Digital control implementation: how is integral (I) action realized on a digital controller?
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AA digital controller cannot implement integral mode
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BThe error is divided into discrete amounts but not accumulated
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CThe controller sums the error over discrete sampling intervals and accumulates it
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DAll of the above
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ENone of the above
Answer
Correct Answer: The controller sums the error over discrete sampling intervals and accumulates it
Explanation
Introduction / Context:Integral action removes steady-state error by accumulating past error. In digital control (PLC, DCS, microcontrollers), I action must be implemented numerically because signals are sampled in time.
Given Data / Assumptions:
- Sampling period Ts is fixed and sufficiently small.
- Error e[k] = setpoint − process_variable at sample k.
- Controller state stores the accumulated sum.
Concept / Approach:Discrete integral is a running sum (or sum with scaling), e.g., I[k] = I[k−1] + Ki * Ts * e[k] The integral state I[k] contributes to the control output. Practical implementations include anti-windup (clamping, back-calculation) to prevent integrator growth during saturation.
Step-by-Step Solution:Represent continuous integral as a discrete sum over samples.Accumulate the error term each cycle to form the integral state.Add the term to controller output with proper scaling and limits.
Verification / Alternative check:Controller vendor function blocks (PI/PID) describe I action exactly as a sum/accumulator with tuning parameter Ti or Ki and options for anti-windup.
Why Other Options Are Wrong:(a) Digital controllers do implement integral routinely. (b) Dividing error without accumulation is not integral action. (d) Cannot be true since (a) and (b) are incorrect.
Common Pitfalls:Ignoring anti-windup; poor scaling of Ki with Ts; changing Ts without retuning.
Final Answer:The controller sums the error over discrete sampling intervals and accumulates it