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INDUSTRIAL AUTOMATION (Getting Started week -1)

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Contents PID Controller. Implementation of PID Controller. Response under actuator Saturation. PID with Anti Reset windup. Tuning methods of PID Controller.

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PID controller Consists of three modes: 1. P roportional. 2. I ntigral. 3. D erivative.

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PID Contd. the output of the PID controller u(t) can be expressed in terms of the input e(t).

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Basic terms related to PID Kp : Proportional gain. PB : Proportional Band Ki : Intigral gain = Kp/Ti Kd : Derivative gain = Kp.Td where, Ti =Intigral Time :Time taken to repeat the proportional control for a step signal(min/repeat). Td =Derivative time: Time taken for the proportional term to equal the derivative term for a ramp signal.

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Implementation of PID Controller Integrator Windup under Actuator Saturation

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Implementation Contd. PID Controller with anti reset Windup.

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Tuning of PID Controller Involves selection of the proper values of Kc,Tau_I and Tau_d. Best method, Ziegler-Nichols method of tuning. the values of controller parameters that bring the closed-loop system to the verge of instability by 1. Simulation. 2. Root Locus Technique. 3. Direct substitution.

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Contd. Using Proportional only control, determine Kc = Ku ( ultimate controller gain) the period of the sustained oscillations Pu ( ultimate period of oscillations). Pu= 2π/ω co If the Kc is increased the process dynamics goes through the following sequence of behaviour

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Tuning methods Contd. By using the values of Ku and Pu, determine the other parameters of PID Controller. summarized as below.

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Contd. Dynamic changes as Kc is increased for a FOPDT process.

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Controller Tuning In Time Domain This is done by approx. model based on the Process Reaction Curve (open -loop).

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Contd. The other parameters of controller can be caluclated as folows.

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Example The given transfer function is as follows. By using SIMULINK/MATLAB. we can get the parametes of PID controller. By the Zeigler-Nichols method, the tuning of PID is done.

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Example Contd The characteristic eqn of the system is given by By using the method of substitution, for P controller only calculate the Ultimate gain.

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Example Contd.

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Example contd. By the measuring ultimate gain and ultimate period we can get the other parameters by Z-N method. Z-N tuning will be : P : Kc = 0.5Ku = 0.83 PI : Kc = 0.45Ku = 0.75; Tau_I = Pu /1.2 = 10.5 min PID : Kc = 0.6Ku = 1.0; Tau_I = Pu /2 = 6.3 min; Tau_D = Pu /8 = 1.6

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Example contd. Final Response for PID controller.

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Thank you

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