Two-input Two-output System Research Articles

An Application of the Individual Channel Analysis and Design Approach to Control of a Two-input Two-output Coupled-tanks System

Frequency-domain methods have provided an established approach to the analysis and design of single-loop feedback control systems in many application areas for many years. Individual Channel Analysis and Design (ICAD) is a more recent development that allows neo-classical frequency-domain analysis and design methods to be applied to multi-input multi-output control problems. This paper provides a case study illustrating the use of the ICAD methodology for an application involving liquid-level control for a system based on two coupled tanks. The complete nonlinear dynamic model of the plant is presented for a case involving two input flows of liquid and two output variables, which are the depths of liquid in the two tanks. Linear continuous proportional plus integral controllers are designed on the basis of linearised plant models to meet a given set of performance specifications for this two-input two-output multivariable control system and a computer simulation of the nonlinear model and the controllers is then used to demonstrate that the overall closed-loop performance meets the given requirements. The resulting system has been implemented in hardware and the paper includes experimental results which demonstrate good agreement with simulation predictions. The performance is satisfactory in terms of steady-state behaviour, transient responses, interaction between the controlled variables, disturbance rejection and robustness to changes within the plant. Further simulation results, some of which involve investigations that could not be carried out in a readily repeatable fashion by experimental testing, give support to the conclusion that this neo-classical ICAD framework can provide additional insight within the analysis and design processes for multi-input multi-output feedback control systems.

Correlation-based Direct Tuning of Multivariable Controller with Stability Constraints by Convex Optimization

This paper proposes the model-free controller tuning method for MIMO systems ensuring closed-loop stability by imposing a set of constraints for discretely defined frequency points. This constraints are defined as a set of convex constraints on maximum singular values of a specific transfer function matrix estimated by spectral analysis. For linearly parameterized controllers, the optimal parameters can be obtained by convex optimization using the acquired I/O data. The resulting controller guarantees to stabilize the plant as the data length tends to infinity. The effectiveness of the proposed method is confirmed by experiments for a tension-and-speed control apparatus which is a two-input two-output system.

Semi Analytical Solution of Constrained Output Feedback Pole Placement in Multi-Input Systems

Pole-placement is one of the oldest control design method used to modify the behavior of a given plant dynamics. In the literature, analytical solution of output feedback pole placement is available only for two-input two-output systems. For general linear time-invariant, multi-input, multi-output (MIMO) systems, static (constant gain) output feedback pole placement is an open non-deterministic polynomial-time (NP) hard problem. This paper proposes a semi-analytical solution of constrained (minimum number of nonzero gains) output feedback pole placement problem in MIMO systems. To get the semi-analytical solution, first an analytical formula is developed for pole-placement in single-input, multi-output (SIMO) systems. This formula is an extension of Bass-Gura's formula used for state feedback pole placement in single-input systems. Along with the gains needed for partial pole-placement, this novel formula computes the coefficients of characteristic polynomial corresponding to the remaining poles of the plant. Using this analytical formula a novel iterative procedure is developed to place all the poles of a multi-input system using output feedback. Proposed iterative method needs only the solution of linear equations at each step of iteration. Starting from the known initial guess, it searches for the solution in a lower dimension space compared to other numerical methods. The algorithm computes a full rank feedback gain matrix. For a decoupled m-input system the proposed method computes the output feedback gains in exactly m-steps, non-iteratively.

Stabilization of TITO Systems over Parallel SNR-Constrained AWN channels

This paper concerns the stabilization of two-input two-output (TITO) discrete-time linear time-invariant (LTI) systems over parallel additive white noise (AWN) channels, in which each individual channel is independently constrained in SNR. Necessary and sufficient conditions for stabilizability are obtained on the SNR's of the channels, in terms of the unstable poles and non minimum phase zeros of the plant, for both state and output feedback control.

