{ "id": "epjd68q5zy", "slug": "smith-predictor", "title": "Smith predictor", "updated": "2026-10-21", "topic_path": [ { "id": "technology", "label": "Technology and the built world", "api_url": "https://www.edgepedia.org/api/v1/topics/technology" }, { "id": "technology.engineering", "label": "Engineering and manufacturing", "api_url": "https://www.edgepedia.org/api/v1/topics/technology.engineering" }, { "id": "technology.engineering.engineering.methods.systems", "label": "Engineering methods and systems engineering", "api_url": "https://www.edgepedia.org/api/v1/topics/technology.engineering.engineering.methods.systems" }, { "id": "technology.engineering.engineering.methods.systems.control-system-design-and-analysis-methods", "label": "Control system design and analysis methods", "api_url": "https://www.edgepedia.org/api/v1/topics/technology.engineering.engineering.methods.systems.control-system-design-and-analysis-methods" } ], "geo": [ { "id": "geo.nongeo.t1946.technology.engineering.engineering.methods.systems", "label": "Non-geographic · 1946 to 2000: Engineering methods and systems engineering", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.technology.engineering.engineering.methods.systems", "path": [ { "id": "geo.nongeo", "label": "Non-geographic", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo" }, { "id": "geo.nongeo.t1946", "label": "Non-geographic · 1946 to 2000", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946" }, { "id": "geo.nongeo.t1946.technology", "label": "Technology and the built world", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.technology" }, { "id": "geo.nongeo.t1946.technology.engineering", "label": "Engineering and manufacturing", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.technology.engineering" }, { "id": "geo.nongeo.t1946.technology.engineering.engineering.methods.systems", "label": "Engineering methods and systems engineering", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.technology.engineering.engineering.methods.systems" } ] } ], "excerpt": "The Smith predictor is a model-based control structure, proposed by Otto J. M. Smith in 1957, that compensates for long dead time by feeding back a delay-free model prediction.", "snippet": "The Smith predictor is a model-based control structure, proposed by Otto J. M. Smith in 1957, that compensates for long dead time by feeding back a delay-free model prediction.", "node": "technology.engineering.engineering.methods.systems.control-system-design-and-analysis-methods", "markdown": "# Smith predictor\n\nThe Smith predictor is a model-based control structure that compensates for long dead time in a process loop by feeding back a delay-free model prediction instead of the delayed measurement alone. Without dead-time compensation, the gain crossover frequency of a feedback loop is bounded by \\( \\omega_{c} < 1/L \\), where \\( L \\) is the dead time, so the achievable speed of response falls in direct proportion to the delay.[1](https://www.eolss.net/sample-chapters/c18/E6-43-03-05.pdf) A conventional PI or PID controller has no knowledge of the dead time and reacts too \"impatiently\", pushing the loop toward instability.[2](https://www.mathworks.com/help/control/ug/control-of-processes-with-long-dead-time-the-smith-predictor.html) The Smith predictor was the first dead-time compensator and remains the best known algorithm of its class.