral or lag module is capable of resetting the state; and

means for combining the feedforward component az_r, the proportional component K_pvz, and the integral or lag components to produce an input u for the system to be controlled, wherein the input is

u=−

K_pvz−

K_ivz_c+aż

_r,

where a is a high frequency gain, K_iv is an integral gain, and

ż

_c=z, if zz_c≧

0

z_c⁺=a_d(t)z_c, if zz_c≦

0,

where a_d is a resetting time varying gain that can allow for switching the resetting off based on a time or state threshold condition, and t is time.

15. A controller for controlling a system, comprising:

a feedforward module to produce a feedforward component az_r, where a is a high frequency gain;

a proportional module to produce a proportional component K_pvz, where K_pv is a proportional gain;

an integral or lag module to produce respective integral or lag components, wherein the feedforward module and the proportional module and the integral or lag module form a controller having a state, and the integral or lag module is capable of resetting the state; and

means for combining the feedforward component az_r, the proportional component K_pvz, and the integral or lag components to produce an input u for the system to be controlled, wherein the input is

u=−

K_pvz−

K_ivz_c+aż

_r,

where a is a high frequency gain, K_iv is an integral gain, and the integral component is

ż

_c=z, if zz_c≧

0

z_c⁺=b_d, if zz_c≦

0,

where b_d is a selected offset, and controller operates as a hybrid resetting controller.