The following is a summary review of, "Tuning Generalized Predictive PI Controllers for Process Control Applications" by Oscar Briones, Ruben Alarcon, Alejandro J. Rojas, Daniel Sbarbaro; ISA Transactions 119 (2022) 184—195. See Samuel Ko Tak Shun's other summaries below:  

 "QRS Detection Using Adaptive Filters: A Comparative Study"

"Design of Minimum Multiplier Fictional Order Differentiator Based on Lattice Wave Digital Filter" 

First of all, the control of systems having time delay is very important from an industrial perspective, since a large set of processes can be modeled as low order models plus delay. Several methods such as optimal PID control, Smith predictors, dead-time compensators, multi-scale continuous-time control, and Model Predictive Controllers (MPC) have been proposed to address the challenges posed by the time delay.

A nonlinear design optimization problem for tuning the controllers parameters was solved, and also carried out a comparison between PPI and PID controllers considering also measurement filters, load disturbance rejection, robustness against model uncertainties, and noise sensitivity. The Frazer-Duncan theorem was applied to demonstrate robust stability and performance of a PPI controller for different tuning methods, compared with a traditional PID.

Even though all the previous works have demonstrated the advantages of PPI over PI—the attainable closed loop responses are constrained to the selection of two parameters; i.e. the proportional and integral gains. In order to overcome this restriction and achieve more freedom in the design of the closed loop response, in this work, we propose a Generalized PPI (GPPI) controller and a systematic tuning methodology to adjust its parameters.

The distinctive feature of this controller is the use of a linear combination of past control actions. Most of the previous papers on PPI controllers have used continuous time representations for analyzing and designing the controllers, and no details of its implementation in industrial control platforms have been addressed. The implementation on digital controllers is in discrete time, and therefore introduces an approximation on the desired continuous time design.

It would be more precise then—in order to avoid the approximation introduced by discretizing—to perform the analysis and design of the controllers directly in the discrete time domain, for example for standard PID controllers. Thus, motivated by this observation, in this work we will analyze the closed loop system in the discrete time domain. Furthermore, we propose an alternative tuning guideline for the PPI controller from what already reported, based on a simple root-locus argument, which we then use for a fair comparison to the GPPI controller.

Finally, we propose a particular state space representation that leads to the same GPPI temporal structure. These characteristics are very important to design a systematic tuning procedure for FOPTD models and implement them in industrial control platforms. Thus, the main contributions of this paper are: a new control structure expanding the flexibility of the classical Predictive PI controller; a systematic tuning methodology; a fair comparison: i.e. considering the same tuning specification among the proposed controllers, PPI and PI controllers; real-time implementation in an industrial equipment (PLC) demonstrating the practical value of the proposed algorithm and its tuning methodology.

General Framework

Concerning general framework, there are many processes—especially in the industry—which can be modeled as FOPTD plant models. This choice is in general due to its simplicity and the ability to capture the essential dynamics of the systems. Furthermore, if necessary, higher order models can be judiciously reduced to FOPTD. In this work, the problem is to design a closed loop system having an over-damped step response.

Controller Structures 

Concerning controller structures to solve the main problem three alternative controller structures are compared. The PI controller as the most common industrial application controller solution; the PPI controller—which achieves better performance for processes with long discrete time delays—and the novel GPPI controller—which grants to the user the freedom to locate the closed loop poles at any given position. We next review the PI and PPI controller structures and introduce the proposed GPPI controller structure.

Controller Tuning 

Concerning controller tuning, in this section, we present a methodology to tune the different controller structures proposed in the previous section in order to solve the main problem of this work. The control design objective is to obtain the fastest over-damped closed loop response. Following similar ideas to the ones reported, we use the root-locus framework for tuning the PI and PPI controllers. We then propose three different tuning for the GPPI controller structure.

The first one is the weighted GPPI tuning based on a desired choice of the closed loop characteristic polynomial, highlighting the greater flexibilty provided by the GPPI structure, but without explicit integral action in the controller. We then propose the nominal GPPI tuning which is capable to handle integral action in the resulting controller. We conclude with the GPPI state feedback tuning which reinterprets the GPPI controller structure as a state feedback controller. Related calculations are being considered and are illustrated from P.186 to P.189 of the ISA Transaction 119 (2022).

