Conical tank level control using fractional order PID controllers: a simulated and experimental study

In this paper, simulated and experimental results on the conical tank level control are presented. PI/PID controllers of integer order (IO) as well as of fractional order (FO) are studied and compared. The tuning parameters are obtained first by using root locus (RL) and Ziegler and Nichols methods, for comparison purposes. Next, particle swarm optimization (PSO) is employed to determine the optimal controllers'' parameters using as fitness function the integral of the absolute value of tracking error (IAE). From the experimental results it is concluded that PI/FOPI are the controllers presenting the lowest IAE indexes, whereas PID/FOPID controllers present the lowest energy consumption by the control signal.     

A new design for a PID plus feedforward controller

In this paper, a new design and tuning procedure for a PID plus feedforward controller is proposed. It consists of determining a feedforward signal in order to achieve a predefined process output transition time assuming a first order plus dead time model of the process. Then, the PID parameters are tuned by any conventional method in order to assure a good load disturbance rejection and the reference signal to the closed-loop system is obtained by filtering appropriately the set-point step signal. Simulation and experimental results show that the method outperforms the typical (inverse) model-based approach despite its simplicity and it is therefore suitable to implement in Distributed Control Systems as well as in single-station controllers.     

Fractional Order PI‐PD Control of Liquid Level in Coupled Two Tank System and its Experimental Validation

This paper presents a level control problem of a coupled two tank single input single output (SISO) system. A cascade control strategy is adopted having a fractional order proportional integral (FOPI) controller and fractional order proportional derivative (FOPD) controller in the outer and the inner loops, respectively. Cascaded integer order proportional integral (IOPI) and integer order proportional derivative (IOPD) controllers are also designed to compare the performances. A frequency domain approach is followed to design all the controllers. It is mathematically shown that the FOPI and FOPD controllers can achieve less steady state error and consume less energy than that of the IOPI and IOPD controllers while meeting the same phase margin and gain crossover frequency. All propositions are validated on an experimental setup.     

A unified design for feedback-feedforward control system to improve regulatory control performance

The PID controller is widely used in industries because of its simplicity and robustness. A simple approach to improve regulatory control performance is to combine both feedback PID and feedforward controllers. The feedforward controller enables early compensation of a measured disturbance before it can seriously affect the process. The conventionally derived non-ideal feedforward controllers are not often used in practice. The reason is that an ideal feedforward controller based on direct inversion of process model is often not physically realizable. Several non-ideal feedforward control designs have been proposed where some of them involve rather intensive tuning procedure to obtain good disturbance rejection. In this paper, we present a new systematic method for designing a combined feedback-feedforward control system. The proposed design method is easy to use and applicable to stable, unstable and integrating deadtime processes where the ideal feedforward controller is physically not realizable.     

Tuning fractional order proportional integral controllers for fractional order systems

In this paper, two fractional order proportional integral controllers are proposed and designed for a class of fractional order systems. For fair comparison, the proposed fractional order proportional integral (FOPI), fractional order [proportional integral] (FO[PI]) and the traditional integer order PID (IOPID) controllers are all designed following the same set of the imposed tuning constraints, which can guarantee the desired control performance and the robustness of the designed controllers to the loop gain variations. This proposed design scheme offers a practical and systematic way of the controllers design for the considered class of fractional order plants. From the simulation and experimental results presented, both of the two designed fractional order controllers work efficiently, with improved performance comparing with the designed stabilizing integer order PID controller by the observation. Moreover, it is interesting to observe that the designed FO[PI] controller outperforms the designed FOPI controller following the proposed design schemes for the class of fractional order systems considered.     

Combining fuzzy, PID and regulation control for an autonomous mini-helicopter

This paper reports on the synthesis of different flight controllers for an X-Cell mini-helicopter. They are developed on the basis of the most realistic mathematical model currently available. Two hybrid intelligent control systems, combining computational intelligence methodologies with other control techniques, are investigated. For both systems, Mamdani-type fuzzy controllers determine the set points for altitude/attitude control. These fuzzy controllers are designed using a simple rule base. The first scheme consists of conventional SISO PID controllers for z-position and roll, pitch and yaw angles. In the second scheme, two of the previous PID controllers are used for roll and pitch, and a linear regulator is added to control altitude and yaw angle. These control schemes mimic the action of an expert pilot. The designed controllers are tested via simulations. It is shown that the designed controllers exhibit good performance for hover flight and control positioning at slow speed.     

