Sampled Data System¶
A feedback system couples a continuous plant to sampled observation, digital control updates, and returned actuation across intersample intervals.
Core Idea¶
A sampled data system is a feedback-control arrangement that links a continuously evolving plant to a digital controller. The controller receives observations at discrete instants, updates a command, and returns that command through an actuation interface. Between updates, the plant keeps changing. That continuous interval is part of the system's identity, not an empty gap in a list of measurements.[1][2]
The distinction is visible in a CNC machine-tool servo drive and a modeled continuously stirred-tank reactor. One controls motion; the other controls a chemical process. In both, sampled information affects a later continuous-plant input. Their particular sampling schedules, sensors, control laws, and zero-order holds are case designs rather than universal requirements.[1][2][3]
Structural Signature¶
Signature: continuous-time plant → sampled output observation → digital control update → returned plant input, with continuous evolution between updates.
- Continuous-time plant. Machine motion or reactor state evolves between controller updates. A wholly discrete state-transition model without such a plant is outside this identity.[1][2]
- Sampled observation. Plant-output information becomes available to the controller at discrete instants. Sampling alone is insufficient if its values never affect a subsequent plant input.[1][2]
- Digital control update. A discrete law uses the observation to compute a command. Without the control update, the arrangement could be monitoring or data acquisition rather than this feedback system.[1][2]
- Return actuation interface. A command is applied back to the continuous plant. An output register and digital-to-analog converter provide a zero-order hold in the CNC case; a zero-order-hold device is used in the reactor model. Another reconstruction or actuation mechanism could fill the same role.[1][2]
- Intersample evolution. The plant continues to move or react between observations. A discrete sampled trace alone can omit this behavior, so performance or stability claims must be tied to the continuous plant and the sampled interface actually modeled.[4][2]
What It Is Not¶
Sampling (signal processing) obtains discrete values from a continuous signal; it does not by itself close a control loop. A one-way sensor log can sample a plant without updating its input. Data acquisition can likewise measure without acting. A continuously observed analog controller lacks the discrete observation-and-update interface required here. A fully discrete plant has no continuous intersample trajectory.[1][4]
The name also does not mean that every system samples periodically, uses a digital encoder, holds a command constant, or is physically deployed. Non-uniform sampling is a studied control setting. The CNC and reactor papers specify particular designs; the reactor example is a modeled and simulated control study, not evidence of an installed plant.[3][1][2]
Scope of Application¶
The entry covers closed sampled-data control of a continuous plant. It can describe mechanical motion and process variables without equating their physical dynamics. It does not make a sampled-equivalent discrete model a mandatory system component: such a model is an analyst's representation, while the plant continues in continuous time.[1][2][4]
Koren and Bollinger analyze a fixed-interval CNC servo with a computer, feedback device, output register and digital-to-analog converter. Their Fig. 1 shows a digital encoder and discusses resolver or inductosyn alternatives; it does not authorize one universal sensing device. Di Ciccio, Bottini and Pepe formulate a continuous reactor and a digital law applied through a zero-order hold. The available publisher passages support those modeled roles, but do not establish specific sensor, valve or programmable-controller hardware.[1][2]
Clarity¶
The decisive question is whether a sampled output changes a later input to the same continuous plant. If it does, one can identify the plant, sampling interface, digital law, return path, and intersample behavior. If the measurement is merely stored or displayed, the loop is absent even though sampling occurred. This distinguishes the system from its sampled signals and from a wholly discrete simulation.[1][4]
The distinction also prevents a sampled trace from being mistaken for the complete plant trajectory. Yamamoto's sampled-data overview emphasizes continuous-time and intersample behavior. A discrete approximation can help design a controller, but conclusions about what happens between observations need the plant/interface assumptions that support them.[4]
Manages Complexity¶
The five roles divide a hybrid loop into questions that can be examined separately: what evolves continuously, what is measured and when, what command is computed, how it is applied, and what occurs before the next update. Koren and Bollinger use this division when choosing sample rate and servo gain against stability, contouring accuracy and bandwidth in their specific CNC design.[1]
The division is not a claim that all sampled-data systems share one numerical model or optimization objective. In the reactor study, the continuous model and sampled approximation have a noted relative-degree distinction, and the digital-control analysis addresses the sampled implementation under its own assumptions. That modeling issue cannot simply be copied into the CNC case or generalized to every plant.[2]
Abstract Reasoning¶
Given a candidate system, first locate the continuing continuous plant. Trace an observed output to a discrete observation, through a digital update, then to a command that reaches the plant. Finally ask what the plant does between updates and which assumptions justify a stability or performance inference. Remove the return path and the system becomes one-way observation; remove the continuous plant and the intersample question disappears.[1][4]
This is a qualitative classification and analysis sequence, not a universal equation. Fixed timing and zero-order hold can make a specific analysis tractable, but neither follows from the identity. The existence of non-uniform sampled-data control makes periodicity an invalid all-instance test.[3]
Knowledge Transfer¶
The same feedback architecture organizes a servo motor/axis and a continuously stirred reactor: sampled outputs inform digital commands applied to continuously evolving states. This transfers the roles and the question about intersample behavior, not the CNC controller gains, the reactor's nonlinear equations, or an observed performance result from one setting to the other.[1][2]
The portable output-return pattern belongs to the live Feedback Prime. Its biological, social, or purely analog instances need neither sampling nor a digital controller. Calling those systems sampled-data systems would import this specialist architecture without evidence. A broader cross-domain hybrid sampled/continuous pattern would require independent admission, not a new direct edge inferred from these two engineering cases.
