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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.
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 Feedback Control System Characteristics Introduction 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 sites.google.com/site/ncpdhbkhn 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 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 output response Disturbance Error (–) Controller Actuator Sensor Process Actual output Measurement noise Measurement output Feedback Closed – loop control system with external disturbances & measurement noise sites.google.com/site/ncpdhbkhn Feedback Control System Characteristics Introduction 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 sites.google.com/site/ncpdhbkhn Error Signal Analysis (1) Td ( s ) R( s) Ea ( s ) ( ) Gc ( s ) G( s) Controller Process H ( s) Y ( s) N ( s) Sensor E ( s) R( s) Y ( s) Y ( s) Gc ( s )G ( s ) Gc ( s )G ( s ) G( s) R( s) Td ( s ) N ( s) Gc ( s )G ( s ) Gc ( s )G ( s ) Gc ( s )G ( s ) E ( s) Gc ( s )G ( s ) G( s) R( s) Td ( s ) N ( s) Gc ( s )G ( s ) Gc ( s )G ( s ) Gc ( s )G ( s ) L( s ) Gc ( s )G ( s ) E ( s) G( s) L( s ) R( s) Td ( s ) N (s) L( s ) L( s ) L( s ) sites.google.com/site/ncpdhbkhn Error Signal Analysis (2) Td ( s ) R( s) Ea ( s ) ( ) Gc ( s ) G( s) Controller Process H ( s) Y ( s) N ( s) Sensor L( s ) Gc ( s )G ( s ) F ( s ) L( s ) S ( s) 1 F ( s ) L( s ) C ( s) L( s ) L( s ) E ( s ) S ( s ) R ( s ) S ( s )G ( s )Td ( s ) C ( s ) N ( s ) S ( s) C ( s) sites.google.com/site/ncpdhbkhn Feedback Control System Characteristics Introduction 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 sites.google.com/site/ncpdhbkhn ` Sensitivity of Control Systems to Parameter Variations (1) Td ( s ) R( s) Ea ( s ) ( ) Gc ( s ) G( s) Controller Process H ( s) Y ( s) N ( s) Sensor Gc ( s )G ( s ) Gc ( s )G ( s ) G( s) Y ( s) R( s) Td ( s ) N ( s) Gc ( s )G ( s ) Gc ( s )G ( s ) Gc ( s )G ( s ) Gc ( s )G ( s ) 1, Td ( s ) 0, N ( s ) Y ( s) R( s) sites.google.com/site/ncpdhbkhn 10 Disturbance Signals in a Feedbak Control System (1) E ( s) G( s) L( s ) R( s) Td ( s ) N ( s) L( s ) L( s ) L( s ) R ( s ) N ( s ) 0, S ( s ) 1 L( s ) G( s) E ( s) Td ( s ) S ( s )G ( s )Td ( s ) L( s ) sites.google.com/site/ncpdhbkhn 18 Ex Disturbance Signals in a Feedbak Control System (2) Va ( s ) E ( s) ( ) I a ( s) Km Ra Td ( s ) Tm ( s ) ( ) Motor back electromotive force http://ftpmirror.your.org/pub/wikimedia/images/wikipedia/fr/d/d9/ ( s) TL ( s ) Js b Kb 1 Js b E ( s) Td ( s ) Td ( s ) 1 Js b K K / R b m a Kb Km Ra Js b Td ( s ) D / s lim E (t ) lim sE ( s ) lim s t s 0 s0 sites.google.com/site/ncpdhbkhn D Js b K b K m / Ra s D 0 ( ) b K b K m / Ra 19 Ex Disturbance Signals in a Feedbak Control System (3) Va ( s ) lim E (t ) t E ( s) ( ) D b K b K m / Ra I a ( s) Km Ra Td ( s ) Tm ( s ) ( ) ( s) TL ( s ) Js b Motor back electromotive force R( s) Ea ( s ) Ka ( ) Amplifier Km ( ) Ra Vt ( s ) Kb Td ( s ) Tm ( s ) ( ) ( s) TL ( s ) Js b Kb Kt Tachometer Ra Js b lim E (t ) D E ( s) Td ( s ) t Ka Km Kt K K Kb 1 a m K t Ra Js b Ka sites.google.com/site/ncpdhbkhn 20 Disturbance Signals in a Feedbak Control System (4) Td ( s ) R( s) Ea ( s ) ( ) Gc ( s ) G( s) Controller Process H ( s) Y ( s) N ( s) Sensor E ( s) Gc ( s )G ( s ) G( s) R( s) Td ( s ) N ( s) Gc ( s )G ( s ) Gc ( s )G ( s ) Gc ( s )G ( s ) sites.google.com/site/ncpdhbkhn 21 Feedback Control System Characteristics Introduction 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 sites.google.com/site/ncpdhbkhn 22 Control of the Transient Response (1) T ( s) d Tm ( s ) ( ) Km ( s) ( s) Ra s TL ( s ) Js b ( ) Load Armature K Back electromotive force b Va ( s ) Km ( s) Va ( s ) s[( Js b) Ra K b K m ] G( s) Km ( s) Va ( s ) [( Js b) Ra K b K m ] Km Ra b K b K m K1 Ra J s 1s Ra b K b K m Va ( s ) ( s) k2 E s K1 k2 E (t ) K1k2 E (1 e t / 1 ) 1s s sites.google.com/site/ncpdhbkhn 23 Control of the Transient Response (2) T ( s) d (t ) K1k2 E (1 e t / 1 ) 1 Tm ( s ) ( ) Km ( s) ( s) Ra s TL ( s ) Js b ( ) Load Armature K Back electromotive force b Va ( s ) Ra J Km , K1 Ra b K b K m Ra b K b K m k E R( s) s Ea ( s ) KaG( s) ( s) R( s ) K a KtG ( s ) (t ) K a K1 1s K a K t K1 Ka ( ) Amplifier Km ( ) Ra Vt ( s ) Td ( s ) Tm ( s ) ( ) ( s) TL ( s ) Js b Kb Kt Tachometer K a K t K1 k2 E K a K t K1 K a K1k2 E exp t exp t K a K t K1 1 Kt 1 sites.google.com/site/ncpdhbkhn 24 Control of the Transient Response (3) 0.8 Speed With feedback Without feedback 0.6 0.4 0.2 0 10 Time (s) 12 sites.google.com/site/ncpdhbkhn 14 16 18 20 25 Feedback Control System Characteristics Introduction 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 sites.google.com/site/ncpdhbkhn 26 Steady – State Error (1) Eopen loop ( s ) R ( s ) Y ( s ) [1 G ( s )]R ( s ) R( s) s Eo ( s ) G( s) s G( s) eo ( ) lim eo (t ) lim sEo ( s ) lim s G (0) t s 0 s 0 s Eclosed loop ( s ) R( s) Gc ( s )G ( s ) R( s) s 1 Ec ( s ) Gc ( s )G ( s ) s 1 ec ( ) lim ec (t ) lim sEc ( s ) lim s t s 0 s 0 G ( s )G ( s ) s Gc (0)G (0) c sites.google.com/site/ncpdhbkhn 27 Steady – State Error (2) Open – loop Closed – loop ec ( ) eo ( ) G (0) G (0) K 1 Gc (0)G (0) Gc (0) 1; G (0) K eo ( ) K K eo ( ) K 0.1 eo ( ) 0.1 K eo ( ) 0.1 0.1 | r (t ) | 1 ec ( ) 1 K K 100 ec ( ) 1/101 K 1 0.1 ec ( ) K 101 91 ec ( ) 0.0011 | r (t ) | sites.google.com/site/ncpdhbkhn 28 Feedback Control System Characteristics Introduction 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 sites.google.com/site/ncpdhbkhn 29 The Cost of Feedback • Feedback control is very good, but • An increased number of components & complexity: – Requires sensor(s) – The sensor is often the most expensive component in a control system – The sensor introduces noise & inaccuracies into the system • The loss of gain: Gc ( s )G ( s ) Gc ( s )G ( s ) Gc ( s )G ( s ) • The possibility of instability sites.google.com/site/ncpdhbkhn 30 Feedback Control System Characteristics Introduction 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 sites.google.com/site/ncpdhbkhn 31 Ex Control System Characteristics Using Control Design Software R( s) ( ) 11s K Controller sites.google.com/site/ncpdhbkhn Td ( s ) ( ) s( s 1) Y ( s) Load 32 ... 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 Feedback Control System Characteristics. .. 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... 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