ECE 382 Feedback Systems Analysis and Design Stan Żak School of Electrical and Computer Engineering Purdue University zak@purdue.edu August 20, 2012 1/49
Today s Class Instructor intro during the first week: Stan Żak https://engineering.purdue.edu/ece/people/ 2/49
Today s Class Instructor intro during the first week: Stan Żak https://engineering.purdue.edu/ece/people/ The rest of the semetster Dr. Rick Meyer 3/49
Today s Class Instructor intro during the first week: Stan Żak https://engineering.purdue.edu/ece/people/ The rest of the semetster Dr. Rick Meyer TA Joelle Lawson 4/49
Today s Class Instructor intro during the first week: Stan Żak https://engineering.purdue.edu/ece/people/ The rest of the semetster Dr. Rick Meyer TA Joelle Lawson Topics covered this week 5/49
Today s Class Instructor intro during the first week: Stan Żak https://engineering.purdue.edu/ece/people/ The rest of the semetster Dr. Rick Meyer TA Joelle Lawson Topics covered this week System concept, control problem formulation 6/49
Today s Class Instructor intro during the first week: Stan Żak https://engineering.purdue.edu/ece/people/ The rest of the semetster Dr. Rick Meyer TA Joelle Lawson Topics covered this week System concept, control problem formulation The Laplace transform review 7/49
Today s Class Instructor intro during the first week: Stan Żak https://engineering.purdue.edu/ece/people/ The rest of the semetster Dr. Rick Meyer TA Joelle Lawson Topics covered this week System concept, control problem formulation The Laplace transform review Block diagrams, modeling 8/49
System concept, control problem formulation A system is a collection of interacting components 9/49
System concept, control problem formulation A system is a collection of interacting components An electric motor, an airplane, as well as a biological unit such as the human arm are examples of systems 10/49
System concept, control problem formulation A system is a collection of interacting components An electric motor, an airplane, as well as a biological unit such as the human arm are examples of systems A system is characterized by two properties: 11/49
System concept, control problem formulation A system is a collection of interacting components An electric motor, an airplane, as well as a biological unit such as the human arm are examples of systems A system is characterized by two properties: 1 the interrelations between the components that are contained within the system 12/49
System concept, control problem formulation A system is a collection of interacting components An electric motor, an airplane, as well as a biological unit such as the human arm are examples of systems A system is characterized by two properties: 1 the interrelations between the components that are contained within the system 2 the system boundaries that separate the components within the system from the components outside 13/49
Representation of a system We represent system s boundaries using a box Input System Output 14/49
Representation of a system We represent system s boundaries using a box Input System Output The system boundaries can be real or imagined 15/49
The system boundaries They are elastic in the sense that we may choose, at any stage of the system analysis, to consider only a part of the original system as a system on its own 16/49
The system boundaries They are elastic in the sense that we may choose, at any stage of the system analysis, to consider only a part of the original system as a system on its own We call it a subsystem of the original system 17/49
The system boundaries They are elastic in the sense that we may choose, at any stage of the system analysis, to consider only a part of the original system as a system on its own We call it a subsystem of the original system On the other hand, we may decide to expand the boundaries of the original system to include new components 18/49
The system boundaries They are elastic in the sense that we may choose, at any stage of the system analysis, to consider only a part of the original system as a system on its own We call it a subsystem of the original system On the other hand, we may decide to expand the boundaries of the original system to include new components The interactions between the system components may be governed, for example, by physical, biological, or economical laws 19/49
The system boundaries They are elastic in the sense that we may choose, at any stage of the system analysis, to consider only a part of the original system as a system on its own We call it a subsystem of the original system On the other hand, we may decide to expand the boundaries of the original system to include new components The interactions between the system components may be governed, for example, by physical, biological, or economical laws In dealing with systems, we are interested in the effects of external quantities upon the behavior of the system quantities 20/49
Open-Loop Versus Closed-Loop Systems An open-loop control system usually contains: 1 A process to be controlled, labeled plant 21/49
Open-Loop Versus Closed-Loop Systems An open-loop control system usually contains: 1 A process to be controlled, labeled plant 2 The controlling variable of the plant, called the plant input, or just input for short 22/49
Open-Loop Versus Closed-Loop Systems An open-loop control system usually contains: 1 A process to be controlled, labeled plant 2 The controlling variable of the plant, called the plant input, or just input for short 3 The controlled variable of the plant, called the plant output, or just output for short 23/49
Open-Loop Versus Closed-Loop Systems An open-loop control system usually contains: 1 A process to be controlled, labeled plant 2 The controlling variable of the plant, called the plant input, or just input for short 3 The controlled variable of the plant, called the plant output, or just output for short 4 A reference input dictates the desired value of the output 24/49
Open-Loop Versus Closed-Loop Systems An open-loop control system usually contains: 1 A process to be controlled, labeled plant 2 The controlling variable of the plant, called the plant input, or just input for short 3 The controlled variable of the plant, called the plant output, or just output for short 4 A reference input dictates the desired value of the output 5 A controller acts upon the reference input in order to form the system input which is to force the behavior of the output in accordance with the reference signal 25/49
A schematic representation of an open-loop system Reference input Desired output Controller Controller output Plant input Plant Actual output 26/49
Characteristics of open-loop systems The output has no influence on the input or reference signal 27/49