Examples¶
CNC machine-tool servo drive. Koren and Bollinger's design samples machine feedback at fixed intervals. A computer processes the sampled signal and issues a drive reference through an output register and digital-to-analog converter, which together act as a zero-order hold in this case. The motor and driven axis continue to evolve between updates. The paper studies sample rate and loop gain in relation to stability, contouring accuracy and bandwidth.[1]
Mapped back: continuous-time plant → servo motor and axis; sampled observation → fixed-interval position/feedback from the Fig. 1 digital encoder arrangement; digital update → computer-produced new drive reference; return interface → output register and converter holding the reference between updates; intersample evolution → continuing motor/axis motion whose sampled design affects performance. The printed design does not establish PWM as the hold or a universal encoder requirement.[1]
Continuous stirred-tank reactor digital control. Di Ciccio, Bottini and Pepe model a reactor by continuous differential equations and apply a digital feedback law through a zero-order-hold device. They discuss sampled reactor variables, including temperature, and a sampled approximation whose relative-degree behavior differs from the original continuous model. Their result is a modeled control analysis with simulations and stated sampling conditions, not evidence of particular installed sensor or valve hardware.[2]
Mapped back: continuous-time plant → nonlinear reactor in the original continuous model; sampled observation → reactor output/state values used by the digital design; digital update → the paper's digital feedback law; return interface → its zero-order hold applying computed input; intersample evolution → continuous reactor dynamics between updates, which the sampled approximation does not automatically preserve in every input-output respect. The relative-degree difference is particular to the cited construction.[2]
Structural Tensions¶
The cited cases do not establish one intrinsic pair of opposed pressures that every sampled-data system must resolve. Koren and Bollinger study sample rate and loop gain against CNC stability, contouring and bandwidth, but those are parameters and objectives of that design. The reactor paper addresses a different model and sampled approximation. A useful diagnostic is whether a claim about sampled instants also covers continuous intersample behavior; that is a scope and evidence test, not a manufactured universal tradeoff.[1][2][4]
Structural–Framed Character¶
The arrangement is strongly structural within control engineering: its roles and return path can be recognized in both a machine drive and a chemical-process model. The definition has little evaluative weight; neither a fast sample rate nor a stable outcome is guaranteed by the name. It depends on engineering practice to select sensors, digital laws and actuation interfaces, but no particular institution confers the identity. The vocabulary of output return and subsequent input travels through the live Feedback Prime, while sampled observation of a continuous plant, digital update and intersample dynamics keep the named system in its control setting. An analyst may recognize the return-loop skeleton elsewhere without importing CNC or reactor hardware; applying the full sampled-data name requires evidence for its hybrid architecture. Its character: a domain-specific engineered feedback system with a portable Feedback skeleton and constitutive continuous/discrete coupling.
