--- title: "Automobile suspension analog; feedback system" subject: "Simulation and Modeling" chapter: 3 key: "semester_8/simulation_and_modeling:analog-suspension-feedback" source: https://www.bctengineer.com/q/semester_8/simulation_and_modeling/analog-suspension-feedback site: BCT Engineering --- # Automobile suspension analog; feedback system Simulation and Modeling · Chapter 3: Continuous system simulation - Asked in: 2073 Magh, 6+4 marks - Video: [Analog Computer Model |Simulation | Model Question Solution | IOE |BCT](https://www.youtube.com/watch?v=Y_1320Mocnw) — Engivault - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_8/simulation_and_modeling/analog-suspension-feedback - Whole chapter: https://www.bctengineer.com/md/semester_8/simulation_and_modeling/chapter-3 ## Question Design and explain the analog method of the automobile suspension problem. Explain feedback system with suitable example. ## Short answer For the suspension Mx''+Dx'+Kx=F(t), the analog circuit uses two integrators: one integrates sum of F/M, -(D/M)x', -(K/M)x to give -x', the second gives x; feedback pots set D/M and K/M. A feedback system returns part of output to input; e.g., a thermostat uses negative feedback to maintain room temperature by switching heater based on error. ## Answer #### Automobile suspension problem A car body of mass M is supported by a spring of stiffness K and a shock absorber (damper) with coefficient D. Let x be the displacement of the body from its equilibrium position and F(t) the external force from the road. ```text F(t) | +-----+ | M | +-----+ | | K D | | ================ wheel / road ``` Forces: inertia `M x''`, damping `D x'`, spring `K x`. Newton's second law: `M x'' + D x' + K x = F(t)` Solving for the highest derivative: `x'' = F(t)/M - (D/M) x' - (K/M) x` #### Analog computer circuit Two integrators in series produce `x'` and `x` from `x''`. Each integrator inverts the sign. ```text F/M ------------\ -(D/M)x' -------- Sum --> [Int 1] --> -x' --> [Int 2] --> x -(K/M)x --------/ | | ^ | | | v v | [pot D/M] [Inverter] | | | | back to Sum -x +------------------[pot K/M]<---------------------+ ``` Steps: 1. Integrator 1 takes the sum `x''` and gives `-x'`. Its initial condition is `-x'(0)`. 2. Integrator 2 takes `-x'` and gives `+x`. Its initial condition is `x(0)`. 3. Output `-x'` goes through potentiometer D/M and returns to the summing input, giving the term `-(D/M) x'`. 4. Output `x` passes through an inverter to give `-x`, then through potentiometer K/M, giving `-(K/M) x`. 5. The forcing term F/M is applied at the input of integrator 1. 6. The output x is recorded against time. Setting D and K pots changes the damping and stiffness, and the displayed curve shows whether the ride is oscillatory, critically damped or over-damped (`D^2` compared with `4 K M`). Amplitude and time scaling are applied so that the voltages stay within the machine's range. #### Feedback system A **feedback system** is a system in which a part of the output is returned to the input and used to control the output. The input to the process is the reference input combined with the fed-back signal. ```text r(t) --> (+)--e--> [ Process ] --> y(t) ^ - | | | +------[ Feedback ]<-------+ ``` - **Negative feedback** subtracts the output from the input; it reduces error and gives stability. - **Positive feedback** adds the output; it increases the effect and may cause instability (e.g. microphone squeal). **Example: room thermostat.** The desired temperature is the reference. A sensor measures the actual room temperature and the difference (error) switches the heater on or off. When the room is below the setting, the heater runs; when it is above, it stops. This keeps the temperature near the set value despite disturbances. The suspension is also a feedback system: the spring and damper forces depend on the displacement x and velocity x', which are the outputs fed back to the input of the mass, as shown in the analog circuit where `-(K/M)x` and `-(D/M)x'` return to the summer. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. In the suspension analog circuit, why is an inverter used on the output x? A. To amplify x B. To integrate x C. To differentiate x D. To get -x, which is needed for the -(K/M)x term, since integrators invert signs Answer: D. Integrator 2 outputs +x, but the summer needs -(K/M)x, so x is inverted before pot K/M. (Key point: Analog circuit sign handling) 2. What is a feedback system? A. A system where part of the output is returned to the input to control the output B. A system with no output C. A system with only an input D. A system where the input is ignored Answer: A. In feedback, the process input combines the reference with the fed-back output signal. (Key point: Feedback system definition) 3. Which is correct about negative and positive feedback? A. Negative feedback adds the output and may cause instability B. Negative feedback subtracts the output, reducing error and giving stability; positive may cause instability C. Both reduce error equally D. Positive feedback gives stability Answer: B. Negative feedback subtracts the output; positive feedback adds it and can cause instability, e.g. microphone squeal. (Key point: Negative vs positive feedback) 4. In the room thermostat, what switches the heater? A. The outside temperature only B. The reference temperature alone C. The error between desired and measured room temperature D. A fixed timer Answer: C. The sensor measures actual temperature and the difference from the setting (error) turns the heater on or off. 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