Revision for ME 460 final exam D-H notation Discrete event controller Production control

Xi Zi+1 Zi Special cases: Two Z axes intersect at point. Two Z axes are in parallel. X0 Xn

D-H notation and coordinate system

Identification of the state variable: Step 1: Identify input variables. Step 2: Identify output variables. Step 3: State variables: output variables + additional state variables Example – 2010 Final exam, 2006 Final exam.

State diagram: Translate the narrative description of control knowledge into the state diagram.

Two forms of BLE – choose one of them State diagram to Boolean logic equation (BLE) Set & Reset (10) (11) Condition (a) and Condition (b) – how to do analysis of the conditions? Step 1: Condition (a)  x=0, assume (setx =1) and (resetx =1) happen at the same time  find all cases  prove that the assumption is untrue for all the cases (i.e. they cannot happen at the same time)  Condition (a) is satisfied. Otherwise, say Case X is true. Go to Step 2. Step 2: To Case X, check that under the above assumption (x=0, setx =1 and resetx =1 ), X+=0 is the required control action  If Yes, Condition (b) is satisfied. Two forms of BLE – choose one of them

X=0 Setx =1 and Resetx =1 Required control behavior X+=0 X+=1 Choice of which one is important, as if we choose Eq. (11), the behavior will be X+=0, while if we choose Eq. (10), the behavior will be X+=1. Required control behavior X=0 Setx =1 and Resetx =1 X+=0 Controller under design X+=1

How to judge whether “X+=0 is the required control behavior (either X+=0 or X+=1)? The above judgement is made by translating all the logic variable expressions to their physical meaning and then to decide the required control behavior based on the physical system. In the case of the motor control with two push-buttons (start, stop), X+=0 means the motor keeps rest when it is in rest, which is the required control behavior from a safety point of view. In the case of X3 in the bottle-filling problem, X3 stands for motor. When X3=0, set X3 =1, reset X3 =1, we get X5=1, BPPS=1, (X4) N.O. =1. The three expressions depict the following situation: Motor is at rest, The overall system is powered on, Bottle has arrived at the required position, The timer has completed the running of T seconds. Under the above situation, the next action of the motor should be: “ to run”, that is X3+=1. This means that the condition (b) is not satisfied. (note that the condition (b) requires X3+=0.) Therefore, for X3, we apply Eq. (10).

Boolean logic equation (BLE) to SLLD to PLC diagram (PLCD):

Reading SLLD

Reading SLLD

Reading SLLD Two views for the same physical system: Contact view or examined for on condition. Not-contact view or examined for off condition.

Reading SLLD While processing BLE (i.e., input variables get 1 or 0), e.g., PB1=1, PB2=0, M+=(1)(M+1)=1, the interpreting of the bottom left to the result of the bottom right.

Latching function CR Timer Controlled Relay: Latching function (consider CR as a state variable but not output variable) Timer (consider timer as a state variable but not output variable) Latching function CR Timer

Physical meaning: The normally open contact is closed, and there is a power through this switch

Controlled Relay -- Latching function: The bottom left is changed to the bottom right as the result of the analysis in the preceding slide.

Controlled Relay -- Latching function:

Controlled Relay -- Latching function: Physical world: Normally closed contact is open Examined for off condition is true

Controlled Relay -- Timer There are two ways to define how the timer works. Definition 1: After energized, timer runs for T. In this situation, normally open (N.O.) contact closes (X N.O. = 1) for T and normally close (N.C.) contact opens (X N.C. = 0) for T. In other words, timer stops after T. In this situation, N.O. contact opens (X N.O. = 0) after T and N.C. contact closes (X N.C. = 1) after T. Definition 2: After energized, timer runs for T. In this situation, normally open (N.O.) contact keeps open (X N.O. = 0) for T and normally close (N.C.) contact keeps close (X N.C. = 1) for T. In other words, timer stops after T. In this situation, N.O. contact closes (X N.O. = 1) after T and N.C. contact opens (X N.C. = 0) after T. From the above discussion, we have: X N.O.= 0 is the same as X N.C.= 1, and X N.O.= 1 is the same as X N.C. = 0. Definition 1 X N.O. = 0 means the N.O. contact remains open and timer does not run or timer has completed running of T. X N.C. = 1 means the N.C. contact closes and the timer does not run. That is to say, X N.O. = 0 is the same as X N.C. = 1. X4 in the bottle-filling problem takes Definition 2. In the slide here, Definition 1 is taken.

Production control: Machine versus system Part versus batch Three types of times MLT APT Efficiency Capacity WIP

End Thank you for taking this class (Robotics and Automation) Email me at chris.zhang@usask.ca if you have any question.