Robust Design of PID and IMC-Based Controllers in the Time Domain

This paper presents an Internal model controller (IMC) for temperature control of heating, ventilation and air conditioning (HVAC) system. Firstly, the temperature of an air-conditioning system of the test room is controlled by using PID controller. The performance and stability of the control process are degraded due to the significant time delay of air-conditioning process. So, smith-predictor scheme is used to compensate the time delay. But when the process has larger system parameters and longer time delay, smith-predictor does not provide better results. To overcome this problem, an internal model (IMC) controller is developed. Simulation results compare the performance of internal model (IMC) controller with conventional PID controller and smith predictor controller. Simulation result shows that an internal model controller gives satisfactory performance with less overshoot and less settling time.

The internal model control (IMC) scheme has been widely applied in the field of process control. This is due to its simple and straightforward controller design procedure as well as its good disturbance rejection capabilities and robustness properties. So far, IMC has been mainly applied to linear processes. This paper discusses the extension of the IMC scheme to nonlinear processes based on local linear models where the properties of the linear design procedures can be exploited directly. The resulting controllers are comparable to gain-scheduled PI or PID controllers which are the standard controllers in process industry. In practice, the tuning of conventional PI or PID controllers can be very time-consuming. In this paper, the design effort of the nonlinear IMC and conventional controller design methods are discussed and the control results are compared by applying it to a Hammerstein process and nonlinear temperature control of a heat exchanger.

We consider methods for synthesizing robust controllers that can be directly implemented in the Internal Model Control (IMC) scheme. We show how to put H design methods into the IMC scheme to improve its robustness. These methods include one degree-of-freedom (one d.o.f.) and two degrees-of-freedom (two d.o.f.) H designs. Explicit state-space formulae for the H one d.o.f. and two d.o.f. IMC-based controllers are derived in discrete time. We show that the IMC controller solves a special H control problem, namely a disturbance feedforward control problem, and it proves robust stability against coprime factor uncertainty and with a degree of robust performance for the two d.o.f. case, in the sense of making the closed-loop system match a pre-specified reference model. A design for a glass tube production process is presented as an illustrative example.

Networked Control Systems (NCS) have revolutionized modern control engineering by facilitating distributed monitoring and operation across critical infrastructure domains. However, the integration of communication networks introduces a dual challenge: network-induced phenomena, such as time delays and packet losses, degrade operational performance, while exposure to sophisticated cyberattacks compromises system integrity and safety. This paper addresses these fundamental challenges through a unified Internal Model Control (IMC)-based framework that simultaneously achieves computational efficiency, systematic realizability, and intrinsic cyber-resilience. Three novel controller architectures are developed: (i) an optimization-free IMC-PID controller for Second-Order Plus Dead Time (SOPDT) systems utilizing maximum sensitivity analysis, delivering closed-form gain expressions with deterministic O ( 1 ) computational complexity; (ii) a physically realizable IMC-based Proportional-Integral-Derivative with Acceleration (PIDA) controller for Third-Order Plus Time Delay (TOPTD) systems, which systematically resolves the persistent realizability challenge through filtered derivative incorporation while preserving single-parameter tuning; and (iii) a cyber-resilient IMC-PID-II controller explicitly designed to mitigate Man-in-the-Middle (MitM) attacks in NCS through double integrator architecture, providing intrinsic resilience against malicious data injection attack. Comprehensive validation through high-fidelity simulations on benchmark processes, microgrid frequency control systems, and DC–DC converters, coupled with experimental verification using WAVECT WCU300 real-time controller, confirms superior transient response, disturbance rejection, parametric robustness, and cyber-attack resilience.

This paper presents the comparative study of Model Predictive Controller (MPC) with PID Controller implemented for flow control loop in LABVIEW. Classical PID controller is mostly used in process instrumentation yet tuning of PID controller is the crucial part to be dealt with. Moreover, changes in the parameters of the loop components affects the tuning of the controller, hence over a period of time retuning of PID controller is required. On the other hand MPC controller works on the process model which predicts and optimizes the process performance. Here, Flow control loop performance was studied for MPC and PID controller. MPC worked on 1st order state space system model and PID was tuned using Internal Model Control (IMC) method. The result of implementation shows that, MPC controller performs much better than PID controller. Set point of with less settling time and zero peak overshoot was observed in MPC whereas PID has comparatively more settling time and peak overshoot.

