A small furnace is held at a set temperature by a controller

PHYSICS · Multi-part · Fermi University Physics · Electronics, Instrumentation & Communication · Feedback, operational amplifiers and analogue signal processing · Signals, systems, control and digital signal processing

Electronics for Measurement, Ch Transfer functions, poles and the stability of a loop

Problem

A small furnace is held at a set temperature by a controller. Its plant, from controller volts to sensor volts, is a lag with time constant τ=120 s\tau = 120\,\mathrm{s} and steady gain 0.0500.050, followed by a transport delay td=20 st_d = 20\,\mathrm{s}. ((a)) With a proportional controller of gain KpK_p, find the frequency at which the loop-gain phase reaches −180∘-180^\circ, and the gain KpK_p at which the loop just oscillates there. ((b)) With Kp=10K_p = 10, find the fraction of a set-point step left as steady-state error. ((c)) Replace the proportional controller by proportional and integral action, C(s)=Kp(1+sTi)/(sTi)C(s) = K_p(1+sT_i)/(sT_i), with TiT_i chosen to cancel the plant's lag. Choose KpK_p for a phase margin of 60∘60^\circ, and give the crossover ωc\omega_c and the steady-state error. ((d)) Find the gain margin of the loop in (c).

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