[3](https://www.sciencedirect.com/science/article/abs/pii/S0959152416000317)\n\n| Key fact | Detail |\n|---|---|\n| Problem addressed | Dead time bounds loop speed at \\( \\omega_{c} < 1/L \\); PID must be detuned as delay grows[1](https://www.eolss.net/sample-chapters/c18/E6-43-03-05.pdf) |\n| Structure | Delay-free fast model plus delay model in an inner loop, predictor error filtered into the outer loop, primary controller[4](https://www.frontiersin.org/journals/control-engineering/articles/10.3389/fcteg.2022.953768/full) |\n| Origin | Otto J. M. Smith, Chemical Engineering Progress 53: 217–219 (1957); ISA Journal 6 (2): 28–33 (1959)[5](https://www.degruyterbrill.com/document/doi/10.1515/cppm-2021-0026/html?lang=en) • [1](https://www.eolss.net/sample-chapters/c18/E6-43-03-05.pdf) |\n| Nominal effect | Removes the delay from the closed-loop poles; the loop behaves as the delay-free plant under the same controller[6](https://www.tamasmolnar.com/publication/2019_Molnar-et-al_SP%20vs%20MSP%20vs%20FSA_SCATDS_book_ch.pdf) |\n| Worked example | Plant with 40.2 s time constant and 93.9 s delay: bandwidth raised to 0.08 rad/s with 90 degrees phase margin, fast response with no overshoot[2](https://www.mathworks.com/help/control/ug/control-of-processes-with-long-dead-time-the-smith-predictor.html) |\n| Main weakness | Sensitive to error in the estimated dead time; ±50% delay errors cause oscillation or sluggish response[7](https://www.yokogawa.com/us/library/resources/yokogawa-technical-reports/performance-improvement-of-smith-predictor-through-automatic-computation-of-dead-time/) |\n| Software support | Discrete-time Smith Predictor Controller block in MATLAB/Simulink, introduced in R2017b[8](https://www.mathworks.com/help/sps/ref/smithpredictorcontroller.html) |\n\n## How it works\n\nThe predictor separates the process model into two parts: a delay-free fast model and a pure delay model. In the inner loop it uses the process model without the dead time to predict an output \\( y_{a} \\), which is fed back to the primary controller \\( C(s) \\) to generate the control signal; the outer loop compares the actual measurement with a delay-inclusive prediction and feeds the gap through a filter, correcting for load disturbances and modeling error.[1](https://www.eolss.net/sample-chapters/c18/E6-43-03-05.pdf) • [2](https://www.mathworks.com/help/control/ug/control-of-processes-with-long-dead-time-the-smith-predictor.html) The result is a feedback system with the dead time outside the loop.[9](https://www.controleng.com/overcoming-process-deadtime-with-a-smith-predictor/)\n\nWith an internal model \\( \\tilde{P}(s)e^{-s\\tilde{\\tau}} \\), the control law can be written\n\n\\[ U(s) = C(s)\\left(R(s) - Y(s) - \\tilde{Y}(s) + \\tilde{Y}(s)e^{s\\tilde{\\tau}}\\right) \\]\n\nand, for a perfect model, the nominal closed-loop transfer function reduces to\n\n\\[ T_{\\mathrm{id}}^{\\mathrm{SP}}(s) = \\frac{C(s)P(s)e^{-s\\tau}}{1 + C(s)P(s)} \\]\n\nso the delay no longer appears in the poles; the loop achieves the delayed response of the delay-free plant under controller \\( C(s) \\).[6](https://www.tamasmolnar.com/publication/2019_Molnar-et-al_SP%20vs%20MSP%20vs%20FSA_SCATDS_book_ch.pdf) When the estimated dead time is wrong by \\( \\Delta L \\), the disturbance response carries the term \\( H(s) = 1 + e^{-s(L+\\Delta L)} - e^{-sL} \\), and the controller gain should give more than 6 dB attenuation at frequencies where \\( H(j\\omega) \\) has resonance peaks.[1](https://www.eolss.net/sample-chapters/c18/E6-43-03-05.pdf)\n\n## How it is done\n\nImplementation follows a model-then-tune sequence. The engineer first identifies a low-order model, typically first-order plus dead time (FOPDT), giving a process gain \\( k_{p} \\), lag time constant \\( \\tau \\), and dead time. For an FOPDT model the primary [PI controller](https://www.edgepedia.org/pi-controller) is tuned with \\( T_{i1} = \\tau \\) and \\( K_{c1} = \\tau/(k_{p} \\cdot T_{m}) \\), where \\( T_{m} \\) is the desired closed-loop time constant; a suitable range for the ratio \\( T_{m}/\\tau \\), accounting for controller saturation and noise sensitivity, is 0.2 to 1.[1](https://www.eolss.net/sample-chapters/c18/E6-43-03-05.pdf) For a second-order plus dead-time model with a PI primary controller, \\( T_{i1} = \\tau_{2} \\) and \\( K_{c1} = 1/(4\\xi^{2} \\cdot k_{p}) \\).