CHEN90032 · Process Simulation and Control
Advanced Control: Direct Synthesis, Delay Compensation, Cascade, Feedforward, Ratio
Advanced Control is the design layer of University of Melbourne CHEN90032 Process Simulation and Control, sitting on top of the transfer-function, stability and PID-tuning skills built earlier in the subject. Instead of tuning a single feedback loop by rule, you design the loop: direct synthesis specifies the closed-loop response you want and inverts the loop algebra to get the controller, Smith-predictor / IMC compensates for dead time, and cascade, feedforward and ratio add structure that a single loop cannot. These strategies are examined both as a large control-scheme / P&ID question and inside the model-based transfer-function question.
What this chapter covers
- 01Direct synthesis: fix the desired closed-loop response G_obj (= target C/R) and solve for the controller G_mc = (1/G_p)[G_obj/(1 − G_obj)]
- 02How direct synthesis collapses to a PI/PID for a FOPTD process: K_c = τ/[K(τ_c + θ)] and T_I = τ
- 03The desired-closed-loop time constant τ_c as the single tuning knob (smaller = faster/aggressive, larger = slower/robust)
- 04Why the process dead time must be kept in G_obj — no controller can act before the transport delay
- 05Time-delay compensation with the Smith predictor / IMC: an internal model pushes e^(−θs) out of the characteristic equation so a higher gain stays stable
- 06Cascade control: a fast inner (secondary) loop nested inside a slow outer (primary) loop, with the primary output as the inner set-point
- 07Feedforward control: measure the disturbance and act before the upset; the ideal compensator G_ff = −G_d/G_p, always paired with feedback trim
- 08Realizability of a feedforward or decoupling element (improper or predictive delay → approximate with a static gain × lead-lag)
- 09Ratio control: hold one flow at a fixed ratio to a measured wild stream, SP = R × F_wild — a special feedforward
- 10Choosing the right strategy on a P&ID and justifying each pairing for the exam's control-design question
Direct synthesis of a PI controller from a FOPTD model
- +1Choose the desired closed-loop response. Keep the process delay and demand a first-order approach to set point: G_obj = e^(−2s)/(4s + 1). The delay 2 min equals the process θ, so the target is physically achievable (a controller cannot beat the transport delay).
- +2Form G_obj/(1 − G_obj). The denominator is (4s + 1) − e^(−2s); approximating the delay by its first-order Taylor term e^(−2s) ≈ 1 − 2s gives (4s + 1) − (1 − 2s) = 6s, so G_obj/(1 − G_obj) ≈ e^(−2s)/(6s).
- +1Multiply by 1/G_p: G_mc = [(10s + 1)/(2 e^(−2s))] · [e^(−2s)/(6s)] = (10s + 1)/(12s). The delays cancel exactly, which is why the target delay had to match the process delay.
- +2Read off the PI form (10s + 1)/(12s) = (10/12)(1 + 1/(10s)) = K_c(1 + 1/(T_I s)), giving K_c = 10/12 = 0.83 %/°C and T_I = 10 min. Cross-check with the standard result K_c = τ/[K(τ_c + θ)] = 10/[2.0(4 + 2)] = 0.83 and T_I = τ = 10 min — consistent.
Key terms
- Direct synthesis
- A model-based design method: specify the desired closed-loop transfer function G_obj (= target C/R), then invert the servo loop relation to obtain the controller G_mc = (1/G_p)[G_obj/(1 − G_obj)]. The controller contains the inverse of the process model, so it is only as good as that model.
- Desired closed-loop time constant τ_c
- The single tuning knob in direct synthesis / IMC, set by choosing G_obj = 1/(τ_c s + 1) (times the process delay). A smaller τ_c demands a faster, more aggressive loop (higher K_c); a larger τ_c gives a slower, more robust loop that tolerates model error.
- Direct-synthesis PI tuning (FOPTD)
- For a first-order-plus-time-delay process K e^(−θs)/(τs + 1) with a first-order desired response, direct synthesis gives a PI controller with K_c = τ/[K(τ_c + θ)] and T_I = τ. Internal Model Control (IMC) yields the identical result.
- Smith predictor
- A time-delay compensator that runs an internal model split into a delay-free part and the dead time, feeding the predicted delay-free response back inside the loop. With a perfect model the dead time e^(−θs) leaves the characteristic equation (1 + G_c G_p* = 0), allowing a higher stable controller gain.
