Improved generalized predictive controllers for decentralized control
Date of Issue2013
School of Electrical and Electronic Engineering
In general, decentralized control refers to the multivariable control of a nxn square process using n SISO (Single-Input Single-Output) control loops designed for the diagonal elements. Under consideration is an equivalent transfer function method for decentralized controller design proposed by Cai et.al. known as the (Relative Normalized Gain Array) RNGA-based decentralized PID design method. The design procedure involves loop pairing using the RNGA, RGA (Relative Gain Array) and NI (Niederlinski Index) analysis, deriving the RNGA-based equivalent transfer functions (ETFs) of the n diagonal elements and using them to design PID controllers for the n loops. The objective of this work was to use the RNGA-based ETFs to design GPCs (Generalized Predictive Controllers) in place of the standard PID in order to exploit some of the inherent features of the GPC such as constraints handling. The GPC or Generalized Predictive Controller is one member of the family of long range predictive controllers (or Model Predictive Controllers) which was proposed in 1979 by Clarke et.al. to handle unstable, non minimum phase processes. It differs from other varieties of Model Predictive Controllers (MPC) in that it uses the CARIMA (Controlled Auto-Regressive Integrated Moving Average) model of the process to derive its output predictions. Simulation studies proved that the SISO unconstrained GPC was unsuitable for direct application to a decentralized structure. Modifications were needed on two fronts: the parameter tuning and disturbance model of the GPC (for Robustness). Research in the tuning direction led to the development of two novel tuning methods: The first is the N*tuning method which is applicable to the conventional GPC for the control of stable and unstable FOPTD (First Order Plus Time Delay) processes. The second is the 2GPC method which is an extension of the general Parallel Control structure (PCS) to predictive control. The 2GPC algorithm is offered as a variant of the conventional GPC. It consists of two GPCs working in tandem; one governs the set-point tracking response and the other controls the disturbance rejection response. However, the 2GPC is formulated as a single optimization problem integrating system constraints. The extent to which the 2GPC algorithm can perform Transparent Online Parameter Tuning (TOPT) is explained. (Transparent Online Parameter Tuning (TOPT) is the facility of the controller to allow the user to independently manipulate online the three most important loop performance attributes - Set-point Tracking Performance, Disturbance Rejection Performance and Robustness - with the use of three seperate parameters). It is shown through derivations that the extent to which the 2GPC method can perform TOPT is maintained even under mismatch conditions. Most importantly, it is also proved that the 2GPC control loop, by utilization of its TOPT feature, can have greater Robustness than a conventional GPC loop. On the disturbance model front, the structure of the GPC was first analysed. The structure of the conventional unconstrained SISO GPC can be split into a primary loop with setpoint filter and an optimal predictor. The filter transfer function of this optimal predictor is inversely proportional to the loop robustness and is also the only transfer funciton in the GPC loop that is a function of the process delay. For higher delays, the filter is such that the Robustness deteriorates. But it is the optimal predictor's filter that is responsible for one of the GPC's most attractive features - guaranteed internal stability even in the case of open loop unstable processes. At the loss of this feature, in order to improve disturbance rejection/robustness, there are variants of the GPC that utilize modified filters, such as the SPGPC (Smith Predictor based GPC). A new GPC is proposed in this work called the CDGPC (or GPC with Constant Disturbance Model). This effectively makes it equivalent to the popular DMC (or Dynamic Matrix Controller) with the exception that the former uses the transfer function model for predictions and can thus work for intergrator systems as well. It is proved that the CDGPC has greater robustness than the conventional GPC and the SPGPC. The CDGPC together with N*tuning method generate the required level of robustness and precision in tuning that enables it to be applied to decentralized control. The CDGPC with N*tuning is designed for the RNGA-based ETFs of the diagonal elements of the MIMO system. Closed loop responses of 2x2 MIMO systems were studied in simulation and were compared to the performance of RNGA-based PID controllers.
DRNTU::Engineering::Electrical and electronic engineering::Control and instrumentation::Control engineering