[1](https://www.eolss.net/sample-chapters/c18/E6-43-03-05.pdf)\n\nThe delay compensation block is the model pair \\( G_{f}(s) = G_{p}(s)e^{-\\tau s} \\), as implemented in the MathWorks Smith Predictor Controller block, parameterized by \\( K_{p} \\), \\( K_{i} \\), a discretized model transfer function, and the dead time in samples.[8](https://www.mathworks.com/help/sps/ref/smithpredictorcontroller.html) The outer-loop filter matters for disturbance rejection: the optimal choice \\( F(s) = e^{\\tau s} \\) is a negative delay and cannot be implemented, and Huang and colleagues proposed the phase-lead approximation \\( e^{\\tau s} \\approx (1+B)/(1+B e^{-\\tau s}) \\) with \\( B \\) a low-pass filter.[2](https://www.mathworks.com/help/control/ug/control-of-processes-with-long-dead-time-the-smith-predictor.html) Because dead-time error is the dominant failure mode, an adaptive law that automatically retunes the model dead time \\( \\tau_{m} \\) can dramatically improve performance, with a higher adaptation coefficient \\( K_{\\tau} \\) speeding convergence.[7](https://www.yokogawa.com/us/library/resources/yokogawa-technical-reports/performance-improvement-of-smith-predictor-through-automatic-computation-of-dead-time/)\n\n## Origin\n\nThe Smith predictor was proposed by Otto J. M. Smith in 1957 in \"Closer control of loops with dead time\", published in Chemical Engineering Progress.[10](https://arrow.tudublin.ie/cgi/viewcontent.cgi?article=1027&context=engscheleart) • [5](https://www.degruyterbrill.com/document/doi/10.1515/cppm-2021-0026/html?lang=en) A companion version, \"A controller to overcome dead time\", appeared in ISA Journal[1](https://www.eolss.net/sample-chapters/c18/E6-43-03-05.pdf), so the founding year is cited as 1957 or 1959 depending on which paper a source treats as primary.\n\n## Variants\n\nMost later dead-time compensators derive from Smith's original idea.[4](https://www.frontiersin.org/journals/control-engineering/articles/10.3389/fcteg.2022.953768/full) The main line of modification addresses processes the classic structure cannot handle:\n\n- **Integrating processes.** Watanabe and Ito proposed in 1981 a modified Smith predictor using a mismatched process model to eliminate steady-state error for a process containing an integrator.[11](https://doi.org/10.1109/tac.1981.1102802) Åström, Hang, and Lim proposed in 1994 a new Smith predictor for a process with an integrator and long dead time[12](https://doi.org/10.1109/9.272329), and Matausek and Micic added a load estimator in 1996[13](https://doi.org/10.1109/9.533684), a scheme judged the most effective for load disturbance compensation on integrating processes.[7](https://www.yokogawa.com/us/library/resources/yokogawa-technical-reports/performance-improvement-of-smith-predictor-through-automatic-computation-of-dead-time/)\n- **Unstable processes.** The Modified Smith Predictor of Mataušek and Ribić covers stable, integrating, and unstable processes.[14](https://doi.org/10.1016/j.jprocont.2011.08.006)\n- **Robustness filtering.** The filtered Smith predictor (FSP) for SISO plants adds a robustness filter that can be tuned to accelerate disturbance rejection and achieve robust performance, and it controls stable, integrative, and unstable processes.[4](https://www.frontiersin.org/journals/control-engineering/articles/10.3389/fcteg.2022.953768/full) • [3](https://www.sciencedirect.com/science/article/abs/pii/S0959152416000317) It was generalized to a unified MIMO dead-time compensator for square processes with multiple delays, and extended to non-square plants in 2014.[15](https://doi.org/10.1016/j.jprocont.2014.02.011)\n- **Industrial PI forms.** Hägglund proposed the predictive PI (PPI) controller as a modification of the Smith predictor[16](https://arrow.tudublin.ie/cgi/viewcontent.cgi?article=1033&context=engscheleart), and Shinskey's PIτ and PIDτ controllers are dead-time compensating PI/PID forms compared against it in simulation studies.[10](https://arrow.tudublin.ie/cgi/viewcontent.cgi?article=1027&context=engscheleart)\n- **Analysis and approximations.