Pid controller examples pdf

A brief description of PSO- 1 0. Section 6 provides conclusion of the present research work. Particularly for unstable systems, the tuning rule proposed for a particular reduced order model will not offer a fitting response for 2. Controller Structure other models higher order models, model with a positive or negative zero, model with a large delay time to process 2. PID Controller. PID controller has a simple structure and time constant ratio, etc.

Most of the classical PID tuning is usually available as a packaged form. To perform well with methods require numerical computations in order to get the the industrial process problems, the controller should have best possible controller parameters. Heuristic algorithms can effectively work for higher 1 dimensional optimization problems compared to the existing classical optimization procedures. They can be used as a vital tool to design classical and and modified structured controllers for a class of unstable process models, irrespective of its model order.

Table 6: Controller settings for Example 4. Jung et al. PID Controller with Prefilter. Figure 2 depicts the struc- a smooth reference tracking performance [18]. It has been proved to be an effective 0.

At early searching Search boundary 0. PSO Algorithm. It is used to control the problems due to its high computational efficiency [6—10, impact of previous velocities on the current velocity at 20—23]. Compared with other population-based stochastic the current time step. The objective values global exploration while small weight factor facilitates local obtained above for the initial particles of swarm are set as the exploration. The best value among all the Further, for high-dimensional problems, dynamical ad- pbest values is identified as gbest.

A review Step 4 evaluation of velocity. The new velocity for each of inertia weight strategies in PSO is given chronologically in particle is computed using 5. The particle position is updated strategy and experimentally found that this strategy increases using 6. The values of the objective function are calculated the convergence of PSO in early iterations of the algorithm.

If the new value is better The linearly decreasing strategy enhances the efficiency and than the previous pbest, the new value is set to pbest. Similarly, performance of PSO. In spite of its ability to converge gbest value is also updated as the best pbest.

In global-local best inertia weight, Step 6 stopping criteria. If the stopping criteria are met, the inertia weight is based on the function of local best and positions of particles represented by pbest are the optimal global best of the particles in each generation. It neither takes values. Otherwise, the above said procedure is repeated from a constant value nor a linearly decreasing time-varying value. Step 4 until the specified iteration is completed. To overcome the weakness of premature convergence to local minimum, adaptive inertia weight strategy [27] is proposed to 3.

Objective Function. The overall performance speed of improve its searching capability. Chen et al. Malik et al. During the search, without loss of generality, minimum fitness function while linearly increasing inertia the constrained optimization problem minimizes a scalar weight gives contribution to quick convergence ability.

Gao et al. Multiobjective optimization always pro- chaos mutation operator. The logarithm decreasing inertia vides improved result compared to single-objective function. In order to overcome the premature convergence and 1,. The optimization search. In this method, the constraints which are based velocity updation. The implementation of PSO has the to be minimized are arranged as weighted sum: following steps.

Iteration In many optimization cases, it is very difficult to satisfy 0. Hence, there should be some 0. Figure 3 depicts the obtainable optimal solution and Iteration stability boundary in the three-dimensional search space. Search boundary for controller parameters is assigned as Figure 7: Optimal controller parameters. Controller Tuning 0 10 20 30 40 50 60 Time s The controller design process is to find the optimal values for controller parameters form the search space that minimizes Best value 1 Best value 2 the considered objective function.

The multiple OF-based controller design troller with a prefilter setup. Table 1 presents three best values among 10 trials. Figure 8 represents the reference tracking and input dis- 2, and maximum generation value of Figure 9 shows the corresponding controller value among the trials is considered to stabilize the process. Similar responses are obtained for the above process 5. Example 1. But the response by the present controller is sluggish than other methods.

From Figure 12, it is observed that the controller performance is also very smooth. Chiha et al. In For this model, Kumar et al. Recently Rajinikanth and Latha proposed the controller values and its performance measure values are and validated the multiple-objective PSO-based PID tuning presented in Tables 3 and 4 respectively. An unity input disturbance troller parameters are presented in Table 5.