Experimental Results 

Concerning experimental results, the experimental results in this section report the implementation of an inlet water flow closed loop control and a water level closed loop control on a laboratory flume. The main components for the flow closed loop control are a centrifugal pump operated by a Rockwell PowerFlex 40 variable frequency drive (VFD) as the actuator and an Endress+Hauser Promag 10 electromagnetic flow meter as the sensor. The level closed loop control, on the other hand, considers the inlet water flow as input, a sluice gate that fixes the output water flow through a step motor, and an Endress+Hauser Prosonic M ultrasonic level sensor.

All the controllers were implemented on a Rockwell ControlLogix Programmable Logic Controller (PLC) using Structured Text programming language. The 3 recursive equations were used for the PI, PPI, and the three proposed GPPI tunings, respectively. FOPTD models were identified for the flow and the level loops, these models were used to tune the controllers. Both the inlet water flow closed loop control and the water level closed loop control are implemented using the PI, PPI, GPPW, GPPI, and GSF tunings.

The desired closed loop response was obtained by using simulations to verify the closed loop performance. The tuned parameters were then transferred to the PLC, and the same closed loop step responses were performed on the real plant. These step responses were contrasted with the simulation results. The most used criteria to evaluate the performance quality of the control solution are related to the control error. We recall two of such indices—the Integral Absolute Error and the Integral Time-weighted Absolute Error—both in continuous and discrete time form. Other performance indicators related to the main problem are considered for a better analysis :

• Settling time is calculated so that the output signal reach a band of 5% of the desired value
• Rise time is the time taken for the output signal to reach 63% of the steady-state response
• The overshoot index (OS)

To quantify relative stability, as a preliminary robustness measure, we also consider the standard gain margin (GM), phase margin (PM), and delay margin (DM) definitions. The variables are normalized between 0 and 100, where 0 is the minimum value equal to zero in all cases, and 100 corresponds to the maximum value reported for each variable. Related experimental results calculations are being considered and are illustrated from P.189 to P.193 of ISA Transaction 119 (2022).

Conclusion 

In conclusion, this work has proposed and analyzed a Generalized Predictive PI (GPPI) controller. Three tuning strategies were developed for the GPPI controller structure—namely the weighted GPPI (GPPW) control, the nominal GPPI (GPPI) control, and GPPI state feedback (GSF) control. Simple tuning guidelines were proposed for PI and PPI controllers using root locus arguments for a fair comparison with the different GPPI tuning strategies.

The PI, PPI, and GPPI controllers were compared through simulation and an experimental implementation on a flow and water level closed loop control for a laboratory flume. All the controllers were experimentally implemented using an industrial PLC and following the tuning strategies proposed in the paper. The obtained results using the proposed GPPI control structure and tuning strategies are encouraging, obtaining better performance with respect to the PI and PPI strategies for two FOPTD plant models with different time constants and time delays.

For example, the achieved settling time reported using the GPPI controller showed a reduction of up to 41.03% for flow control and up to 54.21% for level control with respect to the settling time using the properly tuned PI and PPI controllers. This settling time reduction generates an opportunity for faster control of industrial processes well represented by a FOPTD plant model. The GPPI controller, in comparison to the PPI controller, trade-off increased complexity for better performance.

In our opinion, as long as the real life processes are accurately identified (in particular in this work as FOPTD transfer functions), such a trade-off is feasible and worthwhile. More so, the possibility of reducing the GPPI controller structure complexity was also explored in the experimental results by tuning some closed loop poles to zero. This further suggests that model reduction preserving the improved performance versus the PPI and PI controllers is feasible for the GPPI controller.

Reference 

Tuning Generalized Predictive PI controllers for process control applications”; by Oscar Briones, Ruben Alarcon, Alejandro J. Rojas, Daniel Sbarbaro; ISA Transactions 119 (2022) 184—195.