04-BS-4 · Undated paper

Question 7 of 7: Combinational Logic Design — Wind Turbine Pitch Controller

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Question 7: Combinational Logic Design — Wind Turbine Pitch Controller (15 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Seven binary sensor signals drive three servo commands. Before drawing gates it pays to translate the prose into Boolean expressions for each named condition, since the three sub-questions are really asking for three different output signals (UP, FAST_DOWN, DOWN) built from the same seven inputs.

Given. Inputs A (E-stop pressed), B (at Full-speed limit), C (at Vane limit), D (turbine Ready), E (wind speed too high), F (wind speed too low), G (rotor speed too high) — all active-high (1 = condition true). "Emergency Stop Condition" is explicitly defined in the stem as $A+E+D'$ (E-stop pressed, OR wind too high, OR turbine not ready).

Find. Minimal sum-of-products logic, and a gate-level circuit, for (a) UP, (b) FAST_DOWN under the Emergency Stop Condition, and (c) DOWN for rotor over-speed protection.

Approach. For each of the three named servo motions, identify exactly which sensor combination the text ties to that motion, write it as a Boolean expression, add a "stop once the target limit switch is reached" term so the servo does not keep driving after arrival (standard practice for any position-seeking control, and implicit in "the blade movement should stop when…" language used elsewhere in the stem), and realize each expression directly with AND/OR/NOT gates.

1. Part (a) — normal start, drive to Full-speed. The blades should move UP only when the turbine is genuinely available to run: Ready ($D=1$), no E-stop ($A'$), wind inside the safe band ($E'$ and $F'$), and not already sitting at the Full-speed limit ($B'$, so the motor stops driving once it arrives): $$\boxed{UP = D\cdot A'\cdot E'\cdot F'\cdot B'}$$ Because $D=1$ and $E'=1$ are both required for UP to assert, $D'=0$ and $E=0$ automatically, so $UP=1$ can never coexist with an active Emergency Stop Condition ($A+E+D'$) — the two outputs are mutually exclusive by construction, as a safety interlock should be. Figure 7a realizes this as one 5-input AND gate with four inverters.
2. Part (b) — Emergency Stop Condition. The stem defines the condition itself: "wind speed is too high ($E$), OR turbine is not Ready ($D'$), OR an emergency stop is detected ($A$)," and blades must move fast to Vane. Adding the same "stop on arrival" term ($C'$, not yet at the Vane limit) as in part (a): $$\boxed{FAST\_DOWN = (A+E+D')\cdot C'}$$ Figure 7b realizes the inner OR with a 3-input OR gate ($A$, $E$, and $D$ through an inverter), then ANDs the result with $C'$.
3. Part (c) — rotor over-speed protection. This is a second, independent reason to command the (non-fast) Down motion: "if the maximum rotor speed limit is reached ($G=1$), the blade should move toward Vane position… movement should stop when the rotor speed drops below the speed limit" — i.e. DOWN is asserted for as long as $G=1$, and (as in the other two parts) gated off once the Vane limit switch is actually reached: $$\boxed{DOWN = G\cdot C'}$$ Figure 7c realizes this as a single 2-input AND gate with one inverter. (The stem’s separate low-wind clause — "if wind speed is too low, and turbine is not Ready, blades should move to Vane position," i.e. $F\cdot D'$ — is the same non-emergency Down motion for a different trigger; a full controller would OR it into this same DOWN line, $DOWN=(G+F\cdot D')\cdot C'$, but it is kept separate above since only the rotor-speed trigger was asked for in part (c).)