Proportional-Integral-Plus Research Articles

Proportional‐Integral‐Plus Control of an Intelligent Excavator

Abstract: This article considers the application of Proportional‐Integral‐Plus (PIP) control to the Lancaster University Computerised Intelligent Excavator (LUCIE), which is being developed to dig foundation trenches on a building site. Previous work using LUCIE was based on the ubiquitous PI/PID control algorithm, tuned on‐line, and implemented in a rather ad hoc manner. By contrast, the present research utilizes new hardware and advanced model‐based control system design methods to improve the joint control and so provide smoother, more accurate movement of the excavator arm. In this article, a novel nonlinear simulation model of the system is developed for MATLAB/SIMULINK©, allowing for straightforward refinement of the control algorithm and initial evaluation. The PIP controller is compared with a conventionally tuned PID algorithm, with the final designs implemented on‐line for the control of dipper angle. The simulated responses and preliminary implementation results demonstrate the feasibility of the approach.

Model-based PIP control of the spatial temperature distribution in cars

An on-line mathematical approach was used to model the spatio-temporal temperature distribution in the imperfectly mixed air inside a car. A second-order model proved to be a sufficiently good description of the temperature dynamics (R 2 = 0.985) of the system. Furthermore, it was possible to fully understand the physical meaning of the second-order model structure. Using this model, a proportional integral plus (PIP) climate controller was developed for a single input single output (SISO) system. The controller was able to follow a temperature level of 18–23–21°C at any desirable point, and to robustly react to a random local disturbance.

Proportional-integral-plus (PIP) control of ventilation rate in agricultural buildings

This paper is concerned with proportional-integral-plus (PIP) control of ventilation rate in mechanically ventilated agricultural buildings. The PIP controller can be interpreted as a logical extension of conventional proportional-integral/proportional-integral-derivative (PI/PID) controllers, but with inherent model-based predictive control action. In particular, the paper considers the design of an optimal, scheduled gain PIP algorithm for a 22 m 3 forced ventilation test chamber at the Katholieke Universiteit Leuven. Such a PIP approach proves more robust to pressure disturbances than an equivalent PID design and constitutes a preliminary step towards the development of the complete micro-climate controller.

DESIGN METHODS AND TUNING OF BILINEAR PROPORTIONAL-INTEGRAL-PLUS CONTROLLERS

This paper describes the advantages of extending the existing linear philosophy of proportional-integral-plus (PIP) control to a bilinear case. Investigation of the quasilinearisation, design and tuning procedures together with an additional quasilinearisation parameter are presented. The role of the quasilinearisation parameter and the potential improvements in closed loop performance are demonstrated via simulation studies using a system similar to that found in high temperature furnaces.

STATE-DEPENDENT PARAMETER NONLINEAR SYSTEMS: IDENTIFICATION, ESTIMATION AND CONTROL

A control system design procedure is proposed for a widely applicable class of discrete-time, non-linear systems in which the system nonlinearities are incorporated into a linear model structure in the form of State-Dependent Parameter (SDP) functions. The identification and estimation of both non-parametric and parametric SDP models is discussed briefly. The SDP NMSS model structure is defined, and the SDP Proportional-Integral-Plus (PIP) control algorithm is derived using an optimal LQ technique. The practical utility of the design methodology is illustrated by numerical example.

Design and application of PIP controllers: robust control of the IFAC93 benchmark

Proportional-integral-plus (PIP) controllers exploit the full power of optimal state variable feedback within a nonminimum state space (NMSS) setting. They are simple to implement and provide a logical extension of conventional proportional-integral/proportional-integral-derivative (PI/PID) controllers, with additional dynamic feedback and input compensators introduced automatically when the process is of greater than first order or has appreciable pure time delays. The present paper provides a tutorial introduction to the NMSS/PIP control design methodology and associated system identification procedure. The latter is based on the utilization of the simplified refined instrumental variable (SRIV) algorithm for the estimation of transfer function models. The practical utility of these techniques is illustrated by their application to the IFAC93 benchmark system, a seventh-order stochastic simulation whose parameters vary randomly within specified ranges. This benchmark provides a good simulation example for tutorial purposes, since it requires the control engineer to work through all the usual design steps, including identification of a low-order control model, control system design, and implementation using a standard programming language, in this case ‘C’. Finally, note that the statistical estimation tools described in the paper have been assembled as a tool-box within the Matlab™ software environment.

