Electronic Control Systems Week 7 – Closed Loop Control EET273 Electronic Control Systems Week 7 – Closed Loop Control

Calibration Lab Recap Calibrating a system element means correcting a system’s behavior so that it matches a desired transfer function Notice that the setpoint you are giving the system was a percentage from 0-100%, so was the read-back from the tact board in the PLC software Because the units match (both are percentages), we can directly compare these 2 quantities and calculate an error signal: (e = SP – PV) With this error signal, we can now design some type of a controller, and finally use closed-loop feedback in our system!

Closed Loop Control Readings: Ch. 29:1 – 29:5

Open Loop vs. Closed Loop Simple – no feedback mechanism, simply give the system an input, and get an output Works for very simple systems, usually when the exact value of the PV is not critical, or the system load is very predictable. Closed-loop: Accurately track a process variable (PV) Improve the overall performance of a system, typically this means reducing error quickly and with minimal overshoot/oscillations Stabilize a process – an open loop system can “run away” and become unstable, but a properly designed closed loop system can prevent instability But be careful, an improperly design control loop can actually turn a stable system into an unstable one

Open-loop or closed-loop? Hair dryer Toaster Light switch Air conditioner Dishwasher Clothes dryer In some systems, it depends on how we define the “system” Ex: A car by itself is open-loop, but if the driver is part of the “system”, it’s actually closed-loop. Often humans are the “controller” in an otherwise open loop system

Some definitions Process – the physical system we wish to monitor and control SP – setpoint – input to the control system PV – process variable – output of the system Controller – module that processes the error term, and is applied to the plant input, with the purpose of reducing system error Final Control Element (FCE) – element that is acting on the process variable Manipulated Variable (MV) or Output – Controller output variable Open Loop – no feedback from output to input Closed Loop – with feedback from output to input

Closed Loop Control

Design Criteria Some control systems have very tight requirements for their outputs, and some are much more loose. Which controller design you choose is typically based on the output requirements. Systems with tight requirements: Drone/quadcopter Car cruise controller Systems with more loose requirements: Liquid buffer tank Home heating system / thermostat

System Performance What constitutes “good performance” in a system is application specific, and often subjective 3 ways to quantify “good performance” are: Rise Time 5% - 95% - How quickly does the output go from 5% of the SP to 95% of the SP Settling Time Time it takes for output to settle within a certain percentage of the steady state value Overshoot More much more than the SP the output reaches on it’s initial overshoot

System Performance Rise time How quickly does the output go from x% of the SP to y% of the SP Typically 10% - 90% or 5% - 95%

System Performance Settling time Time it takes for output to settle within a certain percentage of the steady state value Typically defined as 2% or 5% of steady state value

System Performance Overshoot Magnitude of the initial PV overshoot above the SP Usually defined as a percentage Ex: SP = 1V PV peaks at 1.2V 1.2V – 1V = 0.2V 0.2V / 1V = 20% overshoot

Controllers A controller acts on the error signal (e), to modify the input to the plant A controller design can be Simple – on/off control, proportional control Complex – PID control

Controllers We can simplify this system, using the same formula: TF = G / (1 + GH) Except now, G is actually K*G So, the simplification of this system is: TF = KG / (1+ KGH)

On/Off Control Controller output is binary – either 100% ON or 100% OFF Very simple control algorithm, switches input on or off based on relationship between process variable (PV) and setpoint (SP) If PV > USP then Controller = “OFF” If PV < LSP then Controller = “ON” Some applications this may be fine Ex. Water level in a buffer tank Ex. Heating system in your home Others may require more precise control Ex. Car cruise control system

Proportional Control Rather than simply comparing the error to a value and making a binary (ON/OFF) decision, we can design a controller to respond to the magnitude of the error Large error  Large error correction Small error  Small error correction A proportional controller simply takes the error, and multiplies it by some scaling factor (gain), commonly known as 𝐾 𝑃 Tuning a proportional controller simply means adjusting or tuning 𝐾 𝑃

Proportional Control Proportional controllers react to the magnitude of the error This error is the difference between the PV and the SP

Proportional Control Direct-acting controller – output in same direction as PV Reverse-acting controller – output in opposite direction as PV

Proportional Control Another way to refer to gain is the term “Proportional Band” Ex: For 𝐾 𝑃 = 5  PB = 1/5 = 0.2 = 20% The intuition behind this is: If a gain of 5 is required, that means the input to the controller is only 20% of what we’d like it to be (20% * 5 = 100%)

Proportional Control How to set the proportional gain, 𝐾 𝑃 ? Setting 𝐾 𝑃 =∞ is equivalent to ON/OFF control This is how an op-amp comparator works – open-loop gain of an op-amp is infinite How much gain a proportional controller needs depends on the process, and the elements in the control loop Often, finding a good value for 𝐾 𝑃 is a process of trial and error, and a balancing act of system requirements

Proportional Control Too much gain can result in overshoot as the controller converges on the SP Too little gain can results in a PV that cannot respond quickly enough to SP/process changes.

Proportional-only offset Proportional-only offset occurs when: Proportional control is the only type of control (hence the name) A load is present in the system In the world of control, a load is: Anything that tends to induce error into the system: Motor: Friction/physical load Car: air resistance/friction Buffer tank: water leaving the outlet

Proportional-only offset In a proportionally controlled system, any load on a system results in a PV that never fully reaches SP Remember, as the error is reduced, the amount of error correction is reduced (this is how proportional control works) If the load on a system = amount of error correction, the system will reach an equilibrium below the SP. Less gain: More offset Slower response (less chance of oscillation) More gain: Less offset Faster response (may oscillate)

Proportional-only offset Ex: A buffer tank has a proportional controller controlling an inlet valve, an outlet The inlet valve flow rate has a range of 0-100 GPM If there no load on the system (no water is exiting the system), the PV (water level) will eventually reach the SP But what if there is an outlet with a flow rate of 10 GPM? As the tank fills, the error reduces, and the valve closes proportionally When the inlet rate = outlet rate (10 GPM), an equilibrium is achieved, and the tank level remains constant This produces a steady state error, and the water level never reaches the SP

Proportional-only offset This effect can be reduced by increasing the gain 𝐾 𝑃 , but this can cause oscillations A well tuned proportional controller is often a compromise between excessive oscillations and excessive offset.

Proportional-only offset Can we fix this offset with a bias adjustment? We can try, but it won’t work well Any change in load will create a new offset value, and we would need to re-bias the new offset To truly solve this problem, we need…integral control (next lecture)

Proportional Control Example PID control of a DC motor’s position: https://www.youtube.com/watch?v=fusr9eTceEo Ball and Plate: https://www.youtube.com/watch?v=j4OmVLc_oDw Control system simulator: http://www.facstaff.bucknell.edu/mastascu/eControlHTML/Intro/IntroWithPr oblems/Intro00.html

Lab Closed loop intro Controlling the motor speed via on/off and PID control methods “Loading” the motor with the blue potentiometer

Midterm – Week 6 No Quiz on this weeks material (closed loop control) Transfer Functions How to combine transfer functions in series How to simplify a closed loop system into a single block Ladder Logic Identify different ladder logic symbols Draw a ladder logic diagram from a schematic and vice versa Identify the operation of basic ladder logic circuits Sensors/Switches Identify different types of sensors Identify normal state, NO, NC, and understand what type of even triggers a switch/sensor 4-20mA Signaling/Calibration Terms/definitions – live zero, span, zero, etc. Identifying types of calibration errors, span error, zero error, linearity error, hysteresis error