1.1 Conventional Sequential Engineering Design

The familiar handoff¶

Many organizations divide a dynamic-system project into a chain of discipline-specific tasks:

requirements are allocated;
mechanical, electrical, hydraulic, or thermal hardware is designed;
actuators and sensors are selected;
the physical design is frozen;
a model is handed to the controls team; and
the controller is tuned to recover as much system performance as possible.

This workflow is understandable. It aligns with departmental boundaries, supplier contracts, design reviews, and established simulation tools. It also reduces coordination: each team sees a smaller problem with fewer variables.

A comparison of sequential plant-to-control design, nested control co-design, and simultaneous control co-design workflows.

The simplification, however, comes from an assumption that is rarely tested: physical design can be completed before the consequences for feedback are known.

The quarter-car handoff¶

An active quarter-car suspension model with sprung and unsprung masses, suspension spring and damper, tire stiffness, road input, and actuator force.

Let $\mathbf{q}(t)=[z_s(t),\,z_u(t)]^{\mathsf T}$ . With positive actuator force acting upward on the sprung mass and downward on the unsprung mass, the dynamics are

\underbrace{\begin{bmatrix}m_s&0\\0&m_u\end{bmatrix}}_{\mathbf{M}}\ddot{\mathbf{q}} +\underbrace{\begin{bmatrix}c_s&-c_s\\-c_s&c_s\end{bmatrix}}_{\mathbf{C}}\dot{\mathbf{q}} +\underbrace{\begin{bmatrix}k_s&-k_s\\-k_s&k_s+k_t\end{bmatrix}}_{\mathbf{K}}\mathbf{q} =\underbrace{\begin{bmatrix}1\\-1\end{bmatrix}}_{\mathbf{B}_u}u(t) +\underbrace{\begin{bmatrix}0\\k_t\end{bmatrix}}_{\mathbf{B}_r}z_r(t).

The passive plant-design problem sets $u(t)=0$ ; the subsequent control problem computes $u(t)$ for the already selected values of $k_s$ and $c_s$ .

For the suspension, a sequential plant team might choose $k_s$ and $c_s$ by minimizing a passive metric

J_p(k_s,c_s)=w_a\,a_{\mathrm{rms}}^2+w_t\,\delta_{t,\mathrm{rms}}^2+w_m\,m,

subject to packaging and stress limits. After those values are frozen, the controls team tunes gains $K$ to minimize

J_c(K\mid k_s^*,c_s^*)

subject to actuator force, suspension travel, stability, and bandwidth constraints. The vertical bar matters: the controller is optimized conditional on a plant selected for another problem.

The plant team may have made the spring soft to improve passive comfort. The controller then needs more actuator stroke or low-frequency force to regulate body motion. Alternatively, a stiff plant may protect suspension travel while moving the controlled system toward uncomfortable accelerations. Neither team has authority to revisit both sides of the trade.

Sequential design is not automatically poor engineering¶

Sequential design can be effective when interfaces are genuinely weak, a mature platform must be reused, certification freezes the plant, or a standard controller already offers ample margin. Its weakness is not the ordering alone. Its weakness is prematurely removing decisions that strongly affect the system-level optimum.

Hidden assumptions in a handoff¶

A sequential process often embeds assumptions without stating them:

the selected actuator can deliver the required force, rate, and bandwidth;
the chosen sensors reveal the states needed for feedback;
the plant model remains valid over the controller’s operating range;
control effort has negligible effects on mass, heat, energy, and cost;
saturation and delay will not reshape the preferred physical design; and
failure or degraded-control modes remain acceptable.

CCD begins by turning these assumptions into variables, constraints, and testable hypotheses.

Activity 1.1: audit a sequential suspension workflow¶

Activity 1.1: audit a sequential suspension workflow

Consider the reduced body-mode model

m\ddot z+c\dot z+kz=u+d(t), \qquad u=-k_pz-k_d\dot z,

where $m=300$ kg and $c=1200$ N s/m. The plant team selects and freezes $k\in[12,30]$ kN/m. Only afterward does the controls team target $\omega_n=6$ rad/s and $\zeta=0.70$ , subject to $|u|\leq 2$ kN. Matching the unsaturated closed-loop coefficients gives

k_p=m\omega_n^2-k, \qquad k_d=2\zeta m\omega_n-c.

Compute $(k_p,k_d)$ for $k=12$ and 30 kN/m. Explain why a negative $k_p$ is not automatically unstable, and what physical burden active stiffness cancellation places on the actuator.
Run the MATLAB audit file. It retunes the controller for every candidate spring, applies the same half-sine disturbance, enforces actuator saturation, and reports RMS body acceleration and peak commanded force.
Identify which frozen spring choices violate the actuator limit. Does retuning the controller after the handoff recover the same response once saturation occurs?
Rewrite the workflow as a CCD problem with $k$ , $k_p$ , and $k_d$ selected together. Propose one objective and at least three constraints covering comfort, actuator capability, suspension packaging, and closed-loop behavior.

Your conclusion should name the hidden handoff assumption exposed by the calculation and state whether the spring should remain fixed or return to the system-level design space.