Lecture Control system design: Feedback control system characteristics - Nguyễn Công Phương

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Lecture Control system design: Feedback control system characteristics presents the following content: Error signal analysis, sensitivity of control systems to parameter variations, disturbance signals in a feedback control system, control of the transient response, steady – state error, the cost of feedback, control system characteristics using control design software.

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Nội dung Text: Lecture Control system design: Feedback control system characteristics - Nguyễn Công Phương

Nguyễn Công Phương CONTROL SYSTEM DESIGN Feedback Control System Characteristics
Contents I. Introduction II. Mathematical Models of Systems III. State Variable Models IV. Feedback Control System Characteristics V. The Performance of Feedback Control Systems VI. The Stability of Linear Feedback Systems VII. The Root Locus Method VIII.Frequency Response Methods IX. Stability in the Frequency Domain X. The Design of Feedback Control Systems XI. The Design of State Variable Feedback Systems XII. Robust Control Systems XIII.Digital Control Systems sites.google.com/site/ncpdhbkhn 2
Feedback Control System Characteristics 1. Introduction 2. Error Signal Analysis 3. Sensitivity of Control Systems to Parameter Variations 4. Disturbance Signals in a Feedback Control System 5. Control of the Transient Response 6. Steady – State Error 7. The Cost of Feedback 8. Control System Characteristics Using Control Design Software sites.google.com/site/ncpdhbkhn 3
Introduction (1) • An open – loop system operates without feedback & directly generates the output in response to an input signal. • It is highly sensitive to disturbances & to changes in parameters of the process. Disturbance Desired output response Controller Actuator Process Output Open – loop control system (without feedback) sites.google.com/site/ncpdhbkhn 4
Introduction (2) • A closed – loop system uses a measurement of the input signal & a comparison with the desired output to generate an error signal that is used by the controller to adjust the actuator. • Advantages: – Decreased sensitivity of the system to variations in the parameters of the process. – Improved rejection of the disturbances. – Improved measurement noise attenuation – Improved reduction of the steady – state error of the system. – Easy control & adjustment of the transient response of the system. Desired Disturbance output response Error Actual Controller Actuator Process output (–) Measurement Sensor noise Measurement output Feedback Closed – loop control system with external disturbances & measurement noise sites.google.com/site/ncpdhbkhn 5
Feedback Control System Characteristics 1. Introduction 2. Error Signal Analysis 3. Sensitivity of Control Systems to Parameter Variations 4. Disturbance Signals in a Feedback Control System 5. Control of the Transient Response 6. Steady – State Error 7. The Cost of Feedback 8. Control System Characteristics Using Control Design Software sites.google.com/site/ncpdhbkhn 6
Error Signal Analysis (1) Td ( s ) R( s) Ea ( s ) Y ( s) Gc ( s ) G( s) ( ) Controller Process N ( s) H ( s) Sensor E ( s)  R( s)  Y ( s) Gc ( s )G ( s ) G( s) Gc ( s )G ( s ) Y ( s)  R( s)  Td ( s )  N ( s) 1  Gc ( s )G ( s ) 1  Gc ( s )G ( s ) 1  Gc ( s )G ( s ) 1 G( s) Gc ( s )G ( s )  E ( s)  R( s)  Td ( s )  N ( s) 1  Gc ( s )G ( s ) 1  Gc ( s )G ( s ) 1  Gc ( s )G ( s ) L( s )  Gc ( s )G ( s ) 1 G( s) L( s )  E ( s)  R( s)  Td ( s )  N (s) 1  L( s ) 1  L( s ) 1  L( s ) sites.google.com/site/ncpdhbkhn 7
Error Signal Analysis (2) Td ( s ) R( s) Ea ( s ) Y ( s) Gc ( s ) G( s) ( ) Controller Process N ( s) H ( s) Sensor L( s )  Gc ( s )G ( s ) F ( s )  1  L( s ) 1 1 S ( s)   F ( s ) 1  L( s ) L( s ) C ( s)  1  L( s ) E ( s )  S ( s ) R ( s )  S ( s )G ( s )Td ( s )  C ( s ) N ( s ) S ( s)  C ( s)  1 sites.google.com/site/ncpdhbkhn 8
Feedback Control System Characteristics 1. Introduction 2. Error Signal Analysis 3. Sensitivity of Control Systems to Parameter Variations 4. Disturbance Signals in a Feedback Control System 5. Control of the Transient Response 6. Steady – State Error 7. The Cost of Feedback 8. Control System Characteristics Using Control Design Software sites.google.com/site/ncpdhbkhn 9 `
