Analysis

This is the analysis sub-package of the pctools package.

Features

• Analysis tools for practical understanding and design of conventional and advanced control schemes.
• Package content (mainly classes):
  • plant
  • loop

Plant

• potential names for class (plantmatrix, matrix, PVs, plant)

• cross-correlation matrix (see ideas below) - note that this is probably the only analysis in a "matrix" form
  • calculate multiple parameters for each pairing (max corr, delay, 2nd peak info)
    • 2nd peak might be helpful for where there is an obvious controller in the loop causing initial correl, but want the likely process peak)
    • try matplotlib or ?-tree to show ordered list of strong correlations (or just a list!) - a matrix may not really be useful?
• common frequency detection (most dominant frequency, amplitude in each PV (sorted order))
• PCA (how to interpret?, how many PCs explain 95%, perhaps low number or high % for two implies abnormal plant stability?)

Loop

Class name Loop

Assess

• auto-determination of "in-control" periods in data (to handle saturation, constraint control tracking, etc. situations)
  • CO flat-line detection
  • use "max cross-correlation" analysis between error and CO (over windows of short duration; note that CO must be the ultimate CO, e.g. after a constraint controller select block)
• standard analysis data (for quantitative measures) with optional graphics
  • impulse response
    • input-output regression (what exactly does this give me?) - note: due to correlation between independent variables, PCA or ICA should probably be used first! (MDP package in pythonxy)
    • autocorrelation (known to give a closed-loop FIR approximation)
  • frequency content (bandwidth) of controller error (i.e. what is the roll-off frequency (high-pass) of the control correction)
  • resonant frequency, PID tuning estimation, cycling estimation of P vs I action
  • normalised plot of PV vs CO (shows phase lag in controller, valve stiction)
  • performance compared with minimum-variance control (including projected best achievable SD with MV control)
• tabular measures
  • Standard Error (in % of setpoint value)
  • average phase difference PV to CO (how? cross-corr? need to know resonant frequency first!)
  • resonant frequency of loop
  • auto-estimation of existing PID tuning parameters (perhaps need to know if Proportional action is on error or PV for a servo loop)
    • should be able to derive the parameters from the coefficients of a linear regression (dCO = f(Error,dError,ddError)) rather than simulation and fitting using the dynsim.control.PID class.
  • table of max cross-correlations between a set of signals
• analyses dependent on data available
  • PV only
    • autocorrelation / impulse response (stability analysis)
    • cross-correlation analysis with other PVs etc.
  • +SP
    • SD
    • +estimated deadtime
      • minimum variance comparison
  • +CO
    • estimate PID parameters
    • determine periods of active feedback control
    • cross-correlation analysis (CO to PV) - ?
  • +FF
    • multivariable MV assessment (i.e. value of adding FF to loop)
• misc
  • data preprocessing tools (resampling, period selection, basic statistics, FFT, HP/LP filtering/filtfilt, ...)
  • statistical tools?
    • Principal Component Analysis (using PCA (and similar) to assist with process control analysis, not just the algorithm)
  • fit a statistical distribution to a histogram
  • monte-carlo tools
    • random variates from a histogram (concatenate count x (equal bin values) for each bin, then select a value using a uniform dist)
    • multiple correlated variates (i.e. with a correlation matrix)
  • filtering utilities
    • cutoff frequency to/from timeconstant conversion for first order filters.
    • ?

Fit

• controller ID
  • PID parameters
  • do first to help with plant ID? or
  • combined PID and plant ID?
• plant ID
  • 1-input, 1-output at a time or multi-input-one-output
  • impulse response (from step-response or PRBS data)
  • deadtime estimation (using FOPDT assumption below?)
  • FOPDT model (more likely to be local minima involved! - use initial deadtime estimate)
  • for FF as well as plant (multivariable!)
  • need to be able to simulate multivariable FIRs in dynsim!

Tune

• PID tuning program (everything needed for loop tuning, bundling above capability)
  • analysis (of loop data)
  • identification (impulse, FOPDT etc., from step-test or PRBS results)
  • tuning optimisation
  • utility
    • conversion between PID formulations (parallel, ideal, ...)
    • standard tuning formulae (from guidance note?)
• FF tuning (FOPDT)
  • by optimisation (could be calculated but would often need a predictor resulting in more complex design)