Design of an optimized PID controller for non-minimum phase system with delay
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In this paper an optimized proportional plus integral plus derivative (PID) controller is designed to control the non-minimum phase systems (NMP) with delay. The problem associated with the NMP system is the undershoot behaviour of the system caused by zeros of the right half plane and it becomes trivial as delay increases. To improve the system performance the parameters of the PID controller are optimized using grey wolf optimizer (GWO). The GWO algorithm seeks to obtain the global optimal values of the PID controller in the region delineate by the conventional tuning criterion like Ziegler-Nichols (ZN) rule. The parameters are optimized on the basis of minimizing the integral absolute error (IAE) of the system. Simulation results prove that the proposed method advances the transient performance like settling time, rise time, peak time and overshoot of the system.Keywords:
Overshoot (microwave communication)
Settling time
Rise time
Transient (computer programming)
Minimum phase
Genetic Algorithms (GAs) have been in many cases successfully applied to a wide variety of optimisation problems. The work described here focuses on the application of genetic algorithms to the optimisation of linear & non-linear PID controllers. The techniques used here are based around the formulation of a suitable objective function, which, as part of the GA evaluates the fitness of a given PID parameter set. The proposed objective function is based directly on performance criteria specified in terms of the rise time, settling time and peak overshoot of a physical system. The functions are evaluated via a set of trials on a range of systems with varying dynamics and the success rate determined by comparison with sets of target step response characteristics. The results show that the objective function is more robust than ISE based methods in the optimisation of multiple step response objectives, having a low deviation from the target across the range of parameters (rise time, settling time & peak overshoot).
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Settling time
Overshoot (microwave communication)
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Optimal material level control in blending tank can be achieved through the use of a PID controller. However, the major challenges of PID controller are high overshoot and steady-state error, prolong settling time, and slow response which practically causes wastages and equipment downtime. Thus, in this work classical techniques were employed to tune PID controllers to achieve optimum performance of the blending tank level control. The mass balance principle was used to model level of the blending tank while Zigler-Nichols (ZN), Chien-Hrones-Reswick (CHR), and Cohen-Coon (CC) techniques were used to tune the PID controller for optimal performance. The performance of the simulated control schemes MATLAB/Simulink were evaluated using rise time, settling time, peak amplitude, and overshoot. The results revealed that the ZN-PID controller gave the lowest rise time of 2.11s, settling time of 14secs, and peak amplitude of 1.04 while the lowest overshoot of 0% was achieved by both CHR and CC-PID. It can be inferred that ZN-PID gives the best way of controlling the level of the blending tank.
Overshoot (microwave communication)
Settling time
Rise time
Settling
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The most widely used controllers in industries are PI or PID controllers. The major concern with designing of such controllers is the determination of controller parameters. An intelligent method is discussed in this paper to determine the controller parameter to control the dynamic performance of buck converter by optimizing these parameters with the big bang big crunch (BBBC) algorithm. Initially, the mathematical modeling is developed and thereafter the weighted numerical values of overshoot, peak time, rise time and settling time are summed to make a fitness function which is to be minimize for the better dynamic response. The performance of BBBC-PI controller is analyzed by settling time, rise time and overshoot of the output response. The disturbance rejection ability of optimized PI controller is verified by three cases such as step change in input voltage, output voltage and output load resistance. The closed loop operation of buck converter is simulated and verified at the MATLAB/Simulink platform.
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The purpose of this research is to design PID control on BLDC motors using 2 tuning methods, namely Cohen-Coon and Trial & Error. PID control of formula calculations with calculations in Simulink Matlab. From the simulation results shown in graphical form, the use of the PID control gives a better effect than the use of the P and PI controls. This can be seen in the comparison curve which shows the speed of the initial start process when using the PID control. In the Trial & Error method, the response value of the system to controller P is obtained, namely, rise time = 0.0151 s, settling time = 0.6 s, overshoot = 75.9%, peak time = 1.74 s, and time delay = 0.424 s. on the PI controller namely, rise time = 0.0148 s, settling time = 0.591 s, overshoot = 76.3%, peak time = 1.74 s, and time delay = 0.0416 s. on the PID controller namely, rise time = 0.0496 s, settling time = 0.55 s, overshoot = 44 %, peak time = 1.31 s, and time delay = 0.128 s. In the Cohen-Coon method, the response value of the system to controller P is obtained, namely, rise time = 0.0168 s, settling time = 0.575 s, overshoot = 73.3%, peak time = 1.71 s, and time delay = 0.0469 s. on the PI controller namely, rise time = 0.0573 s, settling time = 0.603 s, overshoot = 39.3%, peak time = 1.23 s, and time delay = 0.142 s. on the PID controller namely, rise time = 0.276 s, settling time = 0.658 s, overshoot = 2.42 %, peak time = 0.159 s, and time delay = 0.576 s. From the simulation results it is shown that the value for the Cohen-Coon tuning method is better than the Trial & Error method, perhaps because the input value for the Trial & Error method is larger.