** The predictor fits the [internal model control](https://www.edgepedia.org/internal-model-control) (IMC) structure, and it became the basis for IMC as a design approach.[17](https://www.nature.com/articles/s41598-026-39732-9) The unrealizable time-advance term \\( e^{+\\tau_{m} s} \\) was approximated with \\( B(s) = (a \\cdot s+1)/(a \\cdot s+p) \\), \\( p > 1 \\).[18](https://mural.maynoothuniversity.ie/id/eprint/9525/2/JR-Control-1996.pdf)\n- **Recent extensions.** A 2024 adaptive Smith predictor design addresses industrial processes with time-varying delay, including crude oil preheating furnace temperature control using a modified predictor with a disturbance rejection term.[19](https://www.sciencedirect.com/science/article/pii/S2405896324020858) A 2026 data-driven filtered Smith predictor maps open-loop input-output data, such as step or impulse responses, directly to the primary controller, reference filter, and robustness filter parameters through mean-square minimization, without an explicit parametric model, for stable, integrative, and unstable SISO processes.[20](https://link.springer.com/article/10.1007/s40313-026-01261-1)\n\n## Applications\n\nThe method targets processes whose dead time exceeds the dominant lag time, where classical PID tuning gives unsatisfactory results.[7](https://www.yokogawa.com/us/library/resources/yokogawa-technical-reports/performance-improvement-of-smith-predictor-through-automatic-computation-of-dead-time/) Documented application domains include temperature control of a crude oil preheating furnace, injectable drug formulations, steel slab reheating furnaces, and networked control systems over the internet.[5](https://www.degruyterbrill.com/document/doi/10.1515/cppm-2021-0026/html?lang=en) A 2024 case study applied the Smith predictor to delay compensation in a feeder–conveyor system in an iron ore processing plant, where its main advantage over PID is eliminating the influence of dead time, giving faster responses.[21](https://www.mdpi.com/1424-8220/24/12/3870)\n\nPublished comparisons show gains that depend strongly on how delay-dominant the process is. Seborg and colleagues quote studies putting Smith predictor servo performance up to 30% better than an appropriately tuned PID controller.[16](https://arrow.tudublin.ie/cgi/viewcontent.cgi?article=1033&context=engscheleart) In the [MathWorks](https://www.edgepedia.org/mathworks) example (40.2 s lag, 93.9 s delay), a PI controller alone settles in about 600 seconds and higher gains destabilize the loop, while the Smith predictor raises the open-loop bandwidth to 0.08 rad/s with 90 degrees phase margin and gives much faster response with no overshoot.[2](https://www.mathworks.com/help/control/ug/control-of-processes-with-long-dead-time-the-smith-predictor.html) For a weakly delay-dominant process (\\( \\tau_{m}/T_{m} = 2 \\)), Shinskey's PIDτ achieves ISE 4.39 (servo) and 1.50 (regulator), better than the Smith predictor's 6.46 and 14.65.[10](https://arrow.tudublin.ie/cgi/viewcontent.cgi?article=1027&context=engscheleart)\n\n## Limitations and alternatives\n\nThe classic structure was proposed for open-loop stable plants only. It cannot control open-loop unstable processes because the resulting internal transfer function is unstable, and with a perfect model the modified Smith predictor and finite spectrum assignment can stabilize unstable systems while the basic predictor cannot.[4](https://www.frontiersin.org/journals/control-engineering/articles/10.3389/fcteg.2022.953768/full) • [6](https://www.tamasmolnar.com/publication/2019_Molnar-et-al_SP%20vs%20MSP%20vs%20FSA_SCATDS_book_ch.pdf) Conventional Smith predictors also fail to perform satisfactorily for integrating processes with large dead time because of their non-self-regulating nature.