Analytical Controller Design Research Articles

Low-frequency dynamic modelling and control of matrix converter for power system applications

High-power density of a matrix converter (MC) necessarily introduces tight dynamic input–output coupling, which complicates controller design for high bandwidth applications. Strong contemporary interest in MC-based solutions for synchronous, power system applications demands high dynamic performance out of the MC, operated as a closed-loop system. The requisite system models reported either treat the MC – with its input and output filters – as a ‘black-box’ characterised by a set of eigenvalues, derived from linearised analysis around an equilibrium point. Alternatively, large-signal system analysis was reported for a feed-forward control approach with prescription of a throughput power boundary for stable operation. This study provides a designer's insight into MC modelling, based on linearised analysis, clearly establishing the influence of individual physical sub-systems on the overall dynamic performance. Onset of a cluster of right-half zeros, decided solely by the input filter, power factor, source voltage and power throughput, is shown to be the only factor threatening closed-loop stability. Subsequently, a controller with output feedback is designed to ensure stable operation well beyond the throughput power limit prescribed earlier. Comprehensive simulation and experimental results are provided to validate the analytical model and controller design.

Analytical design of optimal controllers in the class of logic-dynamic (hybrid) systems

The classical problem of analytical design of the optimal controllers which was stated and solved by A.M. Letov for continuous linear systems was considered for the class of logicdynamic (hybrid) systems. Equations to determine the optimal feedback control were derived on basis of the sufficient optimality conditions. In distinction to classical case, the optimal positional control is realized by the piecewise-linear controller with the piecewise-quadratic Bellman function. In contrast to the continuous, discrete or discrete-continuous systems, the optimal processes of logic-dynamic systems, can have multiple switchings in the logic block, thus hindering the optimal control design. Therefore it was suggested to consider a simplified problem where the logic-dynamic system is replaced by a discrete-continuous system admitting instantaneous multiple switchings of the discrete part. The resulting control for the logic-dynamic system becomes suboptimal. Application of the optimality and suboptimality conditions was demonstrated by way of several examples.

Step Response Identification under Inherent-Type Load Disturbance with Application to Injection Molding

Motivated by autotuning of injection velocity in an industrial injection molding machine, a step response identification method is proposed for practical application subject to inherent-type load disturbance. Both models of the process and the inherent-type load disturbance can be simultaneously derived from a step test. Identification algorithms are detailed for obtaining the widely used low-order models of first-order plus dead time (FOPDT) and second-order plus dead time (SOPDT). Based on the identified process and disturbance models, a two-degree-of-freedom (2DOF) internal model control (IMC) structure plus feed-forward control is proposed for improving load disturbance rejection. Analytical controller design formulas and tuning guidelines are developed accordingly. A practical application to the velocity control of an injection molding machine is shown to illustrate the effectiveness and merits of the proposed identification method and control strategy.

On analytical design of controllers

A method to design controllers of linear plants under bounded sectionally continuous external disturbances was proposed.

Self-excitation and control of an induction generator in a stand-alone wind energy conversion system

This study presents a rugged and cost-effective scheme for start-up and operation of a stand-alone squirrel cage induction machine (SCIG) for a wind energy conversion system (WECS). A voltage source converter (VSC) directly interfaces the SCIG with an equivalent dc load network, which could also be the DC link of an inverter. The VSC dc bus is supported by an electrolytic capacitor and the proposed scheme ensures reliable start up with these rudimentary components. The dc bus voltage is ramped to the rated value from a small initial voltage produced by remanent magnetism of the SCIG core. Subsequently, the load is applied. The V/f control paradigm for motoring operation is suitably extended to the SCIG for controlling both voltage build-up and dynamic transients. A controller is specifically designed to maintain constant dc bus voltage under wind speed and electrical load variations. Steady-state machine flux is maintained constant up to the base speed, which maximises machine utilisation and power extraction especially at higher wind speeds. The overall system modelling and analytical control design is presented. The proposed control strategy has been validated through simulation and experimentally verified on a low power (2.2 kW) laboratory prototype.

Analytical Design of Multi-Loop PI Controllers for Interactive Multivariable Processes

In this paper, a simple and efficient design method of multi-loop PI controllers is proposed by extending the Maclaurin series approach to a multi-loop control system. The controller parameter of a multi-loop system is related to that of a SISO non-interacting system with an interaction factor in the simple multiplication form. Based on this relation, analytical tuning rules for a multi-loop PI controller are derived for several representative process models. In order to improve both performance and robustness of the multi-loop control system, the multi-loop Ms criterion is utilized as a performance cost function. The simulation studies confirm the effectiveness of the proposed method.

