06A Self-Tuning Pole Place & PID LabAss2

06A Self-Tuning Pole Place & PID LabAss2 - SYS635...

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SYS635 Adaptive Control Systems KaCC 06A Self-Tuning Pole Place & PID LabAss2 10/08/05 1 SELF-TUNING CONTROLLER Application of Self-Tuning Control is useful when the dynamics of the Plant to be controlled is unknown changes over time varies with operating condition be altered by external and/or internal disturbance The steps in STC involve the following: (Design Specification) Define the Desired Control Specification/Performance Objective time response specification in terms of desired closed-loop poles frequency response specs optimization (System Identification) Estimate a Math Model of the Plant order of the model values of the model parameter (Controller Design) Design a Controller for the Plant based on the Estimated Model simple pole-placement or pole & zero placement methods other methods (Controller Execution) Adjust and implement the Controller TERMINOLOGY MEANING Adaptive controller Continuous adaptive Active adaptive System ID, Controller Design and Execution are carried out in real-time (hence on-line) Auto-tuning Passive adaptive System ID, Controller Design carried out at an operator’s request, Constant parameter controller no adaptation whatsoever Controlled Outputs y Observation of External Environment Command/ Reference Inputs u c Control Signal u Dynamic Plant to be Controlled Controller Executor Disturbance w Supervisory Command Level Decision Controller Designer System Identifier
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SYS635 Adaptive Control Systems KaCC 06A Self-Tuning Pole Place & PID LabAss2 10/08/05 2 SELF-TUNING CONTROLLER FOR A 1 st ORDER SYSTEM A. Continuous-Time to Discrete-Time System Model Consider a simple deterministic 1 st order system with zero-order hold input: CT System DT system where () if 0 1 1 if 0 T T ae T b e α βα = = = CHECK OUT MATLAB COMMANDS: c2d.m and d2c.m Gs s = + β u(kT) y(t) b Gz za = + u(k) y(k) u(s) y(s) u(z) y(z) t u(t) kT or k u(k) y(k) kT or k 063 . t y(t) α ZOH u(z) u(t) y(kT) y(z) T
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SYS635 Adaptive Control Systems KaCC 06A Self-Tuning Pole Place & PID LabAss2 10/08/05 3 B. TIME-SERIES MODEL Transfer function operation () ()() b yz Gzuz uz za == + Polynomial operation ( )() () y z bz += Time series operation (1 ) ( ) yk ayk buk + Also known as an Auto-Regressive Moving Average (ARMA) model . Shorthand notation of the above: Bz Gz Az Azyz Bzuz z a b = =+ = Assumption. We will assume that the input u(k) and output y(k) for the system are accessible for measurements. b = + u(z) y(z)
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SYS635 Adaptive Control Systems KaCC 06A Self-Tuning Pole Place & PID LabAss2 10/08/05 4 C. Parameter Estimation of 1 st order system whose input and output are subjected to noise Consider a strictly proper 1 st order system (transfer function block diagram ) [ ] [ ] ( ) a nonzero constant ( ) a nonzero constant wk vk == EE Derive the input-output relationship for the noisy system : In the mean or average, this means that the systems behave like So a key relationship that can be used for estimating systems parameters is Unknown internal variable x(z) Gz b za () = + Known system input u(z) Known system output y(z) Unknown output
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06A Self-Tuning Pole Place & PID LabAss2 - SYS635...

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