The design and implementation of a multi-stage PID (MS-PID) controller for non-inertial referenced UAVs are highly complex. Symmetrical multirotor UAVs are unstable systems, and it is thought that the kinematics of the symmetrical UAV rotor, such as the quadrotor and hexacopter resembles the kinematics of an inverted pendulum. Several researchers have investigated the structure and design of PID controllers for high-order systems during the last decade. The designs were always concerned with the enhanced response, robustness, model reduction and performance of PID controllers. An accurate tuning process of such a controller depends on the engineer’s experience level. This is due to the number of variables and hyperparameters tuned during the process. An adaptive genetic algorithm (AGA) is utilized to optimize the MS-PID controllers for controlling the quadrotor in this study. The proposed method optimizes the offline-planned approach, providing several possibilities for adapting the controllers with various paths and or varying weather conditions. The MS-PID parameters are optimized in parallel, as every PID controller affects the other controller’s behavior and performance. Furthermore, the proposed AGA generates new chromosomes for “new solutions” by randomly developing new solutions close to the previous best values, which will prevent any local minima solution. This study intends to investigate the design and development of a highly tuned robust multi-stage PID controller for a symmetrical multirotor UAV. The work presents a model for a non-referenced inertial frame multirotor UAV (quadcopter). Once the model is defined, a robust multi-stage PID controller for the non-inertial referenced frame symmetrical multirotor UAV is designed, tuned, and tested. A genetic algorithm (GA) will be used to tune the MS-PID controller. Finally, the performance comparison between the proposed and conventional methods is presented. The results show that the proposed method provides stability improvement, better transient response, and power consumption.

The photovoltaic (PV) system’s nonlinear nature, uncertainty in temperature, and light intensity in the environment are responsible for the fluctuation of the maximum power point (MPP). Many maximum power point tracking (MPPT) algorithms are proven effective in the literature, including use of artificial intelligence. Proportional integral derivative controller and fuzzy controllers found effective to track MPP. Using the combination of Fuzzy-PID controller, swiftly adapt to changes in the atmosphere to confirm the solar array is continually operating at its highest efficiency with MPP. Easy and effective oscillation elimination is possible with PID control. To regulate the maximum power of the PV system combination of Fuzzy-PID self-tuning controllers is found effective.The goal is to enhance a PV system’s dynamic response to in presence of irradiation and temperature fluctuations. For tuning Fuzzy logic controller (FLC), gain scheduler values of the proportional, integral, and derivative constants are fundamental. The design processes for non-linear conventional PID controllers, FLC, and series combination of Fuzzy-PID controller are discussed. It compares the traditional PID controller, FLC, and Fuzzy-PID controller. The comparison of outputs produced for PID, FLC, and series Fuzzy-PID controller confirms the effectiveness of the algorithm. Use of Fuzzy controller helps in self-tuning of PID controller constant value. MATLAB/Simulink based environment used to perform the simulations.

PID controller tuning for the first-order-plus-dead-time process model via Hermite-Biehler theorem

A design method is proposed for low‐gain internal model control (IMC) proportional‐integral‐derivative (PID) controllers based on the second‐order filter. The PID parameters are obtained by approximating the feedback form of the IMC controller with a Maclaurin series, in which the second‐order filter is applied using the IMC approach to achieve a low‐gain PID controller that is suitable for model mismatch problems. Analytical PID tuning rules based on the second‐order filter are derived for several common‐use process models. The second‐order filter is designed from the desired time domain performances of maximum overshoot and settling time. Furthermore, the robustness of the IMC PID controller based on the second‐order filter is analyzed, and results show that its robustness performance is better than the first‐order filter under certain conditions. Finally, three categories of models divided by the ration of time constant and time delay are presented in the comparative numerical simulations to validate the effectiveness and generality of the proposed PID controller design method.

