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4. DISCRETE CONTROLLER DESIGN

•In controller design we try to meet some objective. Typical objectives include,

-positioning - for moving from position to position, where the setpoint is changed suddenly

deadbeat control first order

-tracking - for following paths where setpoints are constantly changing

first order

-disturbance resistant - unexpected variations can be compensated for step response

-multi-stage - for complex systems that need small errors

feed forward disturbance - can reduce effects of disturbances feed forward command - to follow complex motions

cascade - a controller that examines intermediate steps of a process

•typical constraints to be developed are,

-stability - does not diverge over time

-stability - sampling period is short enough (no-aliasing)

-realizable - does not refer to future values

4.1 POSITIONING CONTROLLERS

•In these systems we will focus on how the output relates to the input.

•These techniques work best with simple systems that require a jump from one setpoint to another.

•The general procedure to design a controller is,

1.Model the process (i.e., find Gp)

2.Determine the control objective (i.e. select the desired system response Gdr)

3.Substitute these into the equation below and solve for the controller transfer function,

Gdr( B)	=	cn
		----
		rn

Gc( B)	=	cn
		----
		rn

Gc( B) Gp( B)

=----------------------------------------

1 + Gc( B) Gp( B)

=		1			Gdr	( B)
	--------------				--------------------------
	G	p	(	B)	1 – G	dr	( B)

4.Check the equation for practicality and stability

5.Develop the control equation for the computer

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6.Write the computer program

•Try to derive the expression given above,

Gdr( B)	cn	Gc( B) Gp( B)
	= ----	= ----------------------------------------	( B) Gp( B)
	rn	1 + Gc

4.1.1 Dead Beat Control

•It is possible (for a first order process) to match the output function to the input function in one step.

•The desired function is,

cn =	rn – 1				desired posn
Gdr(	B) =	cn	=	B	T
		----
		rn
					actual posn

• Given the process model below, design a deadbeat controller,