Sensitivity of Control Systems to Parameter Variations (1) Td ( s ) R( s) Ea ( s ) Y ( s) Gc ( s ) G( s) ( ) Controller Process N ( s) H ( s) Sensor Gc ( s )G ( s ) G( s) Gc ( s )G ( s ) Y ( s)  R( s)  Td ( s )  N ( s) 1  Gc ( s )G ( s ) 1  Gc ( s )G ( s ) 1  Gc ( s )G ( s ) Gc ( s )G ( s )  1, Td ( s )  0, N ( s )  0  Y ( s)  R( s) sites.google.com/site/ncpdhbkhn 10
Sensitivity of Control Systems to Parameter Variations (2) 1 G( s) Gc ( s )G ( s ) E ( s)  R( s)  Td ( s )  N ( s) 1  Gc ( s )G ( s ) 1  Gc ( s )G ( s ) 1  Gc ( s )G ( s ) G ( s )  G ( s )  G ( s ), Td ( s )  0, N ( s )  0 1  E ( s )  E ( s )  R( s) 1  Gc ( s )[G ( s )  G ( s )] Gc ( s ) G ( s )  E ( s )  R( s) [1  Gc ( s )G ( s )  Gc ( s ) G ( s )][1  Gc ( s ) G ( s )] Gc ( s )G ( s )  Gc ( s ) G ( s ) Gc ( s ) G ( s )  E ( s )  R( s) [1  L( s )]2 1  L( s )  L( s ) 1 G ( s )  E ( s )   R( s) L( s ) G ( s ) sites.google.com/site/ncpdhbkhn 11
Sensitivity of Control Systems to Parameter Variations (3) Td ( s ) R( s) Ea ( s ) Y ( s) Gc ( s ) G( s) ( ) Controller Process N ( s) H ( s) Sensor Y ( s) T ( s)  R( s) T ( s ) / T ( s ) T ( s ) / T ( s )  ln T S   G ( s ) / G ( s ) G ( s ) / G ( s )  ln G System sensitivity is the ratio of the change in the system transfer function to the change of a process transfer function (or parameter) for a small incremental change. sites.google.com/site/ncpdhbkhn 12
Sensitivity of Control Systems to Parameter Variations (4) Td ( s ) R( s) Ea ( s ) Y ( s) Gc ( s ) G( s) ( ) Controller Process N ( s) H ( s) Sensor Gc ( s )G ( s ) T ( s)  1  Gc ( s )G ( s )  ln T S  ln G Gc G T G (1  GcG ) 2 G 1  SG  T .  .  G T G GcG 1  Gc ( s )G ( s ) 1  GcG sites.google.com/site/ncpdhbkhn 13
Sensitivity of Control Systems to Ex. Parameter Variations (5) vout   K a vin T   Ka vin vout  Ka T K a ( 1)K a K a S KT a  .  . 1 K a T K a  Ka  Ka G vin vout T   Ka 1  Ka  1  G  Ka  T 1  Ka  G   1  T 1   Ka vin  Ka vout G 1  Ka  1  K a (   1)  Ka  1  K a (   1) sites.google.com/site/ncpdhbkhn 14
Sensitivity of Control Systems to Ex. Parameter Variations (6)  Ka G vin vout T  G  Ka 1  Ka  1  G 1  K a (   1) S KT a  SGT S KGa 1 G T G (1  G ) 2 G 1 1 1  K a (   1) STG  .  .    G T G G 1 G 1  Ka 1  Ka  1 G 1  K a (   1) 1 K a G K a [1  K a (   1)]2 Ka 1 S KGa  .  .  K a G K a  Ka 1  K a (   1) 1  K a (   1) 1  K a (   1) 1 1  S KT a  .  1  Ka  1  K a (   1) 1  K a  sites.google.com/site/ncpdhbkhn 15
Sensitivity of Control Systems to Ex. Parameter Variations (7) vin vout S KT a 1  Ka System sensitivity is the ratio of the change in the system transfer function to the change of a process transfer function (or parameter) for a small incremental change. vin vout  Ka  1 S KT a  1  Ka  vin  Ka vout G 1  K a (   1) sites.google.com/site/ncpdhbkhn 16
Feedback Control System Characteristics 1. Introduction 2. Error Signal Analysis 3. Sensitivity of Control Systems to Parameter Variations 4. Disturbance Signals in a Feedback Control System 5. Control of the Transient Response 6. Steady – State Error 7. The Cost of Feedback 8. Control System Characteristics Using Control Design Software sites.google.com/site/ncpdhbkhn 17
Disturbance Signals in a Feedbak Control System (1) 1 G( s) L( s ) E ( s)  R( s)  Td ( s )  N ( s) 1  L( s ) 1  L( s ) 1  L( s ) 1 R ( s )  N ( s )  0, S ( s )  1  L( s ) G( s)  E ( s)   Td ( s )   S ( s )G ( s )Td ( s ) 1  L( s ) sites.google.com/site/ncpdhbkhn 18
Disturbance Signals Ex. in a Feedbak Control System (2) Td ( s ) Va ( s ) E ( s) 1 I a ( s) Tm ( s ) (  ) 1 ( s) Km ( ) Ra TL ( s ) Js  b Motor back electromotive force http://ftpmirror.your.org/pub/wikimedia/images/wikipedia/fr/d/d9/ Kb 1 E ( s)  Js  b Td ( s )  1 Td ( s ) 1  Kb 1 Km 1 Js  b  K K b m / Ra Ra Js  b Td ( s )  D / s 1 D  lim E (t )  lim sE ( s )  lim s . t  s 0 s0 Js  b  K b K m / Ra s D   0 (  ) b  K b K m / Ra sites.google.com/site/ncpdhbkhn 19
Disturbance Signals Ex. in a Feedbak Control System (3) Td ( s ) Va ( s ) E ( s) 1 I a ( s) Tm ( s ) (  ) 1 ( s) Km D ( ) Ra TL ( s ) Js  b lim E (t )  t  b  K b K m / Ra Motor back electromotive force Kb Td ( s ) R( s) Ea ( s ) Km Tm ( s ) (  ) 1 ( s) Ka (  ) Amplifier (  ) Ra TL ( s ) Js  b Vt ( s ) Kb Kt 1 Tachometer Js  b  Ra E ( s)  Td ( s )  lim E (t )  D K K 1  Kb  t  Ka Km Kt 1 a m .  t K   Ra Js  b  Ka  sites.google.com/site/ncpdhbkhn 20