MECH 310 Lecture 2 PDF

# MECH 310 - Lecture 2 ## Type: Open-loop control - **Torque vs. Speed & Current** A graph plotted with **Speed (RPM)** on the Y-axis and **Torque (oz-in)** on the X-axis. - The red line represents **current**. It shows **current** increasing linearly with **torque**. - The blue lin...

# MECH 310 - Lecture 2 ## Type: Open-loop control - **Torque vs. Speed & Current** A graph plotted with **Speed (RPM)** on the Y-axis and **Torque (oz-in)** on the X-axis. - The red line represents **current**. It shows **current** increasing linearly with **torque**. - The blue line represents **speed**. It shows **speed** decreasing linearly with **torque**. - The two lines intersect at a point where both **speed** and **torque** are low. - What input current do I supply to this motor to achieve some desired torque? - 12V 5310 RPM "CIM" Brushed DC Motor - https://www.robotshop.com/ca/en/12v-5310-rpm-cim-brushed-dc-motor.html ## Type: Closed-loop control - Feedback/Sensors are used to inform or modify the input command used to drive the system. - **Desired:** Rotate at 100 RPM - **Input:** **Desired** - Reference Command (Ref) - **e(t):** **Desired** - **Actual** - **Adjusted Command:** f(e(t) - **Actual:** Rotating at 90 RPM - **Output:** Rotating at 99.995 RPM (Tuning) - Closed-loop control is a continuous process - the loop cycles and repeats as fast as the components will allow ! - https://www.robotshop.com/media/catalog/product/cache/image/1350x/9df78eab33525d08d6e5fb8d27136e95/r/m/rm-esmo-042_27bd3.jpg.jpg ## Type: Bang-bang closed-loop - Simplest temperature control - A graph plotted with **Temperature (T)** on the Y-axis and **Time (t)** on the X-axis. - The blue line represents **temperature (T)**. - The green line represents **Time (t)**. - The dashed line represents a **desired temperature (Td)** - **if Tactual < Td** -**heater:ON** - **steady state error region (always oscillates)** - **if Tactual > Td** - **heater:OFF** - **Home thermostat** - Shows a temperature control on a thermostat with 70 degrees as the desired temperature. - **STEP Command** - **Tactual** - **To initial temp.** - Shows a diagram of a thermostat - https://static.wikia.nocookie.net/expanse/images/0/0e/ROCINANTE-GUNS-DEPLOYED-SPREADS-_000-EMBED-2020-1602175326-compressed.jpg/revision/latest/scale-to- - width-down/250?cb=20201011231540 - https://www.marssociety.ca/2021/07/15/rpthw-spacecraft-maneuvering/ ## Type: Bang-bang closed-loop - Simplest attitude control - A graph plotted with **Angle (θ)** on the Y-axis and **time (t)** on the X-axis. - The blue line represents **angle (θ)**. - The green line represents **time (t)**. - The dashed line represents a **desired angle (θa)** - **e(t)** - **Bact** - **S** - **θact ≤θa** - **L: ON** - **R: OFF** - **θact ≥θa** - **L: OFF** - **R: ON** - **Spacecraft Reaction Control System (RCS)** - **Pitch control (side view)** - Shows a diagram of a spacecraft attitude control - **Roll control (front view)** - https://static.wikia.nocookie.net/expanse/images/0/0e/ROCINANTE-GUNS-DEPLOYED-SPREADS-_000-EMBED-2020-1602175326-compressed.jpg/revision/latest/scale-to- - width-down/250?cb=20201011231540 - https://www.marssociety.ca/2021/07/15/rpthw-spacecraft-maneuvering/ ## Response shaping - Qualitative effects of P, I, and D terms - **Term primarily affects:** - **P:** Magnitude of response - **I:** Steady-state error - **D:** Speed of response - Overshoot is measured relative to the steady state value (NOT the desired value). - A graph plotted with **ω** on the Y-axis and **time (t)** on the X-axis. - The blue line represents **ω**. - The green line represents **time (t)**. - **ωd** - **desired value** - **ω0** - **initial value** - **ωmax** - **maximum output** - **u(t)= Kp e(t)** - **Kp1:** Kp - under < Kp - crit - **Step response** (**tover**) - **Kp2:** Kp - under > Kp - crit - **Kp3:** Kp - crit - **steady state error** - **ess(t)=** **ωd** - **ωact** - **rise time** - **trise=** **t98%** - **t10%** - **settling time** - **tsett=** 2% **ymax** (t) ## Response shaping - Qualitative effects of P, I, and D terms - **Term primarily affects:** - **P:** Magnitude of response - **I:** Steady-state error - **D:** Speed of response - **P:** Kp - **PI:** Kp, KI - **PI:** Kp2, KI, - Kp2>Kp1 - A graph plotted with **ω** on the Y-axis and **time (t)** on the X-axis. - The blue line represents **ω**. - The green line represents **time (t)**. - **ωd** - **desired value** - **ω0** - **initial value** - **PI** - **PID ** - **de(t)/dt** = Kd - Shows a diagram of a feedback loop - A graph plotted with **ω** on the Y-axis and **time (t)** on the X-axis. - The blue line represents **ω**. - The green line represents **time (t)**. - **ωd** - **desired value** - **ω0** - **initial value**