Structural Core vs. Domain Accent¶
The portable core is output routed back to alter a subsequent input. It is inherited through the approved strict subsumption edge to live Feedback. The domain accent is the continuously evolving plant, discrete observation, digital control update, actuation interface, and resulting intersample analysis. Fixed periods, digital encoders and zero-order holds are narrower case accents rather than requirements of the named system.[1][2][3]
The named sampled-data system does not itself clear the Prime bar: the two positive cases are control-engineering implementations, and no unlike non-control carriers of this exact continuous-plant/digital-controller arrangement have been established. Whether a more general hybrid continuous/discrete feedback skeleton deserves a future Prime is a separate cross-domain admission question. This entry adds no unsupported Prime edge.
Instantiates / Related Primes¶
This entry is a kind of Feedback.
A sampled data system is, in every case, a kind of Feedback: every instance uses an output observation to update an input to the same plant. Feedback can occur without sampling or a digital controller, so a sampled data system is narrower. Sampling (Signal Processing) is related as an observation operation, but it lacks the whole loop; Data Acquisition is likewise a possible component rather than a second broader abstraction. Neither is listed as broader.[1]
Relationships to Other Abstractions¶
Current abstraction Sampled Data System Domain-specific
Parents (1) — more general patterns this builds on
-
Sampled Data System is a kind of Feedback Prime
A sampled plant output is routed through a digital control update to a subsequent plant input.Every admitted sampled-data system closes an output-to-input feedback path around a continuously evolving plant through discrete observation and digital updating. Feedback need not sample or use a continuous physical plant, so the child adds a stable hybrid-control differentia. An open-loop sampled command or a one-way sensor log is outside this entry.
Hierarchy path (1) — routes to 1 parentless root
- Sampled Data System → Feedback
Neighborhood in Abstraction Space¶
Sampled Data System sits in a sparse region of the domain-specific corpus (93rd percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Unclustered & Miscellaneous (2551 abstractions)
Nearest neighbors
- Repetitive Control — 0.86
- Local Time (Mathematics) — 0.78
- Kinetic Scheme — 0.77
- Dead-beat control — 0.77
- Work Output — 0.77
Computed from structural-signature embeddings · 2026-10-08
Not to Be Confused With¶
A one-way sampled logger and an open-loop sequence of computer commands may involve a continuous plant and discrete timing but do not close the admitted feedback path. A continuous analog controller may close a feedback path but lacks the sampled digital update. A sampled-equivalent model is a representation used for analysis, not a substitute for checking the continuous plant. Zero-order hold and periodic sampling describe the two sourced designs, not the class definition.[4][3]
References¶
[1] Yoram Koren and John G. Bollinger, Design Parameters for Sampled-Data Drives for CNC Machine Tools, IEEE Transactions on Industry Applications IA-14(3) (May/June 1978), pp. 255–264, especially abstract, Fig. 1 and Introduction (printed p. 255). registry ↩a ↩b ↩c ↩d ↩e ↩f ↩g ↩h ↩i ↩j ↩k ↩l ↩m ↩n ↩o ↩p ↩q ↩r ↩s
[2] M. P. Di Ciccio, M. Bottini and P. Pepe, Digital Control of a Continuous Stirred Tank Reactor, original publisher article (17 April 2011), DOI 10.1155/2011/439785, especially continuous model §2 and digital-control discussion §3. Publisher indexed passages were available for the stated roles; hardware beyond those passages is not asserted. registry ↩a ↩b ↩c ↩d ↩e ↩f ↩g ↩h ↩i ↩j ↩k ↩l ↩m ↩n ↩o ↩p
[3] Xian-Ming Zhang, Qing-Long Han, Xiaohua Ge, Boda Ning and Bao-Lin Zhang, Sampled-data control systems with non-uniform sampling, A survey of methods and trends, Annual Reviews in Control 55 (2023), pp. 70–91, DOI 10.1016/j.arcontrol.2023.03.004. Title originally punctuated with a colon after “sampling.” Abstract supports the non-uniform-sampling scope point only. registry ↩a ↩b ↩c ↩d ↩e
[4] Yutaka Yamamoto, I. Sampled-Data Systems, From Lifting to Frequency Response, IEEJ Transactions on Electronics, Information and Systems 114(7–8) (1994), pp. 729–734, DOI 10.1541/ieejeiss1987.114.7-8_729. The original title is “I. Sampled-Data Systems: From Lifting to Frequency Response”; the linked comma transcribes that punctuation for citation binding. Used for the continuous-time/intersample distinction, not for CNC or CSTR hardware. registry ↩a ↩b ↩c ↩d ↩e ↩f ↩g ↩h