A control design strategy of a reconfigurable manufacturing system

A Reconfigurable Manufacturing System (RMS) is defined as one that can provide adaptability to quickly adjust the production capacity and functionality in response to fluctuations in customer demand. An advanced analytical modelling approach and control design strategy is introduced to improve the system responsiveness of multistage feedback control RMS. A System Dynamics (SD)-based multistage RMS model is mathematically translated into block diagram representations and transfer functions. A control design technique called Root-Locus is presented to propose a new operation management policy to better predict and control the dynamic responses of a RMS in reduction of inventory and Lead-Time (LT). By applying this graphic view approach, one can improve the RMS responsiveness and also determine its relative system stability without iterative trial-and-error simulation replications as found in discrete event simulation and SD approach.

A robust control for a linear inertial object

The idea of compulsory separation of object motions is the ground of the procedure for synthesizing a robust system with the subsequent solution of the problem of analytical design of optimal controllers for designing a controller that makes it possible to perform partial mutual compensation of these motions.

Analytical design of optimal controllers under permanent stochastic disturbances as applied to the design of vibration isolation systems

An approach to the design of vibroprotection systems for objects subjected to stochastic disturbances was developed on the basis of a procedure for analytical design of the optimal controller. For that, this procedure was generalized to the case of permanently acting stationary stochastic disturbances. When solving the problem of designing the vibration isolation system, the optimizing functional was constructed so that minimization provided reduction in the dynamic actions on the object with the observance of the overall disturbances. Technical feasibility of the vibration isolation system designed using the elastodamping suspensions and dampers with transformation of motion was demonstrated.

The method of analytical design of quasi-optimal control systems with polynomial nonlinearities

A simple and effective method for solving the problem of analytical design of optimal controllers for multidimensional control objects with polynomial nonlinearities is proposed. The method of nonlinear systems synthesis is based on the solution to the two-point boundary problem in the form of a Volterra functional series.

Nonlinear Controller Design: An Iterative Relaxation Method

Analytical design of optimal controllers for nonlinear systems is studied. To refine the method related to minimization of the general work functional, the initial control problem is transformed to a degenerate problem and solved with a suitable strategy. The joint control design strategy is the construction of minimizing sequences, which converge in intervals by stationarity to the optimal process of the initial problem. An illustrative example is given.

Analytical Multiloop PI/PID Controller Design for Two-by-Two Processes with Time Delays

In this paper, an analytical multiloop controller design method is proposed for industrial and chemical two-by-two processes with time delays. By proposing the practically desired closed-loop diagonal transfer functions and the dynamic detuning factors to reduce the interactions between individual loops, the ideally desired multiloop controllers are inversely derived, which, however, are unavoidably involved with time delays in a complex manner and therefore difficult to realize. Hence, the mathematical Maclaurin series expansion is utilized to reproduce them in the form of a conventional PI/PID controller for implementation. Then a corollary derived from the generalized Nyquist stability theorem is provided to ascertain the nominal system stability. Meanwhile, the sufficient and necessary constraints for tuning the proposed multiloop PI/PID controllers to hold the control system robust stability are analyzed in the presence of the process multiplicative uncertainties. Finally, several commonly used simul...

Analytical decoupling control design for dynamic plants with time delay and double integrators

Two control schemes are proposed to control dynamic plants with time delay and double integrators. One adopts the H2 optimal controller, whereas the other utilises a conventional derivative controller for the setpoint tracking in an open-loop control manner. Both of the proposed control schemes are of the two-degree-of-freedom control structure and use an identical disturbance estimator to construct the closed-loop between the plant input and output for load disturbance rejection. In consequence, the setpoint response is decoupled from the load disturbance response. The disturbance estimator is obtained by proposing a desired closed-loop complementary sensitivity function according to the H2 optimal performance objective. The closed-loop robust stability is analysed and corresponding sufficient and necessary conditions are also provided in the presence of the plant multiplicative uncertainty. Consequently a rule-of-thumb for tuning the single adjustable parameter of the disturbance estimator is presented. Finally, illustrative examples are included to show that a good performance can be obtained using the two proposed control schemes, especially the proposed closed-loop for the load disturbance rejection, which can also be successfully utilised to reject ramp-type load disturbances in industrial and chemical processes with one integrator.