ABSTRACTIn this article, we propose practical rules for tuning event-based PID controllers with two sampling strategies: symmetric send-on-delta (SSOD) and regular quantification (RQ). We present a detailed analysis about the effect of the derivative term of the controller when using SSOD or RQ and some guide lines are given to select the derivative filter coefficient. The two sampling strategies are compared, showing that, even when both of them lead to similar controlled output response, systems with RQ have better robustness properties than those with SSOD. The study is based on the describing function and the results are applicable to process with dynamic responses of different types: with time delays, non-minimum phase, under-damped response, etc. The rules presented here are given in terms of phase and gain margins that are measures of robustness used in the design of continuous PID controllers. This allows the application of conventional PID tuning methods to the case of event-based PID. The tuning rules are very simple and can be used for tuning PID, PI, PD and other controller structures.

A two degree freedom internal model control (IMC) is implemented for the temperature control of a single tubular heat exchanger system. The experimental heat exchanger system is a very simple structure, however, the characteristics are regarded as a distributed parameter system and time delay made by software; the plant is regarded as complex system. With the aim of applying IMC structure, we approximate the heat exchanger system to a time delay model from a frequency response examination. In the laboratory experiment, it is clear that: (1) the two degree of freedom IMC is effective for the time delay system; (2) the two degree of freedom performance of IMC was superior to one degree freedom IMC; the disturbance was reduced compared to a PI controller or one degree of freedom IMC design; (3) since the controller had two degrees of freedom, the one tuning filtering parameter of the IMC controller effected the tracking of the reference and the other tuning parameters of IMC reduce disturbance; (4) the design method was as simple as an ordinary one degree of freedom IMC design; and (5) since the IMC controller was constructed from the system model, there were some problems to set up the modeling and identification.

This paper concerns design and implementation of PID and fractional-order PID (FOPID) controllers to control position of an electromagnetically suspended ferromagnetic ball in a magnetic levitation (Maglev) system in real time. The Maglev system, manufactured by Feedback Instruments (Model No 33-210) is used as a platform to test the performance of proposed controllers. Parameters of PID and FOPID controllers are tuned by firefly algorithm (FA). FA is a metaheuristic algorithm based on movement of fireflies toward more attractive and brighter ones. PID and FOPID controllers are implemented in MATLAB and SIMULINK environment inside PC using fractional-order modeling and control toolbox. Controller in the SIMULINK environment inside PC is connected to the Maglev system through Advantech card. Effectiveness of proposed controllers is tested by checking the ability of the suspended ball to track a reference signal. Step change, sine wave, and square wave are used as reference signals. Real-time results have revealed satisfactory transient and steady-state responses over the contemporary existing controllers. FOPID controller showed better results compared to PID.

Improved Decentralized PID Controller design for MIMO Processes

The research on active control of the pantograph has been intensively studied, however, the control results in practice are not satisfactory as expected, for the existence of time delays coming from the input and output measurement. This paper focuses on the problem of time delays in the designing of the control strategy, including the sensor signal input and the action of the actuator. A multibody dynamic pantograph model is established based on the relative coordinate method, combined with the rigid catenary established by the modal superposition method. Firstly, the performance of the traditional PID controller with signal time delay is studied, including the separation or combination of sensor signal input delay and actuator signal output delay. Then, a novel fuzzy PID controller with an improved rule library is proposed, which further improves the control performance of the PID controller. Finally, to deal with the time delay of sensor and actuator well, a dynamic predictive fuzzy adaptive PID (DMC-Fuzzy-PID) controller is proposed by combining dynamic matrix control (DMC) with the improved fuzzy PID controller, which may support the engineering application of active control of pantograph.KeywordsActive controlTime delayRigid catenaryMultibody dynamicsFuzzy PID controller

Development of Lyapunov redesign controller for microgrids with constant power loads