Disturbance Observer Based Speed Control of PMSM Using Fractional Order PI Controller

In this paper, fractional order PI (FOPI) control is developed for speed control of permanent magnet synchronous motor (PMSM). Designing the parameters for FOPI controller is a challenging task, especially for nonlinear systems like PMSM. All three PI controllers in the conventional vector controlled speed drive are replaced by FOPI controllers. Design of these FOPI controllers is based on the locally linearized model of PMSM around an operating point. This operating point changes with the load torque. The novelty of the work reported here is in use of Non Linear Disturbance Observer (NLDO) to estimate load torque to obtain this new operating point. All three FOPI controllers are then designed adaptively using this new operating point. The scheme is tested on simulation using MATLAB/SIMULINK and results are presented.      

Adaptive positioning control of an ultrasonic linear motor system

A 3PRR parallel precision positioning system, driven by three ultrasonic linear motors, was designed for use as the object stage of a scanning electron microscope (SEM). To improve the tracking accuracy of the parallel platform, the positioning control algorithms for the drive joints needed to be studied. The dead-zone phenomenon caused by static friction reduces the trajectory tracking accuracy significantly. Linear control algorithms such as PID (Proportion Integration Differentiation) are unable to compensate effectively for the dead-zone nonlinearity. To address this problem, two types of feedforward compensation control algorithms have been investigated. One is constant feedforward with the integral separation PID; the other is adaptive feedback and feedforward based on the model reference adaptive control (MRAC). Simulations and experiments were conducted using these two control algorithms. The results demonstrated that the constant feedforward with integral separation PID algorithm can compensate for the time-invariant system after identifying the dead-zone depth, while the adaptive feedback and feedforward algorithm is more suitable for the time-varying system. The experimental results show good agreement with the simulation results for these two control algorithms. For the dead-zone nonlinearity caused by the static friction, the adaptive feedback and feedforward algorithm can effectively improve the trajectory tracking accuracy.     

Some investigations on hybrid fuzzy IPD controllers for proportional and derivative kick suppression

Proportional and derivative kick i.e., a large change in control action of a proportional plus integral plus derivative (PID) controller due to a sudden change in reference set-point is generally undesired in process industry. Therefore, the structure of conventional parallel PID controller is modified to integral minus proportional derivative (I-PD) controller. In this paper, three hybrid fuzzy IPD controllers such as a fuzzy I-fuzzy PD (FI-FPD) controller and its hybrid combinations with its conventional counterpart such as fuzzy I-PD (FI-PD) and I-fuzzy PD (I-FPD) are presented in view of above industrial problem. These controllers are based upon the counterpart conventional I-PD controller and contains analytical formulae. Computer simulations are carried out to evaluate the performance of hybrid fuzzy controllers along with conventional I-PD and PID controllers for set-point tracking and disturbance rejection for an induction motor in closed loop using LabVIEW? environment. The gains of conventional and hybrid fuzzy controllers are tuned using genetic algorithm (GA) for minimum overshoot and settling time. It has been observed that hybrid fuzzy controllers along with the conventional I-PD controller significantly remove the kick from the control action in reference set-point tracking. However, in disturbance rejection, I-PD and FI-PD controllers fail to eliminate the kick from the control signal. In contrast, FI-FPD and I-FPD controllers considerably reduced spikes from the control action in disturbance rejection. Among the conventional and hybrid fuzzy IPD controllers, FI-FPD demonstrates much better set-point tracking and disturbance rejection response with spike free control action.     

Control of a grinding mill circuit using fractional order controllers

This paper presents the design and application of fractional single-input–single-output (SISO) controllers to a grinding mill circuit, which is a multiple-input–multiple-output (MIMO) process. Two kinds of controllers are presented: fractional order proportional-integral (FOPI) controllers, and a combination of FOPI and fractional order model reference adaptive controllers (FOMRAC). The parameters of the controller are tuned using off-line particle swarm optimization. In the presence of disturbances and process noise, the SISO fractional controllers achieve similar or better performance compared to linear model predictive control (LMPC).     