Multivariable Repetitive-predictive Control of a Robot Arm with Experimental Results

AbstractA multivariable predictive-repetitive controller has recently been reported that uses a frequency response decomposition technique to detect the dominant frequency components in the reference signal for each output and embeds these in the controller. This paper reports new experimental results on a robot arm configured as a two-input two-output system, which demonstrate the closed-loop performance of the predictive-repetitive control system in terms of reference trajectory following, disturbance rejection, and measurement noise attenuation. Furthermore, it is shown that the bandwidth of the predictive-repetitive control system is strongly dependent on the number of frequencies embedded in the design. The larger the number of frequencies, the wider the bandwidth of the closed-loop system. As a result of wider bandwidth, measurement noise is amplified and unmodeled dynamics in the higher frequency band can cause the closed-loop system to become unstable.

Tuning fuzzy PD and PI controllers using reinforcement learning

In this paper, we propose a new auto-tuning fuzzy PD and PI controllers using reinforcement Q -learning (QL) algorithm for SISO (single-input single-output) and TITO (two-input two-output) systems. We first, investigate the design parameters and settings of a typical class of Fuzzy PD (FPD) and Fuzzy PI (FPI) controllers: zero-order Takagi–Sugeno controllers with equidistant triangular membership functions for inputs, equidistant singleton membership functions for output, Larsen’s implication method, and average sum defuzzification method. Secondly, the analytical structures of these typical fuzzy PD and PI controllers are compared to their classical counterpart PD and PI controllers. Finally, the effectiveness of the proposed method is proven through simulation examples.

PID controller design of TITO system based on ideal decoupler

The proposed method for designing multivariable controller is based on ideal decoupler D( s) and PID controller optimization under constraints on the robustness and sensitivity to measurement noise. The high closed-loop system performance and robustness are obtained using the same controller in all loops. The method is effective despite the values and positions of the right half plane zeros and dead-times in the process transfer function matrix G p( s). The validity of the proposed multivariable control system design and tuning method is confirmed using a test batch consisting of Two-Input Two-Output (TITO) stable, integrating and unstable processes, and one Three-Input Three-Output (TITO) stable process.

Two-stage binaural speech enhancement with Wiener filter for high-quality speech communication

Speech enhancement has been researched extensively for many years to provide high-quality speech communication in the presence of background noise and concurrent interference signals. Human listening is robust against these acoustic interferences using only two ears, but state-of-the-art two-channel algorithms function poorly. Motivated by psychoacoustic studies of binaural hearing (equalization–cancellation (EC) theory), in this paper, we propose a two-stage binaural speech enhancement with Wiener filter (TS-BASE/WF) approach that is a two-input two-output system. In this proposed TS-BASE/WF, interference signals are first estimated by equalizing and cancelling the target signal in a way inspired by the EC theory, a time-variant Wiener filter is then applied to enhance the target signal given the noisy mixture signals. The main advantages of the proposed TS-BASE/WF are (1) effectiveness in dealing with non-stationary multiple-source interference signals, and (2) success in preserving binaural cues after processing. These advantages were confirmed according to the comprehensive objective and subjective evaluations in different acoustical spatial configurations in terms of speech enhancement and binaural cue preservation.

Improved Coupled Tank Liquid Levels System Based on Swarm Adaptive Tuning of Hybrid Proportional-Integral Neural Network Controller

Problem statement: Accuracy and stability of many systems in chemical and process industries which has Two-Input Two-Output (TITO) is one of the key factors of process which have cross coupling between process input and output. Approach: Unlike traditional neural network weight adaptation using gradient descent method, Particles Swarm Optimization (PSO) technique was utilized for adaptive tuning of neural network weights adjustment and fine tuning the controller’s parameters. Design approach for controlling liquid levels of Coupled Tank TITO system by using hybrid PI-Neural Network (hybrid PI-NN) controllers. Results: Tuning method for parameters of improved hybrid PI-NN controller was also discussed. Conclusion: Performances of proposed method also compared with PID-NN controllers, it was shown that hybrid PI-NN controller exhibited better performance in terms of transient response analysis.

Backstepping-enhanced decentralised PID control for MIMO processes with an experimental study

A novel decentralised PID controller design procedure based on backstepping principles is presented to operate multiple-input multiple-output (MIMO) dynamic processes. First, a control Lyapunov function (CLF) and virtual control variable based on the backstepping method are derived recursively for each loop and a multivariable controller is obtained. Appropriate selection of auxiliary control variables can then eliminate coupling effects between subprocesses, and a decentralised controller can be derived. By analysing the regulation dynamics, external disturbances are rejected via appropriate tuning of the backstepping design parameters. Sufficient stability conditions are then derived using the small-gain theorem for two-input two-output and MIMO closed-loop systems, respectively. Simulation results for the control of the Shell benchmark problem and experimental results with a real-time water-level control system are provided to demonstrate the effectiveness and practicality of the proposed design procedure.

