Salman Bin Abdulaziz University EE3511: Automatic Control Systems PID Controller Dr. Ahmed Nassef EE3511_L12 Salman Bin Abdulaziz University

The need for PID control Desired output r(t) Actual output y(t) Error e(t) Controller u Plant PID controllers More than 50% of industrial controllers Easy to implement Applicable to most control systems Adjustable on site Satisfactory performance. EE3511_L12 Salman Bin Abdulaziz University

Salman Bin Abdulaziz University PID controller Desired output r(t) Actual output y(t) Error e(t) Controller u Plant EE3511_L12 Salman Bin Abdulaziz University

Salman Bin Abdulaziz University PID controller Desired output r(t) Controller Plant Actual output y(t) Error e(t) u How do we select the PID parameters? EE3511_L12 Salman Bin Abdulaziz University

General Guidelines for PID controller Desired output r(t) Controller Plant Actual output y(t) Error e(t) u Steady state error Settling time overshoot Rise time Closed loop response decrease Small change increase Kp eliminate KI KD conflicting objectives EE3511_L12 Salman Bin Abdulaziz University

Salman Bin Abdulaziz University PID controller Desired output r(t) Controller Plant Actual output y(t) Error e(t) u We need to select the PID parameters so that we have Fast rise time Small overshoot No steady state error EE3511_L12 Salman Bin Abdulaziz University

P controller (proportional) Desired output r(t) Controller Plant Actual output y(t) Error e(t) u - With P controller we can Reduce rise time Reduce steady state error But Overshoot may increase EE3511_L12 Salman Bin Abdulaziz University

Salman Bin Abdulaziz University PI controller Desired output r(t) Controller Plant Actual output y(t) Error e(t) u - Integral action of the PI controller Eliminate steady state error Decrease rise time Increase overshoot Increase settling time EE3511_L12 Salman Bin Abdulaziz University

Salman Bin Abdulaziz University PID controller Desired output r(t) Controller Plant Actual output y(t) Error e(t) u - Derivative action of the PID controller Decrease overshoot Decrease settling time EE3511_L12 Salman Bin Abdulaziz University

General guidelines for Designing PID controller Obtain an open loop response and determine what is needed Add proportional gain to reduce rise time Add derivative control to reduce overshoot Add integral control to eliminate steady state error Adjust gains to get desired response EE3511_L12 Salman Bin Abdulaziz University

Salman Bin Abdulaziz University Adjusting PID gains It may not be simple to get the best gains by trial and error. Some rules can be used to get good response Ziegler Nichols Rules is one example EE3511_L12 Salman Bin Abdulaziz University

Salman Bin Abdulaziz University Ziegler Nichols Rules Two Ziegler Nichols Methods Obtaining 25% maximum overshoot in step response Open Loop Method Based on open loop model Closed Loop Method may not be applied for some practical systems EE3511_L12 Salman Bin Abdulaziz University

Open Loop Ziegler Nichols Rules Plot an open loop step response Determine T, L, K K T L Input Output EE3511_L12 Salman Bin Abdulaziz University

Open Loop Ziegler Nichols Rules K L : dead time T : time constant K : process gain T L Step response EE3511_L12 Salman Bin Abdulaziz University

Open Loop Ziegler Nichols Rules Step response K P controller KP =T/L PI controller KP =0.9 T/L, KI=0.3KP/L PID controller KP =1.2 T/L, KI=KP/(2L); KD=0.5KPL T L EE3511_L12 Salman Bin Abdulaziz University

Closed loop Ziegler Nichols Rules Use Proportional control only Generate step response for different KP Increase KP until stable oscillations is achieved. This gain is known as ultimate gain Ku Read the oscillation period Pu Pu EE3511_L12 Salman Bin Abdulaziz University

Closded Loop Ziegler Nichols Rules P controller KP =0. 5*Ku PI controller KP =0.45*Ku, KI=1.2*KP/Pu PID controller KP =0.6 Ku , KI=Kp/(0.5*Pu) ; KD=0.12*Pu*KP Pu Step response EE3511_L12 Salman Bin Abdulaziz University

Salman Bin Abdulaziz University Example Desired output r(t) Controller Plant Actual output y(t) Error e(t) u - 60 X X X -2 -1 0 EE3511_L12 Salman Bin Abdulaziz University

Salman Bin Abdulaziz University Example X jwn X -a -2 -1 X -jwn EE3511_L12 Salman Bin Abdulaziz University

Salman Bin Abdulaziz University Example Ku=K =6 Pu = 2π/ωn = 2π/ , note: Pu =T=1/f P controller KP =0. 5 Ku = 0.5*6 = 3 PI controller KP =0.45 Ku=2.7; KI=1.2*KP/Pu=0.73 PID controller KP =0.6 Ku=3.6 ; KI=Kp/(0.5*Pu)=1.27 ; KD=0.12*Pu* KP =1.92 EE3511_L12 Salman Bin Abdulaziz University