[22](https://link.springer.com/article/10.1007/s42452-019-1186-9)\n\nModel mismatch, especially in dead time, is the central weakness. Dead-time compensators of this type are generally less robust than PID controllers and particularly sensitive to variations in process gain and delay, the parameters most likely to change.[16](https://arrow.tudublin.ie/cgi/viewcontent.cgi?article=1033&context=engscheleart) With ±50% delay estimation mistakes on a process with \\( \\tau = 10T \\), under-estimation causes oscillation around steady state and over-estimation makes the approach to setpoint slow and hesitating[7](https://www.yokogawa.com/us/library/resources/yokogawa-technical-reports/performance-improvement-of-smith-predictor-through-automatic-computation-of-dead-time/); in another test varying modeled dead time by ±50% on a 100 s deadtime process, the Smith predictor diverged until limited only by controller output limits.[23](https://www.controlglobal.com/control/loop-control/article/55264206/face-off-smith-predictor-vs-deadtime-compensated-pid) As process delay increases, instability occurs at lower delay ratios with predictive controllers than with PI/PID controllers.[10](https://arrow.tudublin.ie/cgi/viewcontent.cgi?article=1027&context=engscheleart) The original version also handles feedforward poorly, because the feedforward response appears as model error and provokes harsh controller reactions.[24](https://www.act-control.com/publications/PID-Smith-MBC.pdf) Industrial adoption lags the academic literature: a survey of industrial practice in Scotland found only a single use of the Smith predictor.[16](https://arrow.tudublin.ie/cgi/viewcontent.cgi?article=1033&context=engscheleart)\n\n## References\n\n1. [Smith Predictor And Its Modifications (C.C. Hang, UNESCO-EOLSS)](https://www.eolss.net/sample-chapters/c18/E6-43-03-05.pdf)\n2. [Control of Processes with Long Dead Time: The Smith Predictor (MathWorks)](https://www.mathworks.com/help/control/ug/control-of-processes-with-long-dead-time-the-smith-predictor.html)\n3. [On the filtered Smith predictor with feedforward compensation (Journal of Process Control)](https://www.sciencedirect.com/science/article/abs/pii/S0959152416000317)\n4. [Control of dead-time process: From the Smith predictor to general multi-input multi-output dead-time compensators (Frontiers in Control Engineering, 2022)](https://www.frontiersin.org/journals/control-engineering/articles/10.3389/fcteg.2022.953768/full)\n5. [A comparative study of various Smith predictor configurations (Chemical Product and Process Modeling)](https://www.degruyterbrill.com/document/doi/10.1515/cppm-2021-0026/html?lang=en)\n6. [Smith predictor, modified Smith predictor and finite spectrum assignment (Molnar et al., book chapter)](https://www.tamasmolnar.com/publication/2019_Molnar-et-al_SP%20vs%20MSP%20vs%20FSA_SCATDS_book_ch.pdf)\n7. [Performance Improvement of Smith Predictor Through Automatic Computation of Dead Time (Yokogawa technical report)](https://www.yokogawa.com/us/library/resources/yokogawa-technical-reports/performance-improvement-of-smith-predictor-through-automatic-computation-of-dead-time/)\n8. [Smith Predictor Controller block (MathWorks Simscape)](https://www.mathworks.com/help/sps/ref/smithpredictorcontroller.html)\n9. [How to overcome process deadtime with a Smith predictor (Control Engineering, VanDoren)](https://www.controleng.com/overcoming-process-deadtime-with-a-smith-predictor/)\n10. [Dead-time compensators: performance and robustness issues (O'Dwyer)](https://arrow.tudublin.ie/cgi/viewcontent.cgi?article=1027&context=engscheleart)\n11. [K. Watanabe, M. Ito (1981). A process-model control for linear systems with delay. IEEE Transactions on Automatic Control.](https://doi.org/10.1109/tac.1981.1102802)\n12. [K.J. Astrom, C.C. Hang, B.C. Lim (1994). A new Smith predictor for controlling a process with an integrator and long dead-time. IEEE Transactions on Automatic Control.](https://doi.org/10.1109/9.272329)\n13. [M.R. Matausek, A.D. Micic (1996). A