Dr. D.Y.Patil Institute of Engineering, Management and Research Mechatronics - 302050 UNIT -VI Mrs. Amruta Adwant Syllabus Control Systems P, I and D control actions, P, PI, PD and PID control systems, Transient response:- Percentage overshoot, Rise time, Delay time, Steady state error PID tuning (manual)
Objectives 1. 2. 3. 4. 5. 6. 7. Understand key elements of Mechatronics system, representation into block diagram Understand concept of transfer function, reduction and analysis Understand principles of sensors, its characteristics, interfacing with DAQ microcontroller
Understand the concept of PLC system and its ladder programming, and significance of PLC systems in industrial application Understand the system modeling and analysis in time domain and frequency domain. Understand control actions such as Proportional, derivative and integral and study its significance in industrial applications. Outcomes 1. 2. 3. 4. 5. 6.
Identification of key elements of mechatronics system and its representation in terms of block diagram Understanding the concept of signal processing and use of interfacing systems such as ADC, DAC, digital I/O Interfacing of Sensors, Actuators using appropriate DAQ micro-controller Time and Frequency domain analysis of system model (for control application) PID control implementation on real time systems Development of PLC ladder programming and implementation of real life system Assumed Knowledge Dynamics:
Engineering Mechanics Electrical & Electronics Elements of Electrical Engineering Mathematics Engineering Mathematics (I, II & III) Reference Books Astrom & Hagglund, PID Controllers: Theory, Design & Tuning, Chapter 2, 2nd Ed, Instrument Society of America, 1995. Golnaraghi & Kuo, Automatic Control System, Chapter 1/5/9,
9th Ed, John Wiley & Sons, 2009 Why is Controller Necessary? Blue response resembles an un-controlled system. This response is oscillatory as well as it takes much longer to settle down. For a mechanical system, this could be due to Inertia effect, friction, backlash etc The red response is of a controlled system. This response contains no oscillations and it settles to equilibrium / steady state in lesser time. Job of a control system is to generate a control input / effort that can be used to drive the un-controlled system, albeit externally, to achieve the desired performance. Illustration: What does Controller do? -imaginary
X u -real X Undesirable Open Loop Pole Location X Desired Closed Loop Pole Location X +real X
Control is all about shifting of system poles from un-desirable to desirable location. +imaginary This shifting is done by the control signal, u, provided the system allows it i.e. the system is controllable u Analysis of Response: Transient Specifications Unit Step Response of Second Order System
Transient Response Specifications Percentage Overshoot (% O.S): It is the amount that the response overshoots the steady state, or final, value at the peak time, expressed as a percentage of the steady-state value. Rise Time (Tr): Time required for the step response to rise from 10% to 90% of its final value. Delay Time (Td): Time required for the step response to reach 50% of final value Settling Time (Ts): Time required for the step response to decrease and stay within 2% of its final value Steady State Error (ess): It is the difference between the output and the reference input after the steady state has reached Feedback Controller
Block Diagram of Feedback Controller Feedback controller generates an control signal / effort / external disturbance based on the input signal it receives. The input signal is error; difference between measured value and desired value, or set point. Feedback counters disturbance as well as variation in process Controllability Advanced Learning (Out of Syllabus) Before a controller is implemented it is necessary to determine
is the system is controllable Test the Controllability of the system Controllability is the ability of the system to be controlled provided an external disturbance is available. Proportional Integral Derivative Control Input + e
PID u Plant Output _ Block Diagram of PID Controller PID stands for Proportional Integral Derivative Control. Being robust & easy to implement, it is one of the most widely used closed loop control for precise operation of industrial applications and processes.