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Overshoot (microwave communication)
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Time constant
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In this paper an optimized fractional order proportional, integral and derivative (FOPID) controller is designed to control the non-minimum phase (NMP) systems with time delay. The NMP system shows the undershoot behavior because of having zeros in the right half plane and the response becomes sluggish as the time delay increases. For improving the performance of the NMP system an optimized FOPID controller is designed. The parameters of FOPID are optimized using Nelder's and Mead (NM) optimization Algorithm. NM-optimization seeks to obtain the best optimal values of the FOPID controller in the region. The parameters are optimized on the basis of minimizing the integral absolute error (IAE) of the system. Simulation results verify that the proposed controller improves the transient performance like rise time, settling time and overshoot of the system.
Overshoot (microwave communication)
Settling time
Rise time
Transient (computer programming)
Minimum phase
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A PPI controller is investigated for set-point tracking associated with a highly oscillating secondorder-like process. The controller is tuned using the MATLAB optimization toolbox and five different errorbased objective functions. All the objective functions result in a same time response of the closed-loop control system to a unit step input. The unit step reference input time response of the control system has a zero maximum overshoot and a settling time of 16 seconds. It has an oscillatory nature for a response time up to 10 seconds. The simulation results using the PPI controller are compared with using I-PD, PD-PI, PIPD, PID + first-order lag and PID controllers. The PPI can compete with I-PD, PD-PI and PI-PD controllers regarding the maximum percentage overshoot. However, it cannot compete with all the other five controllers regarding the settling time.
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Controlling the temperature of the glycerin purification process system was not an easy task, as an increase in operating temperature would significantly reduce the quality of the purified glycerin. This is because an unlimited increase in temperature beyond the set point and an excessive prolongation of the heating process would result in the formation of an excessive secondary oxidation product in the final purified glycerin. This paper discusses the transient response characteristics of the glycerin heating process using a parallel PID controller. The glycerin heating process behavior was determined experimentally using step input test and modelled as the First Order plus Delay Time. The controller parameters wereadjusted using Ziegler-Nichols, Cohen-Coon and Wang tuning methods, each of which was analyzed on the basis of the corresponding integral error criterion value. The Integral Square Error, Integral Absolute Error and Integral Time-weighted Absolute Error criteria value were used to evaluate the efficiency of the glycerin heating process. The transient response performances in terms of overshoot, rise time and settling time were also evaluated. Simulation work has shown that the process has experienced high overshoots for Ziegler-Nichols and Cohen-Coon, and has taken longer time to settle. Wang method exhibits with no overshoot but slow response. The lower gain PID controller was found to improve the process response in terms of overshoot but increase in the rise time and settling time. The results indicate that the desired process performance were more or less influenced by the interaction between the tuning parameters. The Ziegler-Nichols PID controller is not recommended for controlling glycerin heating process due to process response oscillations that are difficult to eliminate without prolonging the heating cycle.
Overshoot (microwave communication)
Settling time
Rise time
Transient (computer programming)
Response time
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The purpose of this research is to design a PID control on a DC motor using 2 tuning methods, namely Trial & Error and Ziegler-Nichols. The results showed that the Pittman DC Motor system response from the Pittman DC motor was very unstable, in which there were still many oscillations and a very high overshoot value. In the Trial & Error method, the system response value was obtained on the P controller, namely, rise time = 0.000551 s, settling time = 0.00468 s, overshoot = 37.1 %, peak time = 0.972 s, and time delay = 0.00134 s. on the PI controller namely, rise time = 0.000396 s, settling time = 0.00534 s, overshoot = 47.7%, peak time = 1.23 s, and time delay = 0.00102 s. on the PID controller namely, rise time = 0.000223 s, settling time = 0.00502 s, overshoot = 64.6%, peak time = 1.54 s, and time delay = 0.000601 s. In the Ziegler-NIchols method, the response value of the system to the P controller is obtained, namely, rise time = 0.00118 s, settling time = 0.00564 s, overshoot = 15.4%, peak time = 0.178 s, and time delay = 0.00262 s. on the PI controller namely, rise time = 0.000275 s, settling time = 0.00531 s, overshoot = 58.3%, peak time = 1.44 s, and time delay = 0.000767 s. on the PID controller, namely, rise time = 0.00133 s, settling time = 0.00446 s, overshoot = 12.6 %, peak time = 0.0237 s, and time delay = 0.00288 s. The simulation results show that the value for the Ziegler-Nichols tuning method is better than the Trial & Error method, perhaps because the input value for the Trial & Error method is larger.
Settling time
Overshoot (microwave communication)
Rise time
Settling
Response time
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