Data-based modelling and proportional-integral-plus (pip) control of nitrate in an activated sludge benchmark

This paper presents the result of an investigation into the Proportional Integral Plus (PIP) control of nitrate in the second zone of an activated sludge benchmark. A data-based reduced order model is used as the control model and identified using the Simplified Refined Instrumental Variable (SRIV) identification and estimation algorithm. The PIP control design is based on the Non Minimum State Space (NMSS) form and State Variable Feedback (SVF) methodology. The PIP controller is tested against dynamic load disturbances and compared with the response of a well tuned PI controller.

Proportional-integral-plus (PIP) control of the ALSTOM gasifier problem

Although it is able to exploit the full power of optimal state variable feedback within a non-minimum state-space (NMSS) setting, the proportional-integral-plus (PIP) controller is simple to implement and provides a logical extension of conventional proportional-integral and proportional-integral-derivative (PI/PID) controllers, with additional dynamic feedback and input compensators introduced automatically by the NMSS formulation of the problem when the process is of greater than first order or has appreciable pure time delays. The present paper applies the PIP methodology to the ALSTOM benchmark challenge, which takes the form of a highly coupled multi-variable linear model, representing the gasifier system of an integrated gasification combined cycle (IGCC) power plant. In particular, a straightforwardly tuned discrete-time PIP control system based on a reduced-order backward-shift model of the gasifier is found to yield good control of the benchmark, meeting most of the specified performance requirements at three different operating points.

Modelling and Proportional-integral-plus Control Design for Free Air Carbon Dioxide Enrichment systems

Proportional-integral-plus (PIP) control is employed to maintain gas concentration in a small-scale free air carbon dioxide enrichment (FACE) system. FACE systems are designed to produce controlled concentrations of elevated carbon dioxide, or other atmospheric gases, enabling plant growth experiments to be carried out for in situ vegetation without the use of chambers or other enclosures. Current FACE systems employ control algorithms based on classically derived two- or three-term control laws with manually tuned parameters. However, small FACE plots are more susceptible to turbulent eddies than larger scale systems, making control of concentration particularly difficult. The research described in the present paper employs data from planned FACE experiments to develop PIP control algorithms exploiting model-based predictive control action. Initial trials utilizing this approach yield good results for a small-scale FACE system operating in an uncut arable meadow.

Modelling and PIP control design for open-top chambers

The paper first describes the identification of a control model for carbon dioxide concentration in an open-top chamber (OTC) used in plant physiology atmospheric change experiments. This model is then employed in the design of a gain-scheduled controller utilising the Proportional-Integral-Plus (PIP) control design methodology developed by Young et al. (1987). The system has been evaluated in a number of field trials, yielding good control, well within the required design specifications.

Proportional-integral-plus (PIP) control of time delay systems

The paper shows that the digital proportional-integral-plus (PIP) controller formulated within the context of non-minimum state space (NMSS) control system design methodology is directly equivalent, under certain non-restrictive pole assignment conditions, to the equivalent digital Smith predictor (SP) control system for time delay systems. This allows SP controllers to be considered within the context of NMSS state variable feedback control, so that optimal design methods can be exploited to enhance the performance of the SP controller. Alternatively, since the PIP design strategy provides a more flexible approach, which subsumes the SP controller as one option, it provides a superior basis for general control system design. The paper also discusses the robustness and disturbance response characteristics of the two PIP control structures that emerge from the analysis and demonstrates the efficacy of the design methods through simulation examples and the design of a climate control system for a large horticultural glasshouse system.

Proportional-integral-plus (PIP) design for delta (delta) operator systems Part 2. MIMO systems

The proportional-integral-plus (PIP) controller for single-input, single-output, linear systems described by delta (delta) operator models, as presented in a companion paper, is extended to linear, multi-input, multi-output systems. The resulting multivariable PIP control law exploits the full power of state variable feedback control within a non-minimum state-space setting. In this manner, it allows not only for closed-loop pole assignment or linear quadratic optimal control, but also for the simultaneous achievement of multiple objectives, such as the combination of rapid response, smooth input activation and full, or partial, dynamic decoupling. The effectiveness of the design procedure is illustrated by both simulation and practical examples.