Temporal Stability of a Transparent Mode Group Diversity Multiplexing Link

The temporal behavior of a mode group diversity multiplexing (MGDM) link is examined. MGDM has been proposed as a way of creating parallel, independent communication channels over multimode fiber (MMF) links using different groups of modes. When the effect of dispersion can be neglected, the output electrical signals of an MGDM link are related to the input ones via a real-valued transmission matrix. The transmission matrix is vulnerable to changes in the modal spectrum of the propagating mode groups as well as to the coupling of light at the input and output of the MMF. Measurements of the transmission matrix of a two-input two-output system over 12.7 h show that an MGDM link can be very stable

Integrated control of clamping force and energy-saving in hydraulic injection moulding machines using decoupling fuzzy sliding-mode control

The objective of this research is to implement a novel parallel control of clamping force and energy-saving in hydraulic injection moulding machines (HIMMs) in order to simultaneously achieve accurate force control response and high energy efficiency. In order to verify the feasibility of the integrated control system and compare energy-saving effects, the clamping force control of HIMMs can be integrated with two different energy-saving control systems or integrated with a conventional hydraulic system without energy-saving control. The overall control system is a coupled two-input two-output system. Therefore, a decoupling fuzzy sliding-mode control (DFSMC) strategy, which can reduce the fuzzy rule numbers and counteract the coupling effects, is developed for the integrated control of HIMMs. The experimental results show the outstanding performance of the parallel control in HIMMs with DFSMC .

Robust decentralized parameter identification for two-input two-output process from closed-loop step responses

In this paper, a novel parameter identification method for closed-loop two-input two-output (TITO) processes from step-test is proposed. Through sequential step change of set points, the coupled closed-loop TITO system is decoupled equivalently into four independent single open-loop processes with same input signal acting on the four transfer functions. Consequently, existing identification methods for single-loop process can be extended to TITO systems and the parameters of first- or second-order plus dead-time models for each transfer function can be directly obtained by using the linear regression equations derived for the decoupled identification system. The proposed method is simple for engineering application and robust in the presence of large amounts of measurement noise. Simulation examples are given to show both effectiveness and practicality of the identification method for a wide range of multivariable processes.

The concurrent implementation of high velocity control performance and high energy efficiency for hydraulic injection moulding machines

A high servo control response and a high energy efficiency, which are difficult to achieve simultaneously, are requested in hydraulic servo systems of current hydraulic injection moulding machines. This investigation develops new solutions to concurrently implement energy-saving control and velocity control for simultaneously realising high velocity control response and high energy efficiency for injection moulding machines. Two different hydraulic pump systems, including a variable displacement pump and a variable rotational speed pump, are developed and in each one of them two different energy-saving control concepts, such as load-sensing control and constant supply pressure control, are implemented. Thus, for verifying the feasibility of the integrated control systems and comparing the energy-saving effects, velocity control of the hydraulic cylinder can be integrated with four different energy-saving control systems (ESCSs) and also the conventional hydraulic system without energy-saving control. A fuzzy sliding mode control that can simplify the complex fuzzy rule bases is used for solving the complex two-input two-output systems. The experimental results show the excellent performance of the integrated concurrent control systems.

A signal convolution method for estimation of controller parameter sensitivity functions for tuning of feedback control systems by an iterative process

Optimisation of controller parameters can be achieved through the use of parameter sensitivity functions in an iterative tuning process. Unlike some other methods for the generation of sensitivity functions, the approach described in this paper avoids the need for explicit a priori knowledge of the plant model structure or parameters, systematic adjustments of controller parameters being made entirely through the processing of signals obtained from tests on the closed-loop system. The methods, based on convolution, may be applied to the estimation of controller parameter sensitivity functions in linear closed-loop systems using simple test inputs, such as step signals. This approach differs from the Iterative Feedback Tuning algorithm in that it does not involve repeated experiments involving system outputs from one test being used as reference inputs in a second test. The signal convolution approach is illustrated through an example involving a simple two-input two-output liquid-level control system involving two coupled tanks.

