EENE 1040 Measurement and Control of Energy Systems
- Slides: 29
EEN-E 1040 Measurement and Control of Energy Systems Control I: Control, processes, PID controllers and PID tuning Oct 30 th 2017 If not marked otherwise, graphs and formulas in the presentation are from Åström & Hägglund: PID Controllers - Theory, Design, and Tuning (2 nd Edition)
What is control? • Intentional modification of a system’s state via external means • Used for bringing a system (close) to a state the user desires • Applied to various quantities (temperature, flow, lighting etc. ) • Can be manual or automatic, discrete (ON/OFF) or continuous (proportional)
Example: manual ON/OFF control ACME Electric Heater
Example: automated ON/OFF control with a setpoint ACME Electric Heater MK 2 20. 0 5. 0 30. 0 15. 0 28. 7 set Indoor temperature … … …
Example: automated PID (proportional integral-derivative) control with a setpoint ACME Electric Heater MK 3 PID 20. 0 5. 0 set Indoor temperature … 23. 0 … 19. 0 … 20. 0
Process models • Let’s go back to the electric heater example and present it in the form of a diagram: Setpoint ysp Control variable u Error e Σ Controller Heating element (process) -1 Measured temperature (process variable) y
Process characterization • Static response: if control variable u is fed to a process, what will be the value of the process variable y?
Process characterization • Dynamic response: if control variable u is fed to a process, how will the value of the process variable y behave over time?
Process characterization • Important aspects for control: Dead time, time constant, instability, nonlinearity
Proportional control • Let’s consider our model process from before: Setpoint ysp Control variable u Error e Σ Controller Heating element (process) -1 Measured temperature (process variable) y
Proportional control • ON/OFF control value of u same regardless of magnitude of e – Instability and oscillations • Proportional control: magnitudes of u and e linked – Overreaction to minor errors removed
Proportional control • Controllers with only proportional action have a steady-state error – For derivation, see Åström’s book, pp. 62 -64 • To get rid of the error, we need something else…
PID controller - Background • (P)roportional-(I)ntegral-(D)erivative • By far the most common control algorithm (over 90% of all industrial control loops) • When properly tuned, provides accurate control for a wide variety of processes
PID controller – Formulation • Let’s consider the controller output u as a function of e – the difference between the setpoint and the measured value: P I D
PID controller – Proportional action • With only proportional action, PID controller equation is reduced to • ub is controller bias/reset, often zero but can also be something else
PID controller – Static example of proportional action Measurement noise n Load disturbance l ysp e Σ u x Σ Controller Process Measured temperature (process variable) y Σ Process output -1
PID controller – Static example of proportional action • From the relations obtained from the block diagram, we get • K = controller gain, Kp = process gain, KKp = loop gain • In a system with no measurement noise and zero controller bias, x = y (process variable) high loop gain results in low steady-state error and resistance to load disturbances – Why not always set controller gain to a very high value? • In reality noise is always there and a high loop gain amplifies its effect – Deciding on an optimal loop gain is not easy, and it is always a tradeoff between different objectives for the control
PID controller – Dynamic processes • Almost every real process is dynamic – Time-dependent process gain and load disturbance – Setting loop gain too high leads to instability • How to solve steady-state error?
PID controller – Integral action • Always removes the steady-state error of the control • Steady state: constant error – As long as error is nonzero, u will vary over time • Large Ti slow convergence but less oscillation
PID controller – Derivative action • Dynamic closed loop systems often unstable due to dead time (process reacts to control too slowly) • To avoid this, prediction of future error needed • Consider a PD controller: • First order Taylor series expansion for the error: • Thus, control signal ~ linear approximation of error after time Td
PID controller – Derivative action
PID controller – When to use PI and PID • Derivative control quite often left out • PI sufficient for first order processes (ones that stabilize when control parameter is kept constant) • PID used for second order processes that involve oscillations and/or instability – Also useful for first order processes with dead time
PID controller – Caveats and limitations • Integrator windup – Occurs when control variable saturates due to actuator bounds • For example control valves can never be more than fully open – Typically happens with large sudden variations of setpoint – Can be avoided with modified control algorithm or limitations in setpoint variation • Higher order processes – Typically complicated processes with an order larger than 2 require more than PID for accurate control • Processes with large dead time – Error in the linear approximation via the D term gets large if the prediction needs to be made far into the future – Sophisticated predictive controllers better than PID in these cases
PID tuning – Process reaction curve • Open loop method – Controller set in manual mode – Requires process to be stable • How to do: 1. 2. 3. 4. Start logging the process variable Introduce a step change to the control variable Wait until the system reaches a new steady state Plot the logged data and analyse it to find the controller parameters
PID tuning – Process reaction curve Graph and formulas taken from http: //www. chem. mtu. edu/~tbco/cm 416/cctune. html
PID tuning – Ziegler-Nichols closed loop method • Closed loop method – Controller active during tuning • How to do: 1. 2. 3. 4. 5. Start logging the process variable Remove integral and derivative action from the controller Set the control gain to a constant value Modify the setpoint slightly Observe oscillations in the process variable • • 6. 7. If dampening, increase gain If amplifying, decrease gain Repeat step 5 until stable oscillations are found Record the gain value and the period of the stable oscillations
PID tuning – Ziegler-Nichols closed loop method Graph and formulas taken from https: //controls. engin. umich. edu/wiki/index. php/PIDTuning. Classical
PID tuning – Fine-tuning of a system • Effects of PID parameters when increasing them: Rise Time Overshoot Settling time Steadystate error Stability K Decrease Increase Very small effect Decrease Degrade t. I Decrease Increase Eliminate Degrade t. D Very small effect Decrease No effect Improve if t. D small
Thank you!
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