1 PLCs: Part 2 Rajesh Rajamani Department of Mechanical Engineering University of Minnesota OVERVIEW • Importance of PID Control • Importance of Bode Plots • Video on PLCs • Lab 11: Simulating a Washing Machine Cycle • Final Exam2 IMPORTANCE OF PID CONTROL • PID Control with the Ziegler-Nichols Criterion – Most commonly used industrial control tool Controller P PI PID crK5.0crK45.0crK6.0- 2.1/crPcrP5.0- - crP125.0pKiTdT sTsTKsCdip1)(P C y e u desyIMPORTANCE OF BODE PLOTS • Experimentally determining the dynamic model for a system • Design of vibration isolation mounts • Design of sensors • Design of actuators • Signal processing filters • Control system design • Countless other applications …….3 VIBRATION ISOLATION Designing vibration isolation mounts for a machine k c x m F Objective • Motion of the machine should be less than 1 mm from equilibrium • At 25 Hz, less than 250 N of force should be transmitted to the structure Structure Machine F - mean 5000 N and sinusoidal 1000 N at 25Hz VIBRATION ISOLATION Designing vibration isolation mounts for a machine k c x m F Fkxxcxm kcsmssFsXsG21)()()(kxxcFtkcsmskcssFsFsHt2)()()(Motion of machine Force transmitted to structure4 VIBRATION ISOLATION k c x m F Fkxxcxm 2222211)()()(nnnsskkcsmssFsXsGMotion of machine 10-110010110210-510-410-310-210-1100101deflection amplitude (m)frequency (Hz)Frequency response of deflection for a 5000 N forcek=16000k=100, 000k=5,000,000VIBRATION ISOLATION 222221)()()(nnntssskckcsmskcssFsFsH Force Transmitted 10-1100101102100101102103104105transmitt ed force amplitude (N)frequency (Hz)Frequency response of transmitted force for a 1000 N excitationk=16000k=100,000k=5,000,0005 VIBRATION ISOLATION Designing vibration isolation mounts for a machine k c x m F Conclusions • A very hard spring can restrain motion to be less than 1 mm • But a hard spring increases the high frequency forces transmitted to the structure Structure Machine SENSOR DESIGN Design an accelerometer to measure inertial acceleration k c x m Objective • Estimate acceleration of the casing: • Use the physically measured variable: – Relative position Proof mass y yAyxz 6 SENSOR DESIGN k c x m Proof mass y 2222222 )()( 1- )()()(nnssssYsZkcsmsmskcsmskcssYsZsH10-210010210410-1010-910-810-710-6frequency (Hz)magnitude2221 )()( nnsssAsZMEMS ACCELEROMETER Solid model of a two-axis MEMS accelerometer7 IMPORTANCE OF BODE PLOTS • Experimentally determining the dynamic model for a system • Design of vibration isolation mounts • Design of sensors • Design of actuators • Signal processing filters • Control system design • Countless other applications ……. PLCs • Video of UPS Automated Sortation Facility at Maple Grove, MN • All machinery shown in the video are controlled by PLCs • Video recorded by Jason Quinn8 COUNTERS CTR preset accum In 1 Enable/ reset out inverse out If the enable input is ON and the input In 1 transitions from OFF to ON, then the variable “accum” is increased by 1. When accum become equal to preset, the output out becomes HIGH If Enable goes OFF, accum is reset to zero. transition REAL-TIME CLOCK Y1 Y1 Y1 10 T 0.1 seconds Y2 Y1 Y2 60 CTR minutes Y3 Y2 Y3 60 CTR hours Y4 Y3 Y4 24 CTR days9 REAL-TIME CLOCK secs mins hours days LAB 11 • Washing Machine Motor Gear box Agitator Water valve High level switch Low level switch Drain motor10 WASHING MACHINE • Wash – Open water valve until high level switch is ON – Run agitator motor for 12 minutes – Drain until low level switch is OFF • Rinse – Open water valve until high level switch is ON – Run agitator motor for 6 minutes – Drain until low level switch is OFF • Spin – Run spin motor for 4 minutes WASHING MACHINE • Finish flags – Fill 1 – Wash 1 – Drain 1 – Fill 2 – Wash 2 – Drain 2 – Spin – Total Cycle • Sensors – Start switch – High level switch – Low level switch • Actuators – Agitator motor – Spin motor – Water valve – Drain motor11 WASHING MACHINE Fill 1 Fill 1 High level switch Start Total cycle Using OR logic to set finish flags WASHING MACHINE Wash 1 Fill 1 Fill 1 Start Total cycle Using OR logic to set finish flags T1 72012 WASHING MACHINE Agitator motor Fill 2 Fill 1 Wash 1 Wash 2 Outputs are determined from the finish flags FINAL EXAM • Approximately 25% of grade • 25 questions, multiple choice • Total time: 2 hours 0 minutes (~5 minutes per question) • Cheat sheet: One 8.5” x 11” sheet, both sides • Exam time (1:30 pm – 3:30 pm) : – Tuesday, Dec 16, Room 54 Rapson Hall • Special office hours: Mornings, 9:00-11:00, week of 12/813 FINAL EXAM Sample question Q1. If the input range of a 12-bit A/D converter is –5V~+5V, its resolution isapproximately: (Notice that 212=4096)A. 0.1V.B. 0.01V.C. 0.001V.D. 0.0025V.FINAL EXAM Q. Given the frequency response function31)(jjHThe magnitude of H(j) at  = 2 rad/sec isA. –11.1 dbB. +11.1 dbC. –9.5 dbD. +9.5 dbSample question14 FINAL EXAM Q. A Bode plot is given as below. The approximate bandwidth of the system isclosest toA. 1 rad/sec.B. 1.4 rad/sec.C. 10 rad/sec.D. None of the above.Sample