Figures 13 and 14 signal is applied at 50 s to study the disturbance rejection show the process response and controller output, respectively. The performance by the present method is The proposed methods provide improved reference tracking smooth compared to other methods considered in this study. Table 7: Performance measure values for Example 4. The unstable steady-state model of the bioreactor 3 0.

Figure 17 shows the regulatory response for performance values are tabulated in Table 7 best three the unstable bioreactor model, and Figure 18 shows the values among 10 trials. The performance measure values are corresponding controller output.

Sampling instants Figure Real-time process response for nonlinear spherical tank 0. Initially a reference input of 18 cm is assigned. From this, it is observed sampling instants, respectively. From this result, it can small. The nonlinear spherical tank system recently problem and it can be easily implemented in real time using discussed by Rajinikanth and Latha is considered to show the a MATLAB-supported real-time process loop.

The transfer function model of the system for an operating range 6. Conclusion of 18 cm is 3. The The obtained PID values are then transferred supports enhanced performance for both the reference track- to the real-time controller hardware installed in the process ing and disturbance rejection problems.

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James Thomas. Derek Atherton. A short summary of this paper. Download Download PDF. Translate PDF. Atherton and S. However, these tuning methods may not The objective of the paper is to outline the limitations provide satisfactory closed loop responses in some cir- of classical PID controllers acting on the error signal for cumstances. This im- plants with small delays, which are typical of many plementation avoids the derivative kick problem associ- process plant transfer functions, although the authors ated with derivative action in the forward path, which normally prefer a PI-D implementation.

Difficultiesare still exists when a filter is included. Further, the PD in often found, however, for control of plants with reso- the inner feedback loop enables placement of the open nances, integrators or unstable transfer functions. The and Lewin, Shafiei and Shenton but all give large over- simulation results show significantly improved perfor- shoot responses. Recently Valentine and Chidambaram mance of the proposed control method particularly for [9] suggested a PID controller designed by the domi- the latter processes.

Recently Park et al [7] proposed a PID-P 1 Introduction control strategy with an inner P feedback loop that re- sults in an acceptable overshoot and a small settling PID controllers are used extensively in the process in- time. They suggest an internal P feedback loop to to represent process plants can be easily controlled with convert the integrating process to an open loop stable a PID controller; c as a consequence of b , engineers process first and then use a PID controller in the for- understand the effects of varying the three parameters ward loop.

They tune the PID-P controller differently in the PID controller; d a simple test which can be for the servo and regulator problem to gurantee better done on the closed loop such as those of Ziegler-Nichols control performance. The pa- transfer functions; e the small number of parameters rameters of the controller are obtained by minimisa- available for tuning in the PID controller. Normally the higher the time weight- based on the stable first or second order plus time delay ing used the smaller the overshoot and the longer the model or critical point information for stable processes settling time.

In ing in practice, the transfer function of the plant has recent years, several approaches have been suggested to be available. General Integral Absolute E m r criteria the authors may be used [3]. Alternatively, our current research has shown that autotuning for a PI-PD con- 4 troller may be possible when it is difficult to obtain the process model transfer function.

In section 2, analysis on the performance optimisation is given. In section 2. General Integral Squared Ermr criteria 3, a few examples are illustrated to show the value of the proposed control method followed by conclusions in section 4. It is known that if a control system is designed to min- imise Jo, then the response t o a step has a relatively The forms of the controllers discussed in this paper are high overshoot but this can be decreased by using a given by higher value of i.

The Ji, unlike the Ji integrals, can be evaluated very efficiently using the s-domain formulation. E s is the error used to change the poles of the plant transfer function signal expressed in the frequency domain and the cri- to more desirable locations for control by a PI con- terion is to be minimised for a satisfactory closed loop troller. The possibility to split the P term is available performance of the system. The integral can be opti- in some commercial controllers.

This controller can dard forms of closed loop transfer functions with a zero be converted t o a PE-PD, which we believe provides a which satisfy the J1 criterion have been recently pub- better strategy for design, since it is not easy apart lished [2,4].