Proportional Control u t u P t K P e Offset In Proportional Control, the control signal, u, is directly proportional to the error, e. As the gain is increased the system responds faster to changes in set-point but becomes progressively under damped and eventually unstable. Proportional Control Action P Control Signal
Proportional Control Advantages: Simple and easy to design and tune Rapid Response / Reduces Rise Time Reduces Steady State Error Disadvantages: Not possible to eliminate Steady State Error / Offset Could lead to instability / rise in overshoot/ oscillations Applications: Float Valve, Thermostat etc Derivative Control
u t u D t K D de dt Derivative control produces a control signal proportional to the rate at which the error is changing. Also known as rate controller. While sudden/rapid change in error leads to a control signal of larger magnitude, gradual change leads to small magnitude. Even if the error is huge, the derivative control will generate no
signal if the error is constant Thus, not used alone; used with P control Derivative Control Action D Control Signal Derivative Control Advantages: Reduces Settling time; Adds lead Reduces Overshoot; Adds more stability Disadvantages: Not possible to eliminate Steady State Error / Offset
Not possible to use alone Excessive use may make the system slow Amplifies Noise Applications: In conjunction with P Control Integral Control u t u I t K I edt Rate of change of integral control signal is proportional to error. Control signal proportional to integral of error. When the error is zero, the control signal is a constant value. When the error is constant, the control signal varies at constant
rate. Integral Control Action I Control Signal Integral Control Advantages: Eliminates steady state error/offset Decreases Rise Time Disadvantages: Causes Integral Wind Up Leads to minor increase in overshoot
Could make the system less stable Increases Settling time Applications: In conjunction with P Control Integral Wind Up Advanced Learning (Out of Syllabus) Caused by actuator saturation. What Happens? Feedback loop is broken and the system runs in open loop because the actuator remains saturated. While the error is zero, the integral term will keep building and become very large
over a period of time. This in turn would lead to saturation of control signal. The condition will prevail even when the error changes and it may take a long time before the integrator and the controller output comes inside the saturation range. The consequence is that there are large time delay. PID: Series / Interacting Form D e P Derivate Action interacts with Integral Action
Modification in derivative time constant affects integral action Commercially used controller I + + + +
u Transfer Function of Series Form Transer Function of PID in series : P PD 1 I where, P Proportional Controller, I Integral Controller D Derivative Controller TF P PD PI PID The term PID 0 since Ti 4Td where, Ti Integral Time Constant, Td Derivative Time Constant TF P PI PD Transfer Function of Series Form
Control Signal for PID in series : u t u P t u P t u I t u P t u D t K P e K P K I edt K P K D de dt Where, e Error Difference between reference & measured signal
PID: Parallel / Non-Interacting Form Kds Ki s ysp + Ideal Form Derivative Action does not Interact with Integral Action ui + e -
ud Kp + up + u plant y
Transfer Function of Parallel Form Transer Function : H s K P KI s KDs Where, K P Proportional Gain, K I Integral Gain K D Derivative Gain Control Signal :
u t u P t u I t u D t K P e K I edt K D de dt Where, e Error Difference between reference & measured signal Parallel Form: PI Control H s K P K I
s Where, K P Proportional Gain, K I Integral Gain u t u P t u I t K P e K I edt Proportional Integral (PI) Control helps minimise rise time, settling time as well as eliminate steady state error. PI Control Parallel Form: PD Control H s K P K D s Where,
K P Proportional Gain, K D Derivative Gain u t u P t u D t K P e K D de dt Proportional Derivative (PD) Control helps reduce rise time, settling time as well as minimize overshoot. Proportional Derivative Control
Response of P, I & D w.r.t Error Effect of P, I & D on Transient Specifications Action Rise Time Overshoot Settling Time KP Decrease Increase
Small Change KI Decrease Increase Initially Eliminate Decrease then Increase KD Small
Change Decrease Decrease SS Error Decrease Small Change P, I & D Control Action
PID: Stepwise Procedure for Manual Tuning 1. 2. 3. 4. 5. 6. Obtain an open-loop response and determine what needs to be improved Add a proportional control to improve the rise time Add a derivative control to improve the overshoot Add an integral control to eliminate the steady-state error Adjust each of P, I & D until you obtain a desired overall
response referring to the table shown previously to find out which controller controls what characteristics. It is not necessary to implement all three controllers (P, I & D) into a single system. For example, if a PI controller gives a good enough response, then you don't need to add D control to the system. Simple is better. PID: Stepwise Procedure for Manual Tuning NOTE It is not necessary to implement all three controllers (P, I & D) into a single system. For example, if a PI controller gives a good enough response, then you don't need to add D control to the system. Simple is better!
Applications of PID Control 90% processes are controlled using PID. Regulation of Processes in Industry; for e.g. 1. 1. Flow 2. Temperature
3. Pressure etc 2. Servo / DC motor Control 3. Linear Position Control
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