Proportional-integral-plus (PIP) design for delta (delta) operator systems Part 1. SISO systems

The paper presents a general approach to state variable feedback control of rapidly sampled linear systems described by discrete differential or delta (delta) operator transfer function models. This is based on the formulation of a special nonminimum state-space representation of the system which ensures that the state variable feedback control law can be implemented in terms of realizable compensation filters, thus avoiding the complication and limitations of state reconstruction filter (observer or Kalman filter) design. The necessary and sufficient conditions for the controllability and pole assignability of the proportional-integral-plus (PIP) controller obtained in this manner are developed and, in the case of SVF pole assignment, the relationships between the coefficients of the desired closed-loop characteristic polynomial and the control feedback gains are developed. Singleinput single-output deterministic systems are considered, but the approach can be extended to multivariable and stochastic systems, as described in two companion papers. The effectiveness of the design procedure is illustrated by both simulation and practical examples.

Modelling and Control Design for Free Air CO2 Enrichment Systems Used in Plant Physiology Atmospheric Change Experiments

The Proportional-Integral-Plus (PIP) control methodology is applied to a Free-Air CO 2 Enrichment (FACE) system at the Institute of Terrestrial Ecology (ITE). FACE systems are used to produce predicted atmospheric change conditions, enabling plant growth experiments to be carried out in elevated carbon dioxide concentrations for in situ crops. Evaluation was started at ITE in December 1996 with promising initial results.

Multivariable DELTA (δ) Operator Control in a Plant Physiology Experiment

This paper describes the use of the True Digital Control (TDC) approach (Young, et al ., 1987) in the design, simulation and implementation of Proportional-Integral-Plus (PIP) control of the temperature and relative humidity within an enclosed plant physiology cabinet. Control of the temperature and relative humidity was originally carried out using separate single-input single-output (SISO) controllers running simultaneously (McKenna, et al ., 1997). Due to the high degree of cross coupling which exists between these two channels it is more appropriate to use an optimal linear quadratic (LQ) design philosophy based upon the estimation of a multi-input multi-output (MIMO) model.

Optimal Control of Crop Production in Horticultural Glasshouses

Abstract The paper will discuss the addition of a plant growth module onto the preexisting micro-climate control model of a Venlo-type glasshouse developed on the Matlab/SIMULINK package (Young et al ., 1994). The existing model, using True Digital Control (TDC) and Proportional-Integral-Plus (PIP) methods (Young et al., 1987; Lees et al ., 1996) monitors and simulates optimal climatic conditions in the glasshouse via control of temperature, relative humidity and carbon dioxide concentration. This is achieved by a complex simulation model which takes account of both internal and external climatic considerations, and produces impressive simulated results which have been validated (Young et al. , 1994).

Indirect Model Reference Adaptive PIP Control

Abstract The paper presents an extension of the proportional-integral-plus (PIP) control using model reference techniques and indirect adaptation. Recursive least squares method is used to estimate the process parameters. The constant trace method is treating the covariance matrix. The identifiability conditions may not be satisfied for every PIP structure. The global convergence of the RLS and the stability of the controlled process are ensured. Simulation is carried out to demonstrate the control properties. Satisfactory control performance - convergence and stability - is achieved in both deterministic and stochastic cases.

Forecasting and Control of Interurban Traffic Networks Using a State-Space Formulated Traffic Model

This paper first presents a statistical ‘data assimilation’ approach to handling the large volume of real time measurements now available from instrumented traffic networks. The dynamic state-space modelling technique employed, herein called the Statistical Traffic Model (STM), transforms on-line roadside measurements of traffic flow into explicit assessments of the current and future state of an inter-urban road network, and provides transport management with a tool for monitoring, prediction and control. The paper then goes on to discuss the application of adaptive Proportional-Integral-Plus (PIP) control systems to a non-linear STM simulation of the Amsterdam ring road.

Modelling and Control Design for Open Top Chambers used in Plant Physiology Climate Change Experiments

The paper describes the identification of a control model for carbon dioxide concentration in an Open-Top Chamber (OTC) used in plant physiology climate change experiments. This model is used to design an advanced, model-based, gain-scheduled controller using the Proportional-Integral-Plus (PIP) control design methodology developed by Young et al. (1987). Prior to implementation, the controller is evaluated by simulation, utilising realistic disturbance data

Delta Operator PIP Control of a Plant Physiology Experiment

This paper outlines a novel approach to the control of the environment within a cabinet used in a study of plant-gas exchange mechanisms. The innovative use of the delta' (δ) operator in the control design process is introduced and results of implementing delta operator Proportional-Integral-Plus (PIP) controllers on the temperature, relative humidity and carbon dioxide concentration within the cabinet are presented