Neural network compensation control for mechanical systems with disturbances

Two novel compensation schemes based on accelerometer measurements to attenuate the effect of external vibrations on mechanical systems are proposed in this paper. The first compensation algorithm exploits the neural network as the feedback-feedforward compensator whereas the second is the neural network feedforward compensator. Each compensation strategy includes a feedback controller and a neural network compensator with the help of a sensor to detect external vibrations. The feedback controller is employed to guarantee the stability of the mechanical systems, while the neural network is used to provide the required compensation input for trajectory tracking. Dynamics knowledge of the plant, disturbances and the sensor is not required. The stability of the proposed schemes is analyzed by the Lyapunov criterion. Simulation results show that the proposed controllers perform well for a hard disk drive system and a two-link manipulator.     

Bidirectional active control of structures with type-2 fuzzy PD and PID

Proportional-derivative and proportional-integral-derivative (PD/PID) controllers are popular algorithms in structure vibration control. In order to maintain minimum regulation error, the PD/PID control require big proportional and derivative gains. The control performances are not satisfied because of the big uncertainties in the buildings. In this paper, type-2 fuzzy system is applied to compensate the unknown uncertainties, and is combined with the PD/PID control. We prove the stability of these fuzzy PD and PID controllers. The sufficient conditions can be used for choosing the gains of PD/PID. The theory results are verified by a two-storey building prototype. The experimental results validate our analysis.     

Control of a non-isothermal continuous stirred tank reactor by a feedback-feedforward structure using type-2 fuzzy logic controllers

A control system that uses type-2 fuzzy logic controllers (FLC) is proposed for the control of a non-isothermal continuous stirred tank reactor (CSTR), where a first order irreversible reaction occurs and that is characterized by the presence of bifurcations. Bifurcations due to parameter variations can bring the reactor to instability or create new working conditions which although stable are unacceptable. An extensive analysis of the uncontrolled CSTR dynamics was carried out and used for the choice of the control configuration and the development of controllers. In addition to a feedback controller, the introduction of a feedforward control loop was required to maintain effective control in the presence of disturbances. Simulation results confirmed the effectiveness and the robustness of the type-2 FLC which outperforms its type-1 counterpart particularly when system uncertainties are present.     

Robust ℋ︁∞ PID control for multivariable networked control systems with disturbance/noise attenuation

In this paper, we study the design problem of PID controllers for networked control systems (NCSs) with polyhedral uncertainties. The load disturbance and measurement noise are both taken into account in the modeling to better reflect the practical scenario. By using a novel technique, the design problem of PID controllers is converted into a design problem of output feedback controllers. Our goal of this paper is two‐fold: (1) To design the robust PID tracking controllers for practical models; (2) To develop the robust ??_∞ PID control such that load and reference disturbances can be attenuated with a prescribed level. Sufficient conditions are derived by employing advanced techniques for achieving delay dependence. The proposed controller can be readily designed based on iterative suboptimal algorithms. Finally, four examples are presented to show the effectiveness of the proposed methods. Copyright © 2011 John Wiley & Sons, Ltd.     

Selftuning control of some pilot plant processes

This paper reviews the results of some experimental tests carried out to evaluate the performance of selftuning (ST) controllers for temperature control of a continuous stirred tank heater, composition control of a binary distillation column and pH control of an acidic effluent. All the pilot plant units have been controlled using a single variant selftuning control, and a newly developed multivariant ST controller was used for simultaneous control of the terminal compositions of the distillation column. The control performance of the units operating under ST control is compared to that obtained using very well tuned proportional plus integral (PI) or proportional plus integral plus derivative (PID) conventional controllers. Control of pH is shown using a technique of electrochemical neutralisation coupled with a single variant ST controller. The control algorithms have been programmed on a number of microprocessor- and minicomputer-based systems. Z80 for stirred tank heater control, LS1-11 for pH control and HP1000 distributed computer system for distillation control.     

Robust analysis of flatness based control using interval methods

In this paper a new approach to the robustness analysis of flatness based tracking controllers using interval methods is proposed. This methodology allows us to explicitely determine admissible intervals for the uncertain parameters such that specified error bounds for the state space trajectories are not violated. In contrast to earlier approaches no additional controllers have to be considered to take robustness properties into account. The presented approach also poses no a priori restrictions on the velocity of the reference trajectory. The application of the robustness analysis is demonstrated for a feedforward as well as a feedback tracking controller for the Van de Vusse type continuous stirred tank reactor (CSTR).     