Analytical design of multiloop PID controllers for desired closed‐loop responses

Most chemical processes are basically multiple input/multiple output (MIMO) systems. Despite considerablework on advanced multivariable controllers for MIMO sys-tems, multiloop proportional-integral-derivative (PID) con-trollers remain the standard for many industries because oftheir adequate performance with most simple, failure toler-ant, and easy to understand structure. In a multiloop system,once a control structure is fixed, control performance is thendetermined mainly by tuning each multiple single-loop PIDcontroller. However, because the interactions that exist be-tween the control loops make the proper tuning of themultiloop PID controllers quite difficult, only a relativelyfew tuning methods are available to the multiloop PIDcontrollers and most of them require nonanalytical formswith complex iterative steps (Loh et al., 1993; Luyben,1986; Skogestad and Morari, 1989). The analytical tuningrule is very attractive, with respect to its practicality, but themathematical complexity attributed to the loop interactionshas mainly prevented the analytical approach to the mul-tiloop systems.In this article, we propose an analytical design method forthe multiloop PID controllers to give desired closed-loopresponses by extending the generalized IMC–PID methodfor single input/single output (SISO) systems (Lee et al.,1998) to MIMO systems. Simple but efficient tuning rulesare obtained for general process models by using the fre-quency-dependent property of the closed-loop interactions.

Optimality Conditions for a Degenerate Problem of Analytical Design of Controllers

A degenerate problem of analytical design of optimal controllers is studied. For a nonlinear object and nonclassical functional with affine controls, necessary and sufficient conditions of local optimality are formulated. These conditions are useful in identifying a class of objects with singularities in minimizing the generalized work functional. An example is given.

Vibration Control of a Rotating Shaft: An Analytical Solution

It has been shown that a rotating shaft in the Rayleigh beam model has only a finite number of whirl speeds and vibration modes when the rotating speed is higher than half of the whirl speed. The system’s unbalanced response can therefore be written analytically by the vibration modes and the generalized coordinates. This paper presents an analytical controller design of optimal sensor/actuator location and feedback gain for minimizing the steady-state unbalanced response. Because all of the critical speeds and vibration modes are included in the controller design, there will be no residual mode, hence no spillover. An example is used to illustrate that the controller design in collocated or noncollocated configuration not only guarantees the closed-loop stability but also effectively suppresses the unbalanced response.

New methodology for analytical and optimal design of fuzzy PID controllers

Describes a methodology for the systematic design of fuzzy PID controllers based on theoretical fuzzy analysis and, genetic-based optimization. An important feature of the proposed controller is its simple structure. It uses a one-input fuzzy inference with three rules and at most six tuning parameters. A closed-form solution for the control action is defined in terms of the nonlinear tuning parameters. The nonlinear proportional gain is explicitly derived in the error domain. A conservative design strategy is proposed for realizing a guaranteed-PID-performance (GPP) fuzzy controller. This strategy suggests that a fuzzy PID controller should be able to produce a linear function from its nonlinearity tuning of the system. The proposed PID system is able to produce a close approximation of a linear function for approximating the GPP system. This GPP system, incorporated with a genetic solver for the optimization, will provide the performance no worse than the corresponding linear controller with respect to the specific performance criteria. Two indexes, linearity approximation index (LAI) and nonlinearity variation index (NVI), are suggested for evaluating the nonlinear design of fuzzy controllers. The proposed control system has been applied to several first-order, second-order, and fifth-order processes. Simulation results show that the proposed fuzzy PID controller produces superior control performance to the conventional PID controllers, particularly in handling nonlinearities due to time delay and saturation.

Modelling and control of an air-to-air heat recovery system

Analytical modelling, controller design and simulation of an air-to-air runaround coil heat recovery system are studied. The system consists of two plate-fin-tube coils, a storage tank, two circulating pumps, an auxiliary heater and associated distribution network. Simulation results showing the transient response characteristics of the open-loop and closed-loop system are given. Results show that the designed controllers are able to hold the preheat temperature and the storage tank temperature at their respective setpoints irrespective of changes in outdoor and exhaust (source heat) temperatures.

Robust Control of Delay Feedback Systems with Bounded Uncertainty

The problem of the analytical design of controllers for a class of delay plants with uncertain parameters is considered. The proposed procedure of the synthesis of a class of robust time-invariant linear and nonlinear control systems with delay is based on the consideration of an optimal control problem with a specified performance index for a linear plant with specified parameters.

Analytical Bode Design of Controllers

This paper extends an approach for the analytical design of controllers by frequency-response techniques to include the dc gain as a design parameter. Additionally, the technique is extended to the design of proportional-integral (PI) and proportional-derivative (PD) controllers, and a more direct proof of the design technique is given.