## 1 Introduction
In [27], the authors used a feed-forward controller based on a mathematical model in combination with a variable P-gain PI controller to combat the effect of hysteresis in the system. Ref. [28] uses a model-based controller with both feed-forward and feedback components with a structure similar to a PD controller to position a soft robot. Similarly ref. [29] used feedback linearisation to decouple the actuators of a soft pneumatic robot manipulator to achieve very precise and dynamic movements. The controller for this application was a model-based, feed-forward controller combined with a low gain PD controller In [30], a planar platform actuated by pneumatic muscles was controlled using three fuzzy controllers synchronized through an ANFIS (adaptive neuro-fuzzy inference system)-based controller. Ref. [15] applied a simple constant-gain PID controller for positioning of a parallel platform actuated by four pneumatic muscles. The authors of Ref. [31] have demonstrated a nonlinear SMC (sliding-mode controller) based on a PID-type sliding surface combined with a lumped element model-based controller to control a soft pneumatically actuated robot. In [32], the authors use a fourier series-based adaptive sliding-mode controller with \(H\infty\) tracking performance to address the high non-linearity and time-varying problem in a parallel platform actuated by rod-less pneumatic cylinders. while dealing with a tendon-driven redundant manipulator, the authors of Ref. [33] proposes a population-based model-free control method that could be applied to pneumatically actuated manipulators. Based on our previous work we have set out to develop the mechanical design and control system for a rugged redundant cascade manipulator driven by pneumatic bellows,intended for both research and agricultural use. The most difficult part of the development was the controller design for each separate module, as noted in previously mentioned articles. This task is notoriously difficult due to the inherent nonlinear hysteresis behaviour of the chosen actuator type and MIMO system as a whole. In previous research, a similar approach to in pneumatic parallel platform module control was taken by relying on experimental data. This concept was expanded upon by applying two regression steps to the data to obtain a mathematical model of the module, which took the place of a feed-forward controller. This feed-forward controller was then supplemented by a variable gain I-controller that facilitates disturbance rejection. The gain of the I controller is time-varying, allowing for specific adaptation dependent on the control error. The advantages of the ability to dynamically change the gains of a PID controller have been demonstrated by many authors. For example [34] presents a sigmoid-based variable coefficient PIDwhere a modified sigmoid function is used to limit the variability of the PID controller coefficients in a predefined range. Refs. [34; 35] added a nonlinear sine cosine algorithm to tune the coefficients of the PID controller. Ref. [36] utilized reinforcement learning and gain scheduling to tune the coefficients of their PID controller. Here, we present a hybrid controller design which, allows for a on demand change in stiffness of the system during operation and lends itself well to be a part of complete control system for the whole cascade manipulator. Based on previous papers survey, the novelty of the paper can be defined as follows:  
* Development of a novel hybrid FFvI controller (Feed-forward variable gain integral controller) with time-varying gain and experimentally derived model using two regression steps;
* Establishment of controller design methodology for cascade redundant robots;
* Experimental positioning analyses under dynamic disturbance effects. This paper focuses on the development of a novel controller for a 2 DOF pneumatic parallel platform that represents one module of the pneumatic manipulator PneuTrunk (see Figure 1), developed by our ARM-Lab.