Solution of the discrete-time stochastic optimal control problem in the 2-domain

The design of discrete-time optimal multivariate systems is considered in the z-domain. The constant plant can be non-square, unstable and/or non-minimum phase and feedback system dynamics can be modelled. The stationary coloured noise processes are assumed to be represented by discrete rational spectral densities. The system can contain transport delay elements and the effects of plant saturation can be limited by the choice of performance criterion. The system inputs are assumed to contain both stochastic and deterministic components.

The two-stage design procedure is original and it enables the stochastic and deterministic control functions to be separated, A performance criterion is first defined which is insensitive to the deterministic signals and this defines the closed-loop optimal controller. The resulting closed-loop system acts as an optimum regulator to minimize the effects of stochastic disturbances. A second tracking error performance criterion is then specified which determines the optimal reference input to the closed-loop system. This reference signal is generated by two further discrete-time controllers. The first controller ensures that the plant is following a desired trajectory and the second acts as a feedforward controller to counteract measurable disturbances. The minimum variance regulators of Astrom (1970) and Peterka (1972) are also derived from these results.     

Stabilizing and robust fractional order PI controller synthesis for first order plus time delay systems

For all the stable first order plus time delay (FOPTD) systems, a fractional order proportional integral (FOPI) or a traditional integer order proportional integral derivative (IOPID) controller can be designed to fulfill a flat phase constraint and two design specifications simultaneously: gain crossover frequency and phase margin. In this paper, a guideline for choosing two feasible or achievable specifications, and a new FOPI/IOPID controller synthesis are proposed for all the stable FOPTD systems. Using this synthesis scheme, the complete feasible region of two specifications can be obtained and visualized in the plane. With this region as the prior knowledge, all combinations of two specifications can be verified before the controller design. Especially, it is interesting to compare the areas of these two feasible regions for the IOPID and FOPI controllers. This area comparison reveals, for the first time, the potential advantages of one controller over the other in terms of achievable performances. A simulation illustration is presented to show the effectiveness and the performance of the designed FOPI controller compared with the optimized integer order PI controller and the IOPID controller designed following the same synthesis for the FOPI in this paper.     

Precise piston trajectory control for a free piston engine

A free piston engine removes the mechanical constraint on the piston motion by eliminating the crankshaft. The extra degree of freedom offers many advantages for reducing fuel consumption and emissions. Nevertheless, stability and robustness of the engine operation has been affected in the meantime. To ensure smooth engine operation, an active motion controller, which utilizes robust repetitive control, was developed previously to regulate the piston motion of a hydraulic free piston engine to track pre-defined trajectories. However, the long piston stroke length, high operating frequency and system nonlinearity impose challenges to precise piston motion control. Therefore, feedforward controllers are investigated in this paper to complement the repetitive control to further improve the tracking performance. The first feedforward design involves the inversion of a linear plant model that describes the dynamics of the engine operation, and the second design is based on the flatness approach, which involves the inversion of a nonlinear model of the system. The two feedforward controllers are designed and implemented on the free piston engine. The experimental and simulation results demonstrate the effectiveness of the proposed control under various operating conditions and reference piston trajectories.     

Fuzzy attitude control for a nanosatellite in low Earth orbit

In order to develop and introduce intelligent systems in the space field, an adaptive fuzzy logic controller is designed for a nanosatellite. Attitude determination and control subsystem (ADCS) and its performance and efficiency are compared with a traditional proportional integrative derivative (PID) controller. Fuzzy controllers have already been studied for satellite attitude control; however their performance has not been compared with the classical PID controllers typically being implemented on board spacecrafts currently. Both controllers have been designed and implemented in order to be tested on board a nanosatellite (QBITO) in a nearby mission (QB50), a constellation of 50 nanosatellites. Due to the requirements imposed by the mission, the orbit, and the significant limitations in the power available in these small spacecrafts, an efficient ADCS is required in order to fulfill the mission objectives. The comparison between the classical PID and the fuzzy controllers shows that the fuzzy controller is much more efficient in single maneuver (up to 65% less power required), achieving better precision in general than the PID. This shows that the use of this type of intelligent control systems is a great advantage over conventional control systems currently being used in satellite attitude control, and open new possibilities of application of intelligent controllers in the field of space technologies.