Characteristics of open-loop systems The output has no influence on the input or reference signal The controller operates without taking into account the output 28/49
Characteristics of open-loop systems The output has no influence on the input or reference signal The controller operates without taking into account the output Thus, the plant input is formed with no influence of the output 29/49
Characteristics of open-loop systems The output has no influence on the input or reference signal The controller operates without taking into account the output Thus, the plant input is formed with no influence of the output A household appliance such as an iron is a simple example of an open-loop control system 30/49
Characteristics of open-loop systems The output has no influence on the input or reference signal The controller operates without taking into account the output Thus, the plant input is formed with no influence of the output A household appliance such as an iron is a simple example of an open-loop control system Simple construction 31/49
Characteristics of open-loop systems The output has no influence on the input or reference signal The controller operates without taking into account the output Thus, the plant input is formed with no influence of the output A household appliance such as an iron is a simple example of an open-loop control system Simple construction Requires recalibration 32/49
Characteristics of open-loop systems The output has no influence on the input or reference signal The controller operates without taking into account the output Thus, the plant input is formed with no influence of the output A household appliance such as an iron is a simple example of an open-loop control system Simple construction Requires recalibration No way to compensate for erros due to disturbances 33/49
Closed-loop system We can convert an open-loop system into a closed-loop system by adding, to an open-loop system, the following components: 6 The feedback loop the output signal is measured with a sensor and then the measured signal is fed back to the summing junction 34/49
Closed-loop system We can convert an open-loop system into a closed-loop system by adding, to an open-loop system, the following components: 6 The feedback loop the output signal is measured with a sensor and then the measured signal is fed back to the summing junction 7 The summing junction the measured output signal is subtracted from the reference, command, input signal in order to generate an error signal, also labeled as an actuating signal 35/49
Closed-loop system block diagram Desired output Reference input Actuating signal + Controller Controller output Plant input Plant Actual output Measured output Sensor 36/49
Charactersistics o closed-loop systems The error signal causes an appropriate action of the controller 37/49
Charactersistics o closed-loop systems The error signal causes an appropriate action of the controller The controller instructs the plant to behave in a certain way in order to approach the desired output, as specified by the reference input signal 38/49
Charactersistics o closed-loop systems The error signal causes an appropriate action of the controller The controller instructs the plant to behave in a certain way in order to approach the desired output, as specified by the reference input signal The output information is fed back to the controller, and the controller then appropriately modifies the plant output behavior 39/49
Charactersistics o closed-loop systems The error signal causes an appropriate action of the controller The controller instructs the plant to behave in a certain way in order to approach the desired output, as specified by the reference input signal The output information is fed back to the controller, and the controller then appropriately modifies the plant output behavior Thus, a central component of the closed-loop system is feedback 40/49
Charactersistics o closed-loop systems The error signal causes an appropriate action of the controller The controller instructs the plant to behave in a certain way in order to approach the desired output, as specified by the reference input signal The output information is fed back to the controller, and the controller then appropriately modifies the plant output behavior Thus, a central component of the closed-loop system is feedback Feedback is a method of controlling a system by reinserting into it the results of its past performance Norbert Wiener, 1954 41/49
Closed-loop system example Watt s governor 42/49
Formulation of the Control Problem We are interested in specifying the system inputs that force the system states or outputs to behave with time in some pre-specified manner 43/49
Formulation of the Control Problem We are interested in specifying the system inputs that force the system states or outputs to behave with time in some pre-specified manner That is, we are interested in controlling the system states or outputs 44/49
Formulation of the Control Problem We are interested in specifying the system inputs that force the system states or outputs to behave with time in some pre-specified manner That is, we are interested in controlling the system states or outputs This is accomplished by means of a controller whose task is to produce the required system s inputs that in turn result in the desired system s outputs 45/49
Formulation of the Control Problem We are interested in specifying the system inputs that force the system states or outputs to behave with time in some pre-specified manner That is, we are interested in controlling the system states or outputs This is accomplished by means of a controller whose task is to produce the required system s inputs that in turn result in the desired system s outputs Constructing a controller is a part of the control problem 46/49
Essential Elements of the Control Problem 1 a dynamical system to be controlled 47/49
Essential Elements of the Control Problem 1 a dynamical system to be controlled 2 a specified objective for the system 48/49
Essential Elements of the Control Problem 1 a dynamical system to be controlled 2 a specified objective for the system 3 a set of admissible controllers, and 49/49
Essential Elements of the Control Problem 1 a dynamical system to be controlled 2 a specified objective for the system 3 a set of admissible controllers, and 4 a means of measuring the performance of any given control strategy to evaluate its effectiveness 50/49
Controller Design Example Double-inverted-pendulum-on-a-cart (DIPC) 51/49
Controller Design Example Double-inverted-pendulum-on-a-cart (DIPC) Follow four steps of the control problem 52/49