- Cascade control
- A structure of two nested feedback loops sharing one final valve: a fast inner (secondary) loop on an intermediate variable and a slow outer (primary) loop on the controlled variable. The primary controller's output is the inner loop's set-point, and the inner loop must be several times faster than the outer.
- Feedforward control (G_ff = −G_d/G_p)
- A strategy that measures a disturbance and acts before it upsets the output. The ideal compensator that fully cancels the load is G_ff = −G_d/G_p, where G_d is the disturbance (load) transfer function and G_p the process transfer function. It sits outside the feedback loop, so it cannot change stability, and is always paired with feedback trim.
- Feedback trim
- The feedback loop added alongside feedforward. Because feedforward is open-loop and model-based, it leaves offset and ignores unmeasured disturbances; the feedback trim loop drives the residual error to zero and rejects everything the feedforward path cannot see.
- Ratio control
- Holding one flow at a fixed ratio to another by measuring the uncontrolled wild stream F_wild and setting the controlled stream's set-point to SP = R × F_wild. It is a special case of feedforward with a static gain R, used for example to hold an air:fuel ratio. A feedforward or decoupling element is only realizable if it is proper and needs no predictive delay e^(+θs); otherwise approximate it with a static gain times a lead-lag.
Advanced Control: Direct Synthesis, Delay Compensation, Cascade, Feedforward, Ratio FAQ
How is direct synthesis different from Ziegler–Nichols or Tyreus–Luyben tuning?
Ziegler–Nichols and Tyreus–Luyben are empirical rules: you find the ultimate gain K_cu and ultimate period P_u (from a Bode plot or a relay test) and read the controller constants off a table. Direct synthesis is model-based: you write down the process transfer function and the closed-loop response you want, then solve algebraically for the controller. For a first-order-plus-time-delay process it produces a PI/PID with K_c = τ/[K(τ_c + θ)] and T_I = τ, and its one knob τ_c lets you dial the closed-loop speed directly — at the cost of needing an accurate model. All three appear on the tuning side of the subject; the provided formula sheet lists the Ziegler–Nichols and Tyreus–Luyben rules; the Smith predictor structure itself is not on the sheet, so be ready to sketch and explain it.
When should I use feedforward, cascade or ratio instead of plain feedback?
Use cascade when a measurable, fast intermediate variable (a flow, a jacket temperature) sits between the valve and the slow controlled variable and a disturbance enters there — the fast inner loop catches it before it reaches the primary variable. Use feedforward when the main disturbance can be measured directly: the ideal compensator G_ff = −G_d/G_p acts before the upset, and you always add a feedback trim loop for offset and unmeasured disturbances. Use ratio control (a static-gain feedforward, SP = R × F_wild) when one flow must track another, such as air:fuel. None of these replaces feedback for stability; they add structure on top of it.
Can AI help me with advanced control strategies in CHEN90032?
Yes, as a study aid. Sia can explain each method step by step — how to invert the loop algebra for direct synthesis, why the Smith predictor removes dead time from the characteristic equation, how the primary controller output becomes the inner set-point in cascade, and how to derive G_ff = −G_d/G_p and check its sign and realizability — and it can walk you through your own practice problems and unit work. Treat it as a tutor that builds your method and reasoning, not a source of ready-made assessment answers: it does not sit your exam or guarantee a mark, and deriving the controllers and drawing the schemes yourself is what earns credit and clears the exam hurdle.
Studying with AI? Sia — free AI chemical engineering tutor works through CHEN90032 step by step.
Exam move
Learn each strategy as one clean idea plus one equation, and rehearse writing the equation with its sign and units before touching numbers: direct synthesis G_mc = (1/G_p)[G_obj/(1 − G_obj)] collapsing to K_c = τ/[K(τ_c + θ)], T_I = τ; the Smith-predictor characteristic equation 1 + G_c G_p* = 0; cascade with the primary output as the inner set-point; feedforward G_ff = −G_d/G_p plus feedback trim; and ratio SP = R × F_wild. Practise adding cascade, feedforward and ratio loops to a P&ID and justifying each pairing, since that is a large part of the control-design question. The written final is 4 questions and 100 marks over 3 hours (plus 15 minutes reading), closed book with a provided formula sheet, worth 60% with a hurdle you must pass — confirm the exact date on Canvas for the ~June end-of-Semester-1 exam period. At about 1.8 minutes per mark, a 35-mark control-design question is roughly 63 minutes and a 15-mark part about 27 minutes, so spend the first minutes labelling variables and choosing the strategy before you draw or derive.