Parallel Control of Velocity Control and Energy-Saving Control for a Hydraulic Valve-Controlled Cylinder System Using Self-Organizing Fuzzy Sliding Mode Control.

Conventional hydraulic valve-controlled systems that incorporate positive displacement pumps and relief valves have a problem of low energy efficiency. The objective of the research is to implement parallel control of energy-saving control in an electro-hydraulic load-sensing system and velocity control in a hydraulic valve-controlled cylinder system to achieve both high velocity control accuracy and low input power simultaneously. The overall control system is a two-input two-output system. For that, the control strategy of self-organizing fuzzy sliding mode control (SOFSMC) is developed in this study to reduce the fuzzy rule number and to self-organize on-line the fuzzy rules. To compare the energy-saving performance, the velocity control is implemented under three different energy-saving control systems, such as load-sensing control system, constant supply pressure control system and conventional hydraulic system. The parallel control of the velocity control and energy-saving control by the SOFSMC is implemented experimentally.

Worst-Case Optimal Static Output Feedback for Uncertain Systems

This paper proposes a worst-case optimal approach to the synthesis of a static output feedback for a linear, time-invariant, multivariable system depending on uncertain parameters which nonlinearly affect a given state-space model. The aim is to seek an output-to-input feedback matrix that robustly stabilizes the closed- loop system while minimizing, over the uncertain parameter domain, the (worst-case) maximum of a composite quadratic index. The emerging minimax problem is shown to be exactly equivalent to a semi-infinite optimization problem for which an estimate of a global solution is obtained through a genetic/interval algorithm. This is a hybrid algorithm that combines a genetic algorithm (at the upper level) with an interval procedure (acting at the lower level). Computational results for a two-input two-output (TITO) system are included.

Fuzzy logic control of a nitrogen laser

Traditionally, the stability of the output of a laser is controlled through scientific means or by a simple feedback loop. For multiinput multioutput control and for medium- to high-power lasers, however, these control schemes may break down. We report on the use of a fuzzy logic control scheme to improve the stability of a pulsed nitrogen laser. Specifically, the nitrogen laser is modeled as a two-input two-output system. The two input parameters are the discharge voltage (V) and nitrogen pressure (P), and the two output parameters are the pulse energy (E) and pulse width (PW). The performance of the fuzzy logic controller is compared with a decoupled two-channel PID (proportional + integral + derivative) controller. In our experiment, the long-term stabilities of the open-loop system are 1.82% root mean square (rms) for pulse energy and 4.58% rms for pulse width. The PID controller achieves better performance with long-term stabilities of 1.46% rms for pulse energy and 4.46% rms for pulse width. The fuzzy logic controller performs the best with long-term stabilities of 1.02% rms for pulse energy and 4.24% rms for pulse width, respectively.

A SIMPLE TITO PI TUNING METHOD SUITABLE FOR INDUSTRIAL APPLICATIONS

A simple tuning method for TITO (Two-Input, Two-Output) PI controllers will be presented in this article. The method is an extension of the SISO PID tuning method based on Internal Model Control (IMC). An approximate model for tuning purpose will be developed using the information from the interaction measure of the TITO system. The procedure of the tuning method is very simple and straightforward utilizing only two bias-relay feedback tests. The tuning method can easily be applied to various industrial situations with almost no need for a priori process knowledge. Various TITO examples will be used to demonstrate the performance of this tuning method. Both setpoint and load disturbance responses will be examined

An algorithm for dual-channel noiseless signal reconstruction and its performance analysis

We present an algorithm for estimating a two-input two-output system and recovering its inputs from noise-free observations of its outputs. The algorithm involves minimization of a set of cross-correlations between the reconstructed signals and a nonlinear function of these signals. A performance analysis of the algorithm is presented. It is shown that for the optimal choice of the nonlinear function, the performance of the algorithm is close to the Cramer-Rao lower bound (CRLB). Other choices of the function provide insights into the performance of moment/cumulant-based deconvolution techniques.