Arun Chotai

Direct digital and adaptive control by input-output state variable feedback pole assignment

The paper describes a general approach to state variable feedback pole assignment for linear discrete-time systems. This is based on the definition of a non-minimal state space (NMSS) whose state variables are defined only in terms of the present and past values of the system output and the past values of its input. In more conventional block-diagram terms, it can be interpreted as an extension to a proportional-integral (PI) control system in which linear feedback and forward path digital filters are introduced to ensure the required closed-loop pole assignment, For this reason, we refer to it as a proportional-integral-plus or PIP system. The paper discusses the conditions for pole assignability. Practical examples which illustrate the performance of the PIP system in fixed gain and self tuning/adaptive applications are also discussed.

State space control system design based on non-minimal state-variable feedback: Further generalization and unification results

This paper shows how proportional-integral-plus linear-quadratic (PIP-LQ) control, based on non-minimal state space (NMSS) control system design, can be constrained to yield exactly the same control algorithm as both generalized predictive control (GPC) and standard, minimal state, linear quadratic gaussian (LQG) design methods. However, while NMSS includes these other approaches as special cases, it is less constrained and so more flexible in general terms: for example, while PIP-LQ has the simplicity of GPC, it is formulated like LQG in the powerful context of state variable feedback (SVF) control, which allows for ready access to modern robust control methods. Furthermore, the paper suggests that the NMSS approach provides the greater design freedom, with a wider range of possible LQ solutions than its minimal state space equivalent.

Modelling and PIP control of a glasshouse micro-climate

The paper discusses the modelling and control of the climate in a horticultural glasshouse system. A linear, reduced order, control model is obtained using identification and estimation techniques applied to a multivariable, nonlinear simulation model of the glasshouse microclimate. This control model is then used as the basis for the design of Proportional-Integral-Plus (PIP) control systems which regulate the levels of the major climate variables in the glasshouse. Finally, full multivariable extensions of this glasshouse control system design methodology are discussed and evaluated.

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.

Identification, Estimation and Control of Continuous-Time Systems Described by Delta Operator Models

This Chapter outlines a unified approach to the identification, estimation and control of linear, continuous-time, stochastic, dynamic systems which can be described by delta (δ) operator models with constant or time-variable parameters. It shows how recursive refined instrumental variable estimation algorithms can prove effective both in off-line model identification and estimation, and in the implementation of self-tuning or self-adaptive True Digital Control (TDC) systems which exploit a special Non-Minimum State Space (NMSS) formulation of the δ operator models.

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 the ALSTOM gasifier problem

Abstract 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.

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

Abstract 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.

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.

Macroscopic traffic flow modelling and ramp metering control using Matlab/Simulink

Computer programs to simulate traffic flow offer an opportunity to evaluate new strategies for reducing delays, congestion, fuel consumption and pollution. This paper describes a Statistical Traffic Model or STM, which is based on accepted macro-modelling concepts, such as the conservation of vehicles and the fundamental traffic diagram. In this case, the model is constructed using the well known Matlab/Simulink™ software package, so providing an integrated approach for data processing, graphical presentation of data, control system design and macroscopic simulation in one straightforward to use, widely available environment. To illustrate the methodology, the STM is applied to a section of the M3/M27 Ramp Metering Pilot Scheme in the UK. This Highways Agency sponsored project, based in the Southampton area, utilises traffic lights at the on-ramp entrances to regulate access to the main carriageway of the motorway, in an attempt to maintain flow close to the capacity. The paper utilises the model to help design a locally-coordinated ramp metering algorithm, based on proportional-integral-plus (PIP) control methods. In this manner, the STM proves particularly valuable for the application of multi-objective optimisation techniques in the design of new traffic management systems.