modified Smith predictor for controlling a process with an integrator and long dead-time. IEEE Transactions on Automatic Control.](https://doi.org/10.1109/9.533684)\n14. [Miroslav R. Mataušek, Aleksandar I. Ribić (2011). Control of stable, integrating and unstable processes by the Modified Smith Predictor. Journal of Process Control.](https://doi.org/10.1016/j.jprocont.2011.08.006)\n15. [Tito L.M. Santos, Rodolfo C.C. Flesch, Julio E. Normey-Rico (2014). On the filtered Smith predictor for MIMO processes with multiple time delays. Journal of Process Control.](https://doi.org/10.1016/j.jprocont.2014.02.011)\n16. [A reference guide to Smith predictor based methods for the compensation of dead-time processes (O'Dwyer)](https://arrow.tudublin.ie/cgi/viewcontent.cgi?article=1033&context=engscheleart)\n17. [Measurement noise attenuation in modified Smith predictor and automatic offset controllers for integrator plus dead-time system | Scientific Reports](https://www.nature.com/articles/s41598-026-39732-9)\n18. [The control of a process with time delay by using a modified Smith predictor compensator (O'Dwyer & Ringwood, 1996)](https://mural.maynoothuniversity.ie/id/eprint/9525/2/JR-Control-1996.pdf)\n19. [Adaptive Smith Predictor Controller Design for Industrial Processes with Time Varying Time Delay (IFAC Proceedings, 2024)](https://www.sciencedirect.com/science/article/pii/S2405896324020858)\n20. [Data-Driven Filtered Smith Predictor for SISO Dead-Time Processes (Journal of Control, Automation and Electrical Systems)](https://link.springer.com/article/10.1007/s40313-026-01261-1)\n21. [Delay Compensation in a Feeder–Conveyor System Using the Smith Predictor: A Case Study in an Iron Ore Processing Plant (Sensors, 2024)](https://www.mdpi.com/1424-8220/24/12/3870)\n22. [Improved disturbance rejection with modified Smith predictor for integrating FOPTD processes (SN Applied Sciences)](https://link.springer.com/article/10.1007/s42452-019-1186-9)\n23. [Face-off: Smith Predictor vs. deadtime compensated PID (Control Global)](https://www.controlglobal.com/control/loop-control/article/55264206/face-off-smith-predictor-vs-deadtime-compensated-pid)\n24. [Dealing with long deadtime – a comparison between PID, PI, Smith Predictor and Model Based Control (ACT Control)](https://www.act-control.com/publications/PID-Smith-MBC.pdf)\n\n---\n*Topic: Encyclopedia › Technology and the built world › Engineering and manufacturing › Engineering methods and systems engineering › Control system design and analysis methods*\n\n*Initially written Sep 29, 2026 · Edited: Oct 15, 2026; Oct 21, 2026*\n\n*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*\n\nLicense: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license\n", "same_as": [], "url": "https://www.edgepedia.org/smith-predictor", "markdown_url": "https://www.edgepedia.org/smith-predictor.md", "license": { "name": "Edgepedia Community License 1.0", "url": "https://www.edgepedia.org/edgepedia/license", "summary": "Free with credit, commercial use included. AI training is open to everyone. For other uses, organizations over USD 100M in revenue or 100M monthly users license separately.", "spdx": "LicenseRef-Edgepedia-Community-1.0" }, "credit": "\"Smith predictor\", Edgepedia (EdgeChat), https://www.edgepedia.org/smith-predictor. Edgepedia Community License 1.0.", "credit_md": "\"[Smith predictor](https://www.edgepedia.org/smith-predictor)\", Edgepedia (EdgeChat), [https://www.edgepedia.org/smith-predictor](https://www.edgepedia.org/smith-predictor). [Edgepedia Community License 1.0](https://www.edgepedia.org/edgepedia/license).", "credit_html": "\"Smith predictor\", Edgepedia (EdgeChat), https://www.edgepedia.org/smith-predictor. Edgepedia Community License 1.0.", "speakable": "The Smith predictor is a model-based control structure, proposed by Otto J. M. Smith in 1957, that compensates for long dead